idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
|---|---|---|---|---|---|---|
41,401 | Modelling count data with extreme underdispersion - what distribution? | The Conway-Maxwell-Poisson model has recently been shown to handle arbitrarily small underdispersion (see Huang 2020). For example, it is possible to have a mean of 15 and a variance of 2, say, by selecting the dispersion parameter large enough. In the extreme limits, it is even possible to have a mean of 15 and 0 vari... | Modelling count data with extreme underdispersion - what distribution? | The Conway-Maxwell-Poisson model has recently been shown to handle arbitrarily small underdispersion (see Huang 2020). For example, it is possible to have a mean of 15 and a variance of 2, say, by sel | Modelling count data with extreme underdispersion - what distribution?
The Conway-Maxwell-Poisson model has recently been shown to handle arbitrarily small underdispersion (see Huang 2020). For example, it is possible to have a mean of 15 and a variance of 2, say, by selecting the dispersion parameter large enough. In ... | Modelling count data with extreme underdispersion - what distribution?
The Conway-Maxwell-Poisson model has recently been shown to handle arbitrarily small underdispersion (see Huang 2020). For example, it is possible to have a mean of 15 and a variance of 2, say, by sel |
41,402 | Doubt about Rigged election in South Korea | If the voters are split randomly between A and B, it would not be surprising that their voting behaviour be the same and (given the large numbers involved) that the proportions of votes to each party under each regime A and B were also nearly the same.
However, I would expect that elder people with less mobility from... | Doubt about Rigged election in South Korea | If the voters are split randomly between A and B, it would not be surprising that their voting behaviour be the same and (given the large numbers involved) that the proportions of votes to each party | Doubt about Rigged election in South Korea
If the voters are split randomly between A and B, it would not be surprising that their voting behaviour be the same and (given the large numbers involved) that the proportions of votes to each party under each regime A and B were also nearly the same.
However, I would expec... | Doubt about Rigged election in South Korea
If the voters are split randomly between A and B, it would not be surprising that their voting behaviour be the same and (given the large numbers involved) that the proportions of votes to each party |
41,403 | Doubt about Rigged election in South Korea | I am not very familiar with how election results should look like, e.g how big is the variation and how much it would differ from the null hypothesis contingency table.
Looking the result, we can do a chi-sq test similar to what you have:
M = matrix(c(15797,6185,11335,4460,5296,2073),ncol=3)
chisq.test(M)
Pearson... | Doubt about Rigged election in South Korea | I am not very familiar with how election results should look like, e.g how big is the variation and how much it would differ from the null hypothesis contingency table.
Looking the result, we can do | Doubt about Rigged election in South Korea
I am not very familiar with how election results should look like, e.g how big is the variation and how much it would differ from the null hypothesis contingency table.
Looking the result, we can do a chi-sq test similar to what you have:
M = matrix(c(15797,6185,11335,4460,52... | Doubt about Rigged election in South Korea
I am not very familiar with how election results should look like, e.g how big is the variation and how much it would differ from the null hypothesis contingency table.
Looking the result, we can do |
41,404 | Front-Door Adjustment formula: confusing notation | It means
$$
P(y|\text{do}(X=x)) = \sum_z \left[ P(z|x) \sum_{x'} \left\{ P(y|x',z) P(x') \right\} \right].
$$
This can be seen from equation (3.15) on p. 68 which is
$$
P(y|\text{do}(X=x)) = \sum_z \sum_{x'} \left\{ P(y|x',z) P(x') P(z|x) \right\}
$$
and can be rearranged to be
$$
P(y|\text{do}(X=x)) = \sum_z \sum_{x'}... | Front-Door Adjustment formula: confusing notation | It means
$$
P(y|\text{do}(X=x)) = \sum_z \left[ P(z|x) \sum_{x'} \left\{ P(y|x',z) P(x') \right\} \right].
$$
This can be seen from equation (3.15) on p. 68 which is
$$
P(y|\text{do}(X=x)) = \sum_z \s | Front-Door Adjustment formula: confusing notation
It means
$$
P(y|\text{do}(X=x)) = \sum_z \left[ P(z|x) \sum_{x'} \left\{ P(y|x',z) P(x') \right\} \right].
$$
This can be seen from equation (3.15) on p. 68 which is
$$
P(y|\text{do}(X=x)) = \sum_z \sum_{x'} \left\{ P(y|x',z) P(x') P(z|x) \right\}
$$
and can be rearrang... | Front-Door Adjustment formula: confusing notation
It means
$$
P(y|\text{do}(X=x)) = \sum_z \left[ P(z|x) \sum_{x'} \left\{ P(y|x',z) P(x') \right\} \right].
$$
This can be seen from equation (3.15) on p. 68 which is
$$
P(y|\text{do}(X=x)) = \sum_z \s |
41,405 | Three way fixed effects vs combining two of the effects | Consider the model
$$(1) \ \ w_{it} = \mathbf x_{it}^\top \beta + \delta_t +\psi_{a(i,t)} + \eta_{k(i,t)} + \epsilon_{it},$$
with the area effect $\psi_a$ and sector effect $\eta_k$ unobserved. Assuming that $\mathbf x_{it}$ is correlated with the area and sector effect the OLS estimator $$\hat \beta_{OLS}:=(\sum_i \s... | Three way fixed effects vs combining two of the effects | Consider the model
$$(1) \ \ w_{it} = \mathbf x_{it}^\top \beta + \delta_t +\psi_{a(i,t)} + \eta_{k(i,t)} + \epsilon_{it},$$
with the area effect $\psi_a$ and sector effect $\eta_k$ unobserved. Assum | Three way fixed effects vs combining two of the effects
Consider the model
$$(1) \ \ w_{it} = \mathbf x_{it}^\top \beta + \delta_t +\psi_{a(i,t)} + \eta_{k(i,t)} + \epsilon_{it},$$
with the area effect $\psi_a$ and sector effect $\eta_k$ unobserved. Assuming that $\mathbf x_{it}$ is correlated with the area and sector... | Three way fixed effects vs combining two of the effects
Consider the model
$$(1) \ \ w_{it} = \mathbf x_{it}^\top \beta + \delta_t +\psi_{a(i,t)} + \eta_{k(i,t)} + \epsilon_{it},$$
with the area effect $\psi_a$ and sector effect $\eta_k$ unobserved. Assum |
41,406 | How can I calculate a joint distribution based on marginal and conditional information? | Sketching a diagram of the joint distribution might firm up your understanding as well as help you get the right answer (and spot incorrect answers that might be offered).
Usually you don't need to work very hard at this--it's primarily a conceptual exercise--but for accuracy I asked a computer to draw this diagram:
T... | How can I calculate a joint distribution based on marginal and conditional information? | Sketching a diagram of the joint distribution might firm up your understanding as well as help you get the right answer (and spot incorrect answers that might be offered).
Usually you don't need to wo | How can I calculate a joint distribution based on marginal and conditional information?
Sketching a diagram of the joint distribution might firm up your understanding as well as help you get the right answer (and spot incorrect answers that might be offered).
Usually you don't need to work very hard at this--it's prima... | How can I calculate a joint distribution based on marginal and conditional information?
Sketching a diagram of the joint distribution might firm up your understanding as well as help you get the right answer (and spot incorrect answers that might be offered).
Usually you don't need to wo |
41,407 | How can I calculate a joint distribution based on marginal and conditional information? | The conditional distribution is $$p_{K|N=n}(k)=\frac{1}{2n},\ \ \ k=1,\dots,2n$$
For joint, you just multiply this with $p_N(n)$, which you already did with slightly wrong conditional, i.e. $1/n$. You don't necessarily have $k$ as a variable in your joint distribution. As far as uniform distribution is concerned, disa... | How can I calculate a joint distribution based on marginal and conditional information? | The conditional distribution is $$p_{K|N=n}(k)=\frac{1}{2n},\ \ \ k=1,\dots,2n$$
For joint, you just multiply this with $p_N(n)$, which you already did with slightly wrong conditional, i.e. $1/n$. Yo | How can I calculate a joint distribution based on marginal and conditional information?
The conditional distribution is $$p_{K|N=n}(k)=\frac{1}{2n},\ \ \ k=1,\dots,2n$$
For joint, you just multiply this with $p_N(n)$, which you already did with slightly wrong conditional, i.e. $1/n$. You don't necessarily have $k$ as ... | How can I calculate a joint distribution based on marginal and conditional information?
The conditional distribution is $$p_{K|N=n}(k)=\frac{1}{2n},\ \ \ k=1,\dots,2n$$
For joint, you just multiply this with $p_N(n)$, which you already did with slightly wrong conditional, i.e. $1/n$. Yo |
41,408 | Difference between non-contextual and contextual word embeddings | Your understanding is correct. Word embeddings, i.e., vectors you retrieve from a lookup table are always non-contextual, not matter in what this is happening. (It is slightly different in ELMo which uses a character-based network to get a word embedding, but it also does consider any context).
However, when people say... | Difference between non-contextual and contextual word embeddings | Your understanding is correct. Word embeddings, i.e., vectors you retrieve from a lookup table are always non-contextual, not matter in what this is happening. (It is slightly different in ELMo which | Difference between non-contextual and contextual word embeddings
Your understanding is correct. Word embeddings, i.e., vectors you retrieve from a lookup table are always non-contextual, not matter in what this is happening. (It is slightly different in ELMo which uses a character-based network to get a word embedding,... | Difference between non-contextual and contextual word embeddings
Your understanding is correct. Word embeddings, i.e., vectors you retrieve from a lookup table are always non-contextual, not matter in what this is happening. (It is slightly different in ELMo which |
41,409 | Difference between non-contextual and contextual word embeddings | In non contextual 'playing' remain same for example 'playing' sport, and 'playing' violin. But it changes in contextual word embedding. Check this post for an illustrative understanding.. https://medium.com/@everlearner42/how-contextual-word-embeddings-are-learnt-in-nlp-a0a52fcad1f9 | Difference between non-contextual and contextual word embeddings | In non contextual 'playing' remain same for example 'playing' sport, and 'playing' violin. But it changes in contextual word embedding. Check this post for an illustrative understanding.. https://medi | Difference between non-contextual and contextual word embeddings
In non contextual 'playing' remain same for example 'playing' sport, and 'playing' violin. But it changes in contextual word embedding. Check this post for an illustrative understanding.. https://medium.com/@everlearner42/how-contextual-word-embeddings-ar... | Difference between non-contextual and contextual word embeddings
In non contextual 'playing' remain same for example 'playing' sport, and 'playing' violin. But it changes in contextual word embedding. Check this post for an illustrative understanding.. https://medi |
41,410 | Spurious relationships: flavours, terminology | Which of these cases are instances of a "spurious relationship"? How could the remaining cases be termed?
I think 1. and 2. are both spurious, but they result from taking a finite sample. If we took independent samples from some distribution, say a normal distribution, we would very likely find that the correlation be... | Spurious relationships: flavours, terminology | Which of these cases are instances of a "spurious relationship"? How could the remaining cases be termed?
I think 1. and 2. are both spurious, but they result from taking a finite sample. If we took | Spurious relationships: flavours, terminology
Which of these cases are instances of a "spurious relationship"? How could the remaining cases be termed?
I think 1. and 2. are both spurious, but they result from taking a finite sample. If we took independent samples from some distribution, say a normal distribution, we ... | Spurious relationships: flavours, terminology
Which of these cases are instances of a "spurious relationship"? How could the remaining cases be termed?
I think 1. and 2. are both spurious, but they result from taking a finite sample. If we took |
41,411 | Spurious relationships: flavours, terminology | As I've noted in a related answer, my view is that it is best to reserve the attribution of "spuriousness" to an incorrect inference from correlation to cause. It is immportant to be able to talk accurately about evidence of correlation (and other nonlinear associations) between variables in statistical analysis, and ... | Spurious relationships: flavours, terminology | As I've noted in a related answer, my view is that it is best to reserve the attribution of "spuriousness" to an incorrect inference from correlation to cause. It is immportant to be able to talk acc | Spurious relationships: flavours, terminology
As I've noted in a related answer, my view is that it is best to reserve the attribution of "spuriousness" to an incorrect inference from correlation to cause. It is immportant to be able to talk accurately about evidence of correlation (and other nonlinear associations) b... | Spurious relationships: flavours, terminology
As I've noted in a related answer, my view is that it is best to reserve the attribution of "spuriousness" to an incorrect inference from correlation to cause. It is immportant to be able to talk acc |
41,412 | What does Sparse PCA implementation in Python do? | Answer:
Your code seems to be in line with the cited paper, and the incosistency is an artefact of non-standard definition of principal components used in scikit-learn of versions < 0.22 (this is mentioned in the deprecation message).
You can get meaningful results by
setting normalize_components=True
dividing the ... | What does Sparse PCA implementation in Python do? | Answer:
Your code seems to be in line with the cited paper, and the incosistency is an artefact of non-standard definition of principal components used in scikit-learn of versions < 0.22 (this is me | What does Sparse PCA implementation in Python do?
Answer:
Your code seems to be in line with the cited paper, and the incosistency is an artefact of non-standard definition of principal components used in scikit-learn of versions < 0.22 (this is mentioned in the deprecation message).
You can get meaningful results by... | What does Sparse PCA implementation in Python do?
Answer:
Your code seems to be in line with the cited paper, and the incosistency is an artefact of non-standard definition of principal components used in scikit-learn of versions < 0.22 (this is me |
41,413 | Fleiss kappa vs Cohen kappa | Fleiss' $\kappa$ works for any number of raters, Cohen's $\kappa$ only works for two raters; in addition, Fleiss' $\kappa$ allows for each rater to be rating different items, while Cohen's $\kappa$ assumes that both raters are rating identical items.
However, Fleiss' $\kappa$ can lead to paradoxical results (see e.g. G... | Fleiss kappa vs Cohen kappa | Fleiss' $\kappa$ works for any number of raters, Cohen's $\kappa$ only works for two raters; in addition, Fleiss' $\kappa$ allows for each rater to be rating different items, while Cohen's $\kappa$ as | Fleiss kappa vs Cohen kappa
Fleiss' $\kappa$ works for any number of raters, Cohen's $\kappa$ only works for two raters; in addition, Fleiss' $\kappa$ allows for each rater to be rating different items, while Cohen's $\kappa$ assumes that both raters are rating identical items.
However, Fleiss' $\kappa$ can lead to par... | Fleiss kappa vs Cohen kappa
Fleiss' $\kappa$ works for any number of raters, Cohen's $\kappa$ only works for two raters; in addition, Fleiss' $\kappa$ allows for each rater to be rating different items, while Cohen's $\kappa$ as |
41,414 | Biased prediction (overestimation) for xgboost | What is described is not very surprising.
Boosting methods usually do not give well calibrated probabilistic predictions (e.g. see
Caruana et al. (2004) "Ensemble Selection from Libraries of Models",
Niculescu-Mizil & Caruana (2005) "Predicting good probabilities with supervised learning"). GLM-based methods provide... | Biased prediction (overestimation) for xgboost | What is described is not very surprising.
Boosting methods usually do not give well calibrated probabilistic predictions (e.g. see
Caruana et al. (2004) "Ensemble Selection from Libraries of Models" | Biased prediction (overestimation) for xgboost
What is described is not very surprising.
Boosting methods usually do not give well calibrated probabilistic predictions (e.g. see
Caruana et al. (2004) "Ensemble Selection from Libraries of Models",
Niculescu-Mizil & Caruana (2005) "Predicting good probabilities with s... | Biased prediction (overestimation) for xgboost
What is described is not very surprising.
Boosting methods usually do not give well calibrated probabilistic predictions (e.g. see
Caruana et al. (2004) "Ensemble Selection from Libraries of Models" |
41,415 | How to compute confidence interval in a case with small sample size, small population size, and one very dominant class? | Judging from its abstract, the JASA article by Weizhen Wang linked in my comment,
gives a method to get (nearly) exact hypergeometric confidence confidence intervals.
Perhaps a more easily computed style of CI, based on a normal approximation to the hypergeometric distribution, will suffice for your purposes.
Main ex... | How to compute confidence interval in a case with small sample size, small population size, and one | Judging from its abstract, the JASA article by Weizhen Wang linked in my comment,
gives a method to get (nearly) exact hypergeometric confidence confidence intervals.
Perhaps a more easily computed s | How to compute confidence interval in a case with small sample size, small population size, and one very dominant class?
Judging from its abstract, the JASA article by Weizhen Wang linked in my comment,
gives a method to get (nearly) exact hypergeometric confidence confidence intervals.
Perhaps a more easily computed ... | How to compute confidence interval in a case with small sample size, small population size, and one
Judging from its abstract, the JASA article by Weizhen Wang linked in my comment,
gives a method to get (nearly) exact hypergeometric confidence confidence intervals.
Perhaps a more easily computed s |
41,416 | visreg visualization of mgcv results (GAM) | The difference arises because you are ignoring the intercept (& the coef for the non-reference levels of the factor; see first Note) when you go via the mgcv:::plot.gam() method. The visreg output is showing the smooth effect of each variable conditional upon the other terms in the model. The blue line shows the estima... | visreg visualization of mgcv results (GAM) | The difference arises because you are ignoring the intercept (& the coef for the non-reference levels of the factor; see first Note) when you go via the mgcv:::plot.gam() method. The visreg output is | visreg visualization of mgcv results (GAM)
The difference arises because you are ignoring the intercept (& the coef for the non-reference levels of the factor; see first Note) when you go via the mgcv:::plot.gam() method. The visreg output is showing the smooth effect of each variable conditional upon the other terms i... | visreg visualization of mgcv results (GAM)
The difference arises because you are ignoring the intercept (& the coef for the non-reference levels of the factor; see first Note) when you go via the mgcv:::plot.gam() method. The visreg output is |
41,417 | Is the independent sum of a continuous random variable and mixed random variable continuous? | There is a relatively elementary demonstration that the sum is continuous.
Let $X$ have a probability distribution function $F_X$ with density function $f_X$ and let the distribution function of $Y$ be $F_Y.$ We do not assume $Y$ has a density function. I claim that $X+Y$ has a density function (implying it is absolu... | Is the independent sum of a continuous random variable and mixed random variable continuous? | There is a relatively elementary demonstration that the sum is continuous.
Let $X$ have a probability distribution function $F_X$ with density function $f_X$ and let the distribution function of $Y$ b | Is the independent sum of a continuous random variable and mixed random variable continuous?
There is a relatively elementary demonstration that the sum is continuous.
Let $X$ have a probability distribution function $F_X$ with density function $f_X$ and let the distribution function of $Y$ be $F_Y.$ We do not assume ... | Is the independent sum of a continuous random variable and mixed random variable continuous?
There is a relatively elementary demonstration that the sum is continuous.
Let $X$ have a probability distribution function $F_X$ with density function $f_X$ and let the distribution function of $Y$ b |
41,418 | Is it advisable to use output from a ML model as a feature in another ML model? | It's perfectly OK, and also widely used. Different models can explain different perspectives of data and stacking them in front of each other, and using outputs/predictions produced by previous layers enables even moderately simple final layer algorithms to perform much better compared to on their own, because they use... | Is it advisable to use output from a ML model as a feature in another ML model? | It's perfectly OK, and also widely used. Different models can explain different perspectives of data and stacking them in front of each other, and using outputs/predictions produced by previous layers | Is it advisable to use output from a ML model as a feature in another ML model?
It's perfectly OK, and also widely used. Different models can explain different perspectives of data and stacking them in front of each other, and using outputs/predictions produced by previous layers enables even moderately simple final la... | Is it advisable to use output from a ML model as a feature in another ML model?
It's perfectly OK, and also widely used. Different models can explain different perspectives of data and stacking them in front of each other, and using outputs/predictions produced by previous layers |
41,419 | In linear regression, why are raw least squares residuals heteroskedastic? | Assuming the usual linear model with constant variance $\sigma^2$. I will use notation (and some results) from Leverages and effect of leverage points. The linear model in matrix form is
$$
Y= X\beta + \epsilon
$$ where $\epsilon$ is a vector of $n$ iid error terms. Then the hat matrix is $H=X(X^TX)^{-1}X^T$, and... | In linear regression, why are raw least squares residuals heteroskedastic? | Assuming the usual linear model with constant variance $\sigma^2$. I will use notation (and some results) from Leverages and effect of leverage points. The linear model in matrix form is
$$
Y= X | In linear regression, why are raw least squares residuals heteroskedastic?
Assuming the usual linear model with constant variance $\sigma^2$. I will use notation (and some results) from Leverages and effect of leverage points. The linear model in matrix form is
$$
Y= X\beta + \epsilon
$$ where $\epsilon$ is a vec... | In linear regression, why are raw least squares residuals heteroskedastic?
Assuming the usual linear model with constant variance $\sigma^2$. I will use notation (and some results) from Leverages and effect of leverage points. The linear model in matrix form is
$$
Y= X |
41,420 | In linear regression, why are raw least squares residuals heteroskedastic? | Suppose you have three $x$-values: $-1,0, +1.$
The corresponding dependent variables $Y_1,Y_2,Y_3$ are where the randomness is.
Now draw the picture. You can see why, if you move $Y_2$ up or down, the fitted line moves up or down. (By just $1/3$ as much as $Y_2$ moves.) But what happens if you move $Y_3$ up or down? Th... | In linear regression, why are raw least squares residuals heteroskedastic? | Suppose you have three $x$-values: $-1,0, +1.$
The corresponding dependent variables $Y_1,Y_2,Y_3$ are where the randomness is.
Now draw the picture. You can see why, if you move $Y_2$ up or down, the | In linear regression, why are raw least squares residuals heteroskedastic?
Suppose you have three $x$-values: $-1,0, +1.$
The corresponding dependent variables $Y_1,Y_2,Y_3$ are where the randomness is.
Now draw the picture. You can see why, if you move $Y_2$ up or down, the fitted line moves up or down. (By just $1/3$... | In linear regression, why are raw least squares residuals heteroskedastic?
Suppose you have three $x$-values: $-1,0, +1.$
The corresponding dependent variables $Y_1,Y_2,Y_3$ are where the randomness is.
Now draw the picture. You can see why, if you move $Y_2$ up or down, the |
41,421 | Is there a random variable $X$ with positive support such that the ratio of the two smallest realizations of an iid sample goes to one? | Yes, there are such distributions where the ratio of the second-smallest to smallest values approaches unity in probability as the sample size grows large. They have to behave "essentially" like distributions with strictly positive support in the sense of approaching zero probability very, very rapidly at the origin. ... | Is there a random variable $X$ with positive support such that the ratio of the two smallest realiza | Yes, there are such distributions where the ratio of the second-smallest to smallest values approaches unity in probability as the sample size grows large. They have to behave "essentially" like dist | Is there a random variable $X$ with positive support such that the ratio of the two smallest realizations of an iid sample goes to one?
Yes, there are such distributions where the ratio of the second-smallest to smallest values approaches unity in probability as the sample size grows large. They have to behave "essent... | Is there a random variable $X$ with positive support such that the ratio of the two smallest realiza
Yes, there are such distributions where the ratio of the second-smallest to smallest values approaches unity in probability as the sample size grows large. They have to behave "essentially" like dist |
41,422 | Distribution of sum of independent exponentials with random number of summands | As detailed in this X validated answer, waiting for a sum of iid exponential $\mathcal E(\lambda)$ variates to exceed one produces an Poisson $\mathcal P(\lambda)$ variate $N$. Hence waiting for a sum of iid exponential $\mathcal E(\lambda)$ variates to exceed $\tau_a$ produces an Poisson $\mathcal P(\tau_a\lambda)$ va... | Distribution of sum of independent exponentials with random number of summands | As detailed in this X validated answer, waiting for a sum of iid exponential $\mathcal E(\lambda)$ variates to exceed one produces an Poisson $\mathcal P(\lambda)$ variate $N$. Hence waiting for a sum | Distribution of sum of independent exponentials with random number of summands
As detailed in this X validated answer, waiting for a sum of iid exponential $\mathcal E(\lambda)$ variates to exceed one produces an Poisson $\mathcal P(\lambda)$ variate $N$. Hence waiting for a sum of iid exponential $\mathcal E(\lambda)$... | Distribution of sum of independent exponentials with random number of summands
As detailed in this X validated answer, waiting for a sum of iid exponential $\mathcal E(\lambda)$ variates to exceed one produces an Poisson $\mathcal P(\lambda)$ variate $N$. Hence waiting for a sum |
41,423 | Literature on $\ell_q$ LASSO, $q < 1$ | Frank & Friedman (1993) suggested the idea of bridge estimates, with penalty function $P_B=\lambda\sum_j|\alpha_j|^\gamma$, as a paradigm for understanding subset selection and ridge regression. The $\ell_0$-norm corresponds to subset selection methods, $\ell_1$ is the LASSO, and $\ell_2$ is ridge regression. They note... | Literature on $\ell_q$ LASSO, $q < 1$ | Frank & Friedman (1993) suggested the idea of bridge estimates, with penalty function $P_B=\lambda\sum_j|\alpha_j|^\gamma$, as a paradigm for understanding subset selection and ridge regression. The $ | Literature on $\ell_q$ LASSO, $q < 1$
Frank & Friedman (1993) suggested the idea of bridge estimates, with penalty function $P_B=\lambda\sum_j|\alpha_j|^\gamma$, as a paradigm for understanding subset selection and ridge regression. The $\ell_0$-norm corresponds to subset selection methods, $\ell_1$ is the LASSO, and $... | Literature on $\ell_q$ LASSO, $q < 1$
Frank & Friedman (1993) suggested the idea of bridge estimates, with penalty function $P_B=\lambda\sum_j|\alpha_j|^\gamma$, as a paradigm for understanding subset selection and ridge regression. The $ |
41,424 | How to calculate ARMA model manually without R or Python | It is unclear in your question what "manual calculation" excludes, and your comment that you cannot use "advanced functions" is also not very helpful. In any case, fitting an ARMA model via maximum-likelihood estimation is an optimisation problem where you need to maximise a function over a set of parameters. For exa... | How to calculate ARMA model manually without R or Python | It is unclear in your question what "manual calculation" excludes, and your comment that you cannot use "advanced functions" is also not very helpful. In any case, fitting an ARMA model via maximum-l | How to calculate ARMA model manually without R or Python
It is unclear in your question what "manual calculation" excludes, and your comment that you cannot use "advanced functions" is also not very helpful. In any case, fitting an ARMA model via maximum-likelihood estimation is an optimisation problem where you need ... | How to calculate ARMA model manually without R or Python
It is unclear in your question what "manual calculation" excludes, and your comment that you cannot use "advanced functions" is also not very helpful. In any case, fitting an ARMA model via maximum-l |
41,425 | Using PCA to reduce dimensionality of training and testing data [duplicate] | Yes this is a common way of overfitting your model to the test data. In NLP a similar mistake is to do vocabulary selection and bag-of-words vectorization on the full train/test data.
This is a bit insidious since doing model selection is a lot easier with most tools once you got your feature matrix. In addition the "b... | Using PCA to reduce dimensionality of training and testing data [duplicate] | Yes this is a common way of overfitting your model to the test data. In NLP a similar mistake is to do vocabulary selection and bag-of-words vectorization on the full train/test data.
This is a bit in | Using PCA to reduce dimensionality of training and testing data [duplicate]
Yes this is a common way of overfitting your model to the test data. In NLP a similar mistake is to do vocabulary selection and bag-of-words vectorization on the full train/test data.
This is a bit insidious since doing model selection is a lot... | Using PCA to reduce dimensionality of training and testing data [duplicate]
Yes this is a common way of overfitting your model to the test data. In NLP a similar mistake is to do vocabulary selection and bag-of-words vectorization on the full train/test data.
This is a bit in |
41,426 | Covariance of An Empirical Distribution Function Evaluated at Different Points | Note that
\begin{align*}\text{Cov}(\frac{1}{n} \sum I\{ X_i \le x\},\frac{1}{n} \sum I\{ X_i \le y\})
&=\frac{1}{n^2}\text{Cov}(\sum I\{ X_i \le x\},\sum I\{ X_i \le y\})\\
&=\frac{1}{n^2}\sum_{i=1}^n\text{Cov}(I\{ X_i \le x\},I\{ X_i \le y\})\\
&\qquad\quad{\text{(since the $X_i$'s are independent)}}\\
&=\frac{1}{n}\t... | Covariance of An Empirical Distribution Function Evaluated at Different Points | Note that
\begin{align*}\text{Cov}(\frac{1}{n} \sum I\{ X_i \le x\},\frac{1}{n} \sum I\{ X_i \le y\})
&=\frac{1}{n^2}\text{Cov}(\sum I\{ X_i \le x\},\sum I\{ X_i \le y\})\\
&=\frac{1}{n^2}\sum_{i=1}^n | Covariance of An Empirical Distribution Function Evaluated at Different Points
Note that
\begin{align*}\text{Cov}(\frac{1}{n} \sum I\{ X_i \le x\},\frac{1}{n} \sum I\{ X_i \le y\})
&=\frac{1}{n^2}\text{Cov}(\sum I\{ X_i \le x\},\sum I\{ X_i \le y\})\\
&=\frac{1}{n^2}\sum_{i=1}^n\text{Cov}(I\{ X_i \le x\},I\{ X_i \le y\... | Covariance of An Empirical Distribution Function Evaluated at Different Points
Note that
\begin{align*}\text{Cov}(\frac{1}{n} \sum I\{ X_i \le x\},\frac{1}{n} \sum I\{ X_i \le y\})
&=\frac{1}{n^2}\text{Cov}(\sum I\{ X_i \le x\},\sum I\{ X_i \le y\})\\
&=\frac{1}{n^2}\sum_{i=1}^n |
41,427 | Is it possible for two independent variables to be correlated, by chance? | The question is confusing, and so maybe misinterpreted by some commenters and answerers. In your citation, there is two random variables $X$ and $Y$ which are independent. Then, there is a theorem saying that they are uncorrelated. It also have an easy proof, which you can find in many probability texts.
But this do n... | Is it possible for two independent variables to be correlated, by chance? | The question is confusing, and so maybe misinterpreted by some commenters and answerers. In your citation, there is two random variables $X$ and $Y$ which are independent. Then, there is a theorem say | Is it possible for two independent variables to be correlated, by chance?
The question is confusing, and so maybe misinterpreted by some commenters and answerers. In your citation, there is two random variables $X$ and $Y$ which are independent. Then, there is a theorem saying that they are uncorrelated. It also have a... | Is it possible for two independent variables to be correlated, by chance?
The question is confusing, and so maybe misinterpreted by some commenters and answerers. In your citation, there is two random variables $X$ and $Y$ which are independent. Then, there is a theorem say |
41,428 | Is it possible for two independent variables to be correlated, by chance? | It's a matter of change.
Yes, it's always possible that on timepoint x, two independent variables can increase or decrease at the same time. At timepoint x it looks like these variables are dependent.
However, if the data is independent they follow their own trends in most of the timepoints. | Is it possible for two independent variables to be correlated, by chance? | It's a matter of change.
Yes, it's always possible that on timepoint x, two independent variables can increase or decrease at the same time. At timepoint x it looks like these variables are dependent | Is it possible for two independent variables to be correlated, by chance?
It's a matter of change.
Yes, it's always possible that on timepoint x, two independent variables can increase or decrease at the same time. At timepoint x it looks like these variables are dependent.
However, if the data is independent they fo... | Is it possible for two independent variables to be correlated, by chance?
It's a matter of change.
Yes, it's always possible that on timepoint x, two independent variables can increase or decrease at the same time. At timepoint x it looks like these variables are dependent |
41,429 | Is it possible for two independent variables to be correlated, by chance? | Yes, and to add to all previous answers and comments, you can easily simulate the accidence.
I.e., this simple R example:
require(magrittr)
lapply(1:1000, function(b){
set.seed(b)
cor(rnorm(100), rnorm(100))
}) %>% do.call(c,.) %>% abs %>% max
Out of 1000 random draws there was a case when two independent normal r... | Is it possible for two independent variables to be correlated, by chance? | Yes, and to add to all previous answers and comments, you can easily simulate the accidence.
I.e., this simple R example:
require(magrittr)
lapply(1:1000, function(b){
set.seed(b)
cor(rnorm(100), | Is it possible for two independent variables to be correlated, by chance?
Yes, and to add to all previous answers and comments, you can easily simulate the accidence.
I.e., this simple R example:
require(magrittr)
lapply(1:1000, function(b){
set.seed(b)
cor(rnorm(100), rnorm(100))
}) %>% do.call(c,.) %>% abs %>% ma... | Is it possible for two independent variables to be correlated, by chance?
Yes, and to add to all previous answers and comments, you can easily simulate the accidence.
I.e., this simple R example:
require(magrittr)
lapply(1:1000, function(b){
set.seed(b)
cor(rnorm(100), |
41,430 | Is it possible for two independent variables to be correlated, by chance? | If X and Y are independent from each other, it can be proven that the correlation coefficient must be zero. However, there are two caveats:
As others point out, just because you have two populations that are uncorrelated, it does not necessarily mean that the samples drawn from the two populations will also be uncorre... | Is it possible for two independent variables to be correlated, by chance? | If X and Y are independent from each other, it can be proven that the correlation coefficient must be zero. However, there are two caveats:
As others point out, just because you have two populations | Is it possible for two independent variables to be correlated, by chance?
If X and Y are independent from each other, it can be proven that the correlation coefficient must be zero. However, there are two caveats:
As others point out, just because you have two populations that are uncorrelated, it does not necessarily... | Is it possible for two independent variables to be correlated, by chance?
If X and Y are independent from each other, it can be proven that the correlation coefficient must be zero. However, there are two caveats:
As others point out, just because you have two populations |
41,431 | Neural network's weight reduction | You might wanna check:
http://yann.lecun.com/exdb/publis/pdf/lecun-90b.pdf
And a more recent paper on the topic:
https://arxiv.org/pdf/1506.02626v3.pdf
However, I was not able to find an implementation of these two. So you will need to implement it yourself. | Neural network's weight reduction | You might wanna check:
http://yann.lecun.com/exdb/publis/pdf/lecun-90b.pdf
And a more recent paper on the topic:
https://arxiv.org/pdf/1506.02626v3.pdf
However, I was not able to find an implementatio | Neural network's weight reduction
You might wanna check:
http://yann.lecun.com/exdb/publis/pdf/lecun-90b.pdf
And a more recent paper on the topic:
https://arxiv.org/pdf/1506.02626v3.pdf
However, I was not able to find an implementation of these two. So you will need to implement it yourself. | Neural network's weight reduction
You might wanna check:
http://yann.lecun.com/exdb/publis/pdf/lecun-90b.pdf
And a more recent paper on the topic:
https://arxiv.org/pdf/1506.02626v3.pdf
However, I was not able to find an implementatio |
41,432 | Neural network's weight reduction | After reading some of the helpful comments and answers, I've did some focused reading on my own.
As mentioned in other answers, this process is called Pruning and like many other ideas in the neural network area, it is not new. From what I can tell, it originates in LeCun's 1990 paper with the lovely "Optimal Brain Dam... | Neural network's weight reduction | After reading some of the helpful comments and answers, I've did some focused reading on my own.
As mentioned in other answers, this process is called Pruning and like many other ideas in the neural n | Neural network's weight reduction
After reading some of the helpful comments and answers, I've did some focused reading on my own.
As mentioned in other answers, this process is called Pruning and like many other ideas in the neural network area, it is not new. From what I can tell, it originates in LeCun's 1990 paper ... | Neural network's weight reduction
After reading some of the helpful comments and answers, I've did some focused reading on my own.
As mentioned in other answers, this process is called Pruning and like many other ideas in the neural n |
41,433 | how to make sense of the number of observations per parameters in deep learning models? | In a classical machine learning (i.e. statistical learning theory) setup, the number of parameters usually enters via the Vapnik–Chervonenkis (VC) dimension and the number of observations via the PAC bound. Very roughly speaking, this says that for classification problems, the worst-case difference in 0-1 loss between ... | how to make sense of the number of observations per parameters in deep learning models? | In a classical machine learning (i.e. statistical learning theory) setup, the number of parameters usually enters via the Vapnik–Chervonenkis (VC) dimension and the number of observations via the PAC | how to make sense of the number of observations per parameters in deep learning models?
In a classical machine learning (i.e. statistical learning theory) setup, the number of parameters usually enters via the Vapnik–Chervonenkis (VC) dimension and the number of observations via the PAC bound. Very roughly speaking, th... | how to make sense of the number of observations per parameters in deep learning models?
In a classical machine learning (i.e. statistical learning theory) setup, the number of parameters usually enters via the Vapnik–Chervonenkis (VC) dimension and the number of observations via the PAC |
41,434 | how to make sense of the number of observations per parameters in deep learning models? | so essentially the answer is regularisation. for NNs this is stopped training (ie initialise weights near zero and stop when you reach minimum in validation error, before you reach minimum on training error), drop out (randomly disable parts of the network) and weight regularisation (l2).
even in the linear case, lasso... | how to make sense of the number of observations per parameters in deep learning models? | so essentially the answer is regularisation. for NNs this is stopped training (ie initialise weights near zero and stop when you reach minimum in validation error, before you reach minimum on training | how to make sense of the number of observations per parameters in deep learning models?
so essentially the answer is regularisation. for NNs this is stopped training (ie initialise weights near zero and stop when you reach minimum in validation error, before you reach minimum on training error), drop out (randomly disa... | how to make sense of the number of observations per parameters in deep learning models?
so essentially the answer is regularisation. for NNs this is stopped training (ie initialise weights near zero and stop when you reach minimum in validation error, before you reach minimum on training |
41,435 | how to make sense of the number of observations per parameters in deep learning models? | For any estimation problem, one would typically require the parameters of the statistical model to be identifiable. The one-to-one correspondence between number of observations and number of parameters actually comes from inspecting whenever the Information Matrix is singular or not. If the information matrix is non-si... | how to make sense of the number of observations per parameters in deep learning models? | For any estimation problem, one would typically require the parameters of the statistical model to be identifiable. The one-to-one correspondence between number of observations and number of parameter | how to make sense of the number of observations per parameters in deep learning models?
For any estimation problem, one would typically require the parameters of the statistical model to be identifiable. The one-to-one correspondence between number of observations and number of parameters actually comes from inspecting... | how to make sense of the number of observations per parameters in deep learning models?
For any estimation problem, one would typically require the parameters of the statistical model to be identifiable. The one-to-one correspondence between number of observations and number of parameter |
41,436 | Time steps in Keras LSTM | As described by Andrey Karpathy, the basic recurrent neural network cell is something like
$$ h_t = \tanh(W_{hh}h_{t-1} + W_{xh}x_t) $$
so it takes previous hidden state $h_{t-1}$ and current input $x_t$, to produce hidden state $h_t$. Notice that $W_{hh}$ and $W_{xh}$ are not indexed by time $t$, we use the same weigh... | Time steps in Keras LSTM | As described by Andrey Karpathy, the basic recurrent neural network cell is something like
$$ h_t = \tanh(W_{hh}h_{t-1} + W_{xh}x_t) $$
so it takes previous hidden state $h_{t-1}$ and current input $x | Time steps in Keras LSTM
As described by Andrey Karpathy, the basic recurrent neural network cell is something like
$$ h_t = \tanh(W_{hh}h_{t-1} + W_{xh}x_t) $$
so it takes previous hidden state $h_{t-1}$ and current input $x_t$, to produce hidden state $h_t$. Notice that $W_{hh}$ and $W_{xh}$ are not indexed by time $... | Time steps in Keras LSTM
As described by Andrey Karpathy, the basic recurrent neural network cell is something like
$$ h_t = \tanh(W_{hh}h_{t-1} + W_{xh}x_t) $$
so it takes previous hidden state $h_{t-1}$ and current input $x |
41,437 | Proof that posterior median is the Bayes estimate of absolute loss? | Second derivative yields
$$2 \pi (\delta | x) \geq 0$$
So the original function is convex and hence the median corresponds to a minimum not an inflection point | Proof that posterior median is the Bayes estimate of absolute loss? | Second derivative yields
$$2 \pi (\delta | x) \geq 0$$
So the original function is convex and hence the median corresponds to a minimum not an inflection point | Proof that posterior median is the Bayes estimate of absolute loss?
Second derivative yields
$$2 \pi (\delta | x) \geq 0$$
So the original function is convex and hence the median corresponds to a minimum not an inflection point | Proof that posterior median is the Bayes estimate of absolute loss?
Second derivative yields
$$2 \pi (\delta | x) \geq 0$$
So the original function is convex and hence the median corresponds to a minimum not an inflection point |
41,438 | Proof that posterior median is the Bayes estimate of absolute loss? | Adding to Xiaomi answer, here is the derivation, using Leibnitz rule:
$\require{cancel}
\frac{\partial \rho}{\partial \delta} = \int_{-\infty}^{\delta}\pi(\theta|x)d\theta - \int_{\delta}^{\infty}\pi(\theta|x)d\theta \\
\frac{\partial^2 \rho}{\partial \delta^2} = \pi(\delta|x)\cdot1 - \cancel{\pi(\delta|x)\cdot0} + \c... | Proof that posterior median is the Bayes estimate of absolute loss? | Adding to Xiaomi answer, here is the derivation, using Leibnitz rule:
$\require{cancel}
\frac{\partial \rho}{\partial \delta} = \int_{-\infty}^{\delta}\pi(\theta|x)d\theta - \int_{\delta}^{\infty}\pi | Proof that posterior median is the Bayes estimate of absolute loss?
Adding to Xiaomi answer, here is the derivation, using Leibnitz rule:
$\require{cancel}
\frac{\partial \rho}{\partial \delta} = \int_{-\infty}^{\delta}\pi(\theta|x)d\theta - \int_{\delta}^{\infty}\pi(\theta|x)d\theta \\
\frac{\partial^2 \rho}{\partial... | Proof that posterior median is the Bayes estimate of absolute loss?
Adding to Xiaomi answer, here is the derivation, using Leibnitz rule:
$\require{cancel}
\frac{\partial \rho}{\partial \delta} = \int_{-\infty}^{\delta}\pi(\theta|x)d\theta - \int_{\delta}^{\infty}\pi |
41,439 | I regularized my linear regression, now what? | One common approach is to now redo the regression (without regularization) using only the variables that were selected by LASSO.
This is called "post-selection inference." See Lee et al. 2016 for finding p-values and confidence intervals on the resulting estimates. | I regularized my linear regression, now what? | One common approach is to now redo the regression (without regularization) using only the variables that were selected by LASSO.
This is called "post-selection inference." See Lee et al. 2016 for find | I regularized my linear regression, now what?
One common approach is to now redo the regression (without regularization) using only the variables that were selected by LASSO.
This is called "post-selection inference." See Lee et al. 2016 for finding p-values and confidence intervals on the resulting estimates. | I regularized my linear regression, now what?
One common approach is to now redo the regression (without regularization) using only the variables that were selected by LASSO.
This is called "post-selection inference." See Lee et al. 2016 for find |
41,440 | I regularized my linear regression, now what? | You may ask yourself, what is the goal of building this model. Are you trying to get a better prediction performance? Or you want a linear model that statistically significant. These two goals are not necessarily aligned.
From machine learning perspective, you always want to know you are overfitting or under-fitting. ... | I regularized my linear regression, now what? | You may ask yourself, what is the goal of building this model. Are you trying to get a better prediction performance? Or you want a linear model that statistically significant. These two goals are not | I regularized my linear regression, now what?
You may ask yourself, what is the goal of building this model. Are you trying to get a better prediction performance? Or you want a linear model that statistically significant. These two goals are not necessarily aligned.
From machine learning perspective, you always want ... | I regularized my linear regression, now what?
You may ask yourself, what is the goal of building this model. Are you trying to get a better prediction performance? Or you want a linear model that statistically significant. These two goals are not |
41,441 | Linear Regression of Indicator Matrix: sum of predictions is 1 | The intercept in the model (a column of 1's in X) is the key.
Write $\hat{Y} = \hat{f}_k(X)$ as the fit of $Y$.
\begin{equation*}
\begin{split}
\sum_{k \in \{1, .., K\}} \hat{f}_k(X) &= \hat{Y}\cdot\textbf{1}_{K} \\
& = X(X^TX)^{-1}X^TY\cdot\textbf{1}_{K} \\
& = P\cdot\textbf{1}_{N}
\end{split}
\end{equation*}
where $... | Linear Regression of Indicator Matrix: sum of predictions is 1 | The intercept in the model (a column of 1's in X) is the key.
Write $\hat{Y} = \hat{f}_k(X)$ as the fit of $Y$.
\begin{equation*}
\begin{split}
\sum_{k \in \{1, .., K\}} \hat{f}_k(X) &= \hat{Y}\cdot\ | Linear Regression of Indicator Matrix: sum of predictions is 1
The intercept in the model (a column of 1's in X) is the key.
Write $\hat{Y} = \hat{f}_k(X)$ as the fit of $Y$.
\begin{equation*}
\begin{split}
\sum_{k \in \{1, .., K\}} \hat{f}_k(X) &= \hat{Y}\cdot\textbf{1}_{K} \\
& = X(X^TX)^{-1}X^TY\cdot\textbf{1}_{K} ... | Linear Regression of Indicator Matrix: sum of predictions is 1
The intercept in the model (a column of 1's in X) is the key.
Write $\hat{Y} = \hat{f}_k(X)$ as the fit of $Y$.
\begin{equation*}
\begin{split}
\sum_{k \in \{1, .., K\}} \hat{f}_k(X) &= \hat{Y}\cdot\ |
41,442 | Linear Regression of Indicator Matrix: sum of predictions is 1 | Yeah, it is straighforward if you're familiar with centered model (or form) of $X$.
Consider that we have $K$ (ranges from $1, ..., K$) classes in our problem; As you showed, we compute a fitted output through the equation (however, a more compact notation is $\hat{f}_k(x)^T$ that denotes the discriminant of the $k$ ... | Linear Regression of Indicator Matrix: sum of predictions is 1 | Yeah, it is straighforward if you're familiar with centered model (or form) of $X$.
Consider that we have $K$ (ranges from $1, ..., K$) classes in our problem; As you showed, we compute a fitted outp | Linear Regression of Indicator Matrix: sum of predictions is 1
Yeah, it is straighforward if you're familiar with centered model (or form) of $X$.
Consider that we have $K$ (ranges from $1, ..., K$) classes in our problem; As you showed, we compute a fitted output through the equation (however, a more compact notation... | Linear Regression of Indicator Matrix: sum of predictions is 1
Yeah, it is straighforward if you're familiar with centered model (or form) of $X$.
Consider that we have $K$ (ranges from $1, ..., K$) classes in our problem; As you showed, we compute a fitted outp |
41,443 | Linear Regression of Indicator Matrix: sum of predictions is 1 | $(1,x^T)\hat{B}\mathbf{1}_{K\times1} = 1$ should hold for any $x \in \mathbb{R}^{p}$ rather than $x$ in the training set.
Since $\mathbf{X}' = [\mathbf{1}_{N \times 1}, \mathbf{X}_{N \times p}] $,
$\begin{align*}\hat{B}\mathbf{1}_{K \times 1} &= (\mathbf{X}'^T\mathbf{X}')^{-1}\mathbf{X}'^T \mathbf{Y}\mathbf{1}_{K \time... | Linear Regression of Indicator Matrix: sum of predictions is 1 | $(1,x^T)\hat{B}\mathbf{1}_{K\times1} = 1$ should hold for any $x \in \mathbb{R}^{p}$ rather than $x$ in the training set.
Since $\mathbf{X}' = [\mathbf{1}_{N \times 1}, \mathbf{X}_{N \times p}] $,
$\b | Linear Regression of Indicator Matrix: sum of predictions is 1
$(1,x^T)\hat{B}\mathbf{1}_{K\times1} = 1$ should hold for any $x \in \mathbb{R}^{p}$ rather than $x$ in the training set.
Since $\mathbf{X}' = [\mathbf{1}_{N \times 1}, \mathbf{X}_{N \times p}] $,
$\begin{align*}\hat{B}\mathbf{1}_{K \times 1} &= (\mathbf{X}... | Linear Regression of Indicator Matrix: sum of predictions is 1
$(1,x^T)\hat{B}\mathbf{1}_{K\times1} = 1$ should hold for any $x \in \mathbb{R}^{p}$ rather than $x$ in the training set.
Since $\mathbf{X}' = [\mathbf{1}_{N \times 1}, \mathbf{X}_{N \times p}] $,
$\b |
41,444 | Comparison of variance between two samples with unequal sample size | Location differences
Mann-Whitney does not test mean differences
I'll begin by knocking off the simpler questions. If your primary question about location differences is a difference in means, then you probably do not want a non-parametric test like the Mann-Whitney test. The Mann-Whitney test is a test of stochastic d... | Comparison of variance between two samples with unequal sample size | Location differences
Mann-Whitney does not test mean differences
I'll begin by knocking off the simpler questions. If your primary question about location differences is a difference in means, then yo | Comparison of variance between two samples with unequal sample size
Location differences
Mann-Whitney does not test mean differences
I'll begin by knocking off the simpler questions. If your primary question about location differences is a difference in means, then you probably do not want a non-parametric test like th... | Comparison of variance between two samples with unequal sample size
Location differences
Mann-Whitney does not test mean differences
I'll begin by knocking off the simpler questions. If your primary question about location differences is a difference in means, then yo |
41,445 | Does class balancing introduce bias? | For the main question:
Does class balancing introduce bias?
Yes, in most cases it does. Since the new data points are generated from the old ones, they can't introduce much variance to the dataset. In most cases they are only slightly different than the original ones.
Does oversampling before spliting introduce bias... | Does class balancing introduce bias? | For the main question:
Does class balancing introduce bias?
Yes, in most cases it does. Since the new data points are generated from the old ones, they can't introduce much variance to the dataset. | Does class balancing introduce bias?
For the main question:
Does class balancing introduce bias?
Yes, in most cases it does. Since the new data points are generated from the old ones, they can't introduce much variance to the dataset. In most cases they are only slightly different than the original ones.
Does oversa... | Does class balancing introduce bias?
For the main question:
Does class balancing introduce bias?
Yes, in most cases it does. Since the new data points are generated from the old ones, they can't introduce much variance to the dataset. |
41,446 | What do neural networks offer that traditional non-linear statistical models do not offer? | The ability to embed structural and algorithmic priors into the model.
The simplest example of this is convolutional neural networks applied to image data. The structural prior is that nearby regions of the image are more closely related / relevant to each other compared to far-away regions.
Graph convolutional network... | What do neural networks offer that traditional non-linear statistical models do not offer? | The ability to embed structural and algorithmic priors into the model.
The simplest example of this is convolutional neural networks applied to image data. The structural prior is that nearby regions | What do neural networks offer that traditional non-linear statistical models do not offer?
The ability to embed structural and algorithmic priors into the model.
The simplest example of this is convolutional neural networks applied to image data. The structural prior is that nearby regions of the image are more closely... | What do neural networks offer that traditional non-linear statistical models do not offer?
The ability to embed structural and algorithmic priors into the model.
The simplest example of this is convolutional neural networks applied to image data. The structural prior is that nearby regions |
41,447 | What do neural networks offer that traditional non-linear statistical models do not offer? | It's my understanding that at this point in time, there is no real solid mathematical reason for why NN have seen as much success as they have. Perhaps that's why you can't find any thing convincing at this time, although there are plenty of heuristic arguments.
The one proof that this brought up a lot (for good reaso... | What do neural networks offer that traditional non-linear statistical models do not offer? | It's my understanding that at this point in time, there is no real solid mathematical reason for why NN have seen as much success as they have. Perhaps that's why you can't find any thing convincing a | What do neural networks offer that traditional non-linear statistical models do not offer?
It's my understanding that at this point in time, there is no real solid mathematical reason for why NN have seen as much success as they have. Perhaps that's why you can't find any thing convincing at this time, although there a... | What do neural networks offer that traditional non-linear statistical models do not offer?
It's my understanding that at this point in time, there is no real solid mathematical reason for why NN have seen as much success as they have. Perhaps that's why you can't find any thing convincing a |
41,448 | Why start with measures of central tendency? | One reason we teach measures of central tendency before measures of spread because many measures of spread involve measures of central tendency: The standard deviation involves the mean, median absolute deviation involves the median. We could teach the range without teaching the mean, but teaching range is not exactly ... | Why start with measures of central tendency? | One reason we teach measures of central tendency before measures of spread because many measures of spread involve measures of central tendency: The standard deviation involves the mean, median absolu | Why start with measures of central tendency?
One reason we teach measures of central tendency before measures of spread because many measures of spread involve measures of central tendency: The standard deviation involves the mean, median absolute deviation involves the median. We could teach the range without teaching... | Why start with measures of central tendency?
One reason we teach measures of central tendency before measures of spread because many measures of spread involve measures of central tendency: The standard deviation involves the mean, median absolu |
41,449 | Is Reinforcement Learning the right choice for painting like Bob Ross? | I would suggest genetic algorithms (GA) or other global optimisers for this search, as your sequential score as you "build" the painting into more complex states is probably not the best guide.
There are a few examples of similar puzzles, such as building Mona Lisa out of circles, and here is a more recent example of t... | Is Reinforcement Learning the right choice for painting like Bob Ross? | I would suggest genetic algorithms (GA) or other global optimisers for this search, as your sequential score as you "build" the painting into more complex states is probably not the best guide.
There | Is Reinforcement Learning the right choice for painting like Bob Ross?
I would suggest genetic algorithms (GA) or other global optimisers for this search, as your sequential score as you "build" the painting into more complex states is probably not the best guide.
There are a few examples of similar puzzles, such as bu... | Is Reinforcement Learning the right choice for painting like Bob Ross?
I would suggest genetic algorithms (GA) or other global optimisers for this search, as your sequential score as you "build" the painting into more complex states is probably not the best guide.
There |
41,450 | Is Reinforcement Learning the right choice for painting like Bob Ross? | I think your skepticism of RL for this task is well-founded. But there has been some research toward building neural networks to reproduce the style of painters. This work leverages the power of convolutional neural networks.
"A Neural Algorithm of Artistic Style"
Leon A. Gatys, Alexander S. Ecker, Matthias Bethge
In ... | Is Reinforcement Learning the right choice for painting like Bob Ross? | I think your skepticism of RL for this task is well-founded. But there has been some research toward building neural networks to reproduce the style of painters. This work leverages the power of convo | Is Reinforcement Learning the right choice for painting like Bob Ross?
I think your skepticism of RL for this task is well-founded. But there has been some research toward building neural networks to reproduce the style of painters. This work leverages the power of convolutional neural networks.
"A Neural Algorithm of ... | Is Reinforcement Learning the right choice for painting like Bob Ross?
I think your skepticism of RL for this task is well-founded. But there has been some research toward building neural networks to reproduce the style of painters. This work leverages the power of convo |
41,451 | Difference between Cholesky decomposition and log-cholesky Decomposition | I think it's less confusing to call it the log-Cholesky paramet(e)rization rather than the log-Cholesky decomposition (i.e., the "decomposition" part doesn't change ...)
From Pinheiro's thesis (1994, UW Madison) - I think it has the same information as the paper you cite:
6.1.2 Log-Cholesky Parametrization If one re... | Difference between Cholesky decomposition and log-cholesky Decomposition | I think it's less confusing to call it the log-Cholesky paramet(e)rization rather than the log-Cholesky decomposition (i.e., the "decomposition" part doesn't change ...)
From Pinheiro's thesis (1994, | Difference between Cholesky decomposition and log-cholesky Decomposition
I think it's less confusing to call it the log-Cholesky paramet(e)rization rather than the log-Cholesky decomposition (i.e., the "decomposition" part doesn't change ...)
From Pinheiro's thesis (1994, UW Madison) - I think it has the same informati... | Difference between Cholesky decomposition and log-cholesky Decomposition
I think it's less confusing to call it the log-Cholesky paramet(e)rization rather than the log-Cholesky decomposition (i.e., the "decomposition" part doesn't change ...)
From Pinheiro's thesis (1994, |
41,452 | How to account for multiple measurements of same person in either two-group comparision or regression? | When analyzing non-independent observations (e.g. two eyes of same person) in regression, is mixed effect model the way to go?
In short: Yes.
Mixed models are capable of modelling the dependence or structure introduced in the data by the study design. In your example of measuring both eyes, you can use a mixed mod... | How to account for multiple measurements of same person in either two-group comparision or regressio | When analyzing non-independent observations (e.g. two eyes of same person) in regression, is mixed effect model the way to go?
In short: Yes.
Mixed models are capable of modelling the dependence | How to account for multiple measurements of same person in either two-group comparision or regression?
When analyzing non-independent observations (e.g. two eyes of same person) in regression, is mixed effect model the way to go?
In short: Yes.
Mixed models are capable of modelling the dependence or structure intr... | How to account for multiple measurements of same person in either two-group comparision or regressio
When analyzing non-independent observations (e.g. two eyes of same person) in regression, is mixed effect model the way to go?
In short: Yes.
Mixed models are capable of modelling the dependence |
41,453 | Back-propagation in Convolution layer | I try to explain the dimensions obtained (5x18x18 -> 3x20x20):
5 -> 3 the flipped convolutions are repeated 3 times, but the effects of each of the 5 filter are summed up, exactly as you do in the forward phase. In any case in a convolutional layer it is possible to give any depth in input and any number of filters in... | Back-propagation in Convolution layer | I try to explain the dimensions obtained (5x18x18 -> 3x20x20):
5 -> 3 the flipped convolutions are repeated 3 times, but the effects of each of the 5 filter are summed up, exactly as you do in the fo | Back-propagation in Convolution layer
I try to explain the dimensions obtained (5x18x18 -> 3x20x20):
5 -> 3 the flipped convolutions are repeated 3 times, but the effects of each of the 5 filter are summed up, exactly as you do in the forward phase. In any case in a convolutional layer it is possible to give any depth... | Back-propagation in Convolution layer
I try to explain the dimensions obtained (5x18x18 -> 3x20x20):
5 -> 3 the flipped convolutions are repeated 3 times, but the effects of each of the 5 filter are summed up, exactly as you do in the fo |
41,454 | Is the negative exponential distribution a member of the exponential family? | This is correct, if $\mu$ is a parameter of the distribution rather than a given, the indicator function implies this distribution is not an exponential family. | Is the negative exponential distribution a member of the exponential family? | This is correct, if $\mu$ is a parameter of the distribution rather than a given, the indicator function implies this distribution is not an exponential family. | Is the negative exponential distribution a member of the exponential family?
This is correct, if $\mu$ is a parameter of the distribution rather than a given, the indicator function implies this distribution is not an exponential family. | Is the negative exponential distribution a member of the exponential family?
This is correct, if $\mu$ is a parameter of the distribution rather than a given, the indicator function implies this distribution is not an exponential family. |
41,455 | How to embed in Euclidean space | These are known as multidimensional scaling algorithms. From wikipedia (https://en.wikipedia.org/wiki/Multidimensional_scaling), "An MDS algorithm aims to place each object in N-dimensional space such that the between-object distances are preserved as well as possible." So essentially you input a distance matrix and ... | How to embed in Euclidean space | These are known as multidimensional scaling algorithms. From wikipedia (https://en.wikipedia.org/wiki/Multidimensional_scaling), "An MDS algorithm aims to place each object in N-dimensional space suc | How to embed in Euclidean space
These are known as multidimensional scaling algorithms. From wikipedia (https://en.wikipedia.org/wiki/Multidimensional_scaling), "An MDS algorithm aims to place each object in N-dimensional space such that the between-object distances are preserved as well as possible." So essentially ... | How to embed in Euclidean space
These are known as multidimensional scaling algorithms. From wikipedia (https://en.wikipedia.org/wiki/Multidimensional_scaling), "An MDS algorithm aims to place each object in N-dimensional space suc |
41,456 | How to embed in Euclidean space | vectors that are similar under the original measure have small
Euclidean distance under the embedding
This is the goal of dimensionality reduction, especially the nonlinear dimensionality reduction, where it is the only goal (because they cannot in general enforce that distances between points that are far apart wil... | How to embed in Euclidean space | vectors that are similar under the original measure have small
Euclidean distance under the embedding
This is the goal of dimensionality reduction, especially the nonlinear dimensionality reduction | How to embed in Euclidean space
vectors that are similar under the original measure have small
Euclidean distance under the embedding
This is the goal of dimensionality reduction, especially the nonlinear dimensionality reduction, where it is the only goal (because they cannot in general enforce that distances betwe... | How to embed in Euclidean space
vectors that are similar under the original measure have small
Euclidean distance under the embedding
This is the goal of dimensionality reduction, especially the nonlinear dimensionality reduction |
41,457 | MLE of $\sqrt{\frac{2}{\pi}}\exp\left({-\frac{1}{2}(x-\theta)}^2\right)$ | For $\theta\le x_{(1)}$ the likelihood is an increasing function of $\theta$ and for $\theta>x_{(1)}$, the likelihood is zero. Hence, the MLE of $\theta$ is $\hat\theta=X_{(1)}$. | MLE of $\sqrt{\frac{2}{\pi}}\exp\left({-\frac{1}{2}(x-\theta)}^2\right)$ | For $\theta\le x_{(1)}$ the likelihood is an increasing function of $\theta$ and for $\theta>x_{(1)}$, the likelihood is zero. Hence, the MLE of $\theta$ is $\hat\theta=X_{(1)}$. | MLE of $\sqrt{\frac{2}{\pi}}\exp\left({-\frac{1}{2}(x-\theta)}^2\right)$
For $\theta\le x_{(1)}$ the likelihood is an increasing function of $\theta$ and for $\theta>x_{(1)}$, the likelihood is zero. Hence, the MLE of $\theta$ is $\hat\theta=X_{(1)}$. | MLE of $\sqrt{\frac{2}{\pi}}\exp\left({-\frac{1}{2}(x-\theta)}^2\right)$
For $\theta\le x_{(1)}$ the likelihood is an increasing function of $\theta$ and for $\theta>x_{(1)}$, the likelihood is zero. Hence, the MLE of $\theta$ is $\hat\theta=X_{(1)}$. |
41,458 | Deep Learning : Using dropout in Autoencoders? | Should i normalize my numerical data values before feeding to any type of autoencoder? If they are int and float values do I still have to normalize?
Normalizing data often improves the model because it amounts to pre-conditioning the inputs so that optimization proceeds more smoothly.
Which activation function shoul... | Deep Learning : Using dropout in Autoencoders? | Should i normalize my numerical data values before feeding to any type of autoencoder? If they are int and float values do I still have to normalize?
Normalizing data often improves the model because | Deep Learning : Using dropout in Autoencoders?
Should i normalize my numerical data values before feeding to any type of autoencoder? If they are int and float values do I still have to normalize?
Normalizing data often improves the model because it amounts to pre-conditioning the inputs so that optimization proceeds ... | Deep Learning : Using dropout in Autoencoders?
Should i normalize my numerical data values before feeding to any type of autoencoder? If they are int and float values do I still have to normalize?
Normalizing data often improves the model because |
41,459 | What is the reason for not including an intercept term in AR and ARMA models? | ARMA models can easily be formulated with an intercept term, and these are in common use. For example an AR($1$) model with an intercept term can be written as:
$$\begin{equation} \begin{aligned}
X_t
&= \mu + \phi (X_{t-1} - \mu) + \varepsilon_t \\[6pt]
&= (1-\phi) \mu + \phi X_{t-1} + \varepsilon_t.
\end{aligned} \e... | What is the reason for not including an intercept term in AR and ARMA models? | ARMA models can easily be formulated with an intercept term, and these are in common use. For example an AR($1$) model with an intercept term can be written as:
$$\begin{equation} \begin{aligned}
X_t | What is the reason for not including an intercept term in AR and ARMA models?
ARMA models can easily be formulated with an intercept term, and these are in common use. For example an AR($1$) model with an intercept term can be written as:
$$\begin{equation} \begin{aligned}
X_t
&= \mu + \phi (X_{t-1} - \mu) + \varepsi... | What is the reason for not including an intercept term in AR and ARMA models?
ARMA models can easily be formulated with an intercept term, and these are in common use. For example an AR($1$) model with an intercept term can be written as:
$$\begin{equation} \begin{aligned}
X_t |
41,460 | What is the reason for not including an intercept term in AR and ARMA models? | To begin with in arima models the constant is mandatory if d=0 i.e.no differencing is in play. If d<>=0 then the constant is optional. If d<>=0 and a constant is in the model there is a steady state constant reflecting a "slope" or growth reflecting growth as compared to deterministic growth via time/counting numbers r... | What is the reason for not including an intercept term in AR and ARMA models? | To begin with in arima models the constant is mandatory if d=0 i.e.no differencing is in play. If d<>=0 then the constant is optional. If d<>=0 and a constant is in the model there is a steady state c | What is the reason for not including an intercept term in AR and ARMA models?
To begin with in arima models the constant is mandatory if d=0 i.e.no differencing is in play. If d<>=0 then the constant is optional. If d<>=0 and a constant is in the model there is a steady state constant reflecting a "slope" or growth ref... | What is the reason for not including an intercept term in AR and ARMA models?
To begin with in arima models the constant is mandatory if d=0 i.e.no differencing is in play. If d<>=0 then the constant is optional. If d<>=0 and a constant is in the model there is a steady state c |
41,461 | How are models combined in locally weighted linear regression? | What you are doing sounds like filtering or smoothening data. It resembles something like
Savitzky–Golay filtering
kernel smoothening
LOcally WEighted/Estimated Scatterplot Smoothening (LOESS/LOWESS)
for which there are many great resources.
If you do something like such smoothening or filtering then you do the algo... | How are models combined in locally weighted linear regression? | What you are doing sounds like filtering or smoothening data. It resembles something like
Savitzky–Golay filtering
kernel smoothening
LOcally WEighted/Estimated Scatterplot Smoothening (LOESS/LOWESS) | How are models combined in locally weighted linear regression?
What you are doing sounds like filtering or smoothening data. It resembles something like
Savitzky–Golay filtering
kernel smoothening
LOcally WEighted/Estimated Scatterplot Smoothening (LOESS/LOWESS)
for which there are many great resources.
If you do so... | How are models combined in locally weighted linear regression?
What you are doing sounds like filtering or smoothening data. It resembles something like
Savitzky–Golay filtering
kernel smoothening
LOcally WEighted/Estimated Scatterplot Smoothening (LOESS/LOWESS) |
41,462 | How are models combined in locally weighted linear regression? | Martijn Weterings posts a valid answer to this question, but I am going to add a bit more to this. With respect to the pseudo-algorithm written in the question, it isn't quite complete. It should be like this:
models = []
for instance in X:
Set current instance as the query point
Compute weights for all instanc... | How are models combined in locally weighted linear regression? | Martijn Weterings posts a valid answer to this question, but I am going to add a bit more to this. With respect to the pseudo-algorithm written in the question, it isn't quite complete. It should be l | How are models combined in locally weighted linear regression?
Martijn Weterings posts a valid answer to this question, but I am going to add a bit more to this. With respect to the pseudo-algorithm written in the question, it isn't quite complete. It should be like this:
models = []
for instance in X:
Set current ... | How are models combined in locally weighted linear regression?
Martijn Weterings posts a valid answer to this question, but I am going to add a bit more to this. With respect to the pseudo-algorithm written in the question, it isn't quite complete. It should be l |
41,463 | How are models combined in locally weighted linear regression? | As I am also working on the same problem as you (CS229!) I have been looking into implementing locally weighted regression in python. The following implementation is heavily based on the version provided by Alexandre Gramfort, an Sklearn developper, on his github page, but uses a bell shaped kernel as you have describe... | How are models combined in locally weighted linear regression? | As I am also working on the same problem as you (CS229!) I have been looking into implementing locally weighted regression in python. The following implementation is heavily based on the version provi | How are models combined in locally weighted linear regression?
As I am also working on the same problem as you (CS229!) I have been looking into implementing locally weighted regression in python. The following implementation is heavily based on the version provided by Alexandre Gramfort, an Sklearn developper, on his ... | How are models combined in locally weighted linear regression?
As I am also working on the same problem as you (CS229!) I have been looking into implementing locally weighted regression in python. The following implementation is heavily based on the version provi |
41,464 | Are maximum likelihood estimator robust estimators? | By the definition of robust estimators, this is true. That is, M-estimators are a type of robust statistics, and MLE's are a special case of M-estimators.
However, it's definitely not the case that MLE's in general have good robustness properties. | Are maximum likelihood estimator robust estimators? | By the definition of robust estimators, this is true. That is, M-estimators are a type of robust statistics, and MLE's are a special case of M-estimators.
However, it's definitely not the case that M | Are maximum likelihood estimator robust estimators?
By the definition of robust estimators, this is true. That is, M-estimators are a type of robust statistics, and MLE's are a special case of M-estimators.
However, it's definitely not the case that MLE's in general have good robustness properties. | Are maximum likelihood estimator robust estimators?
By the definition of robust estimators, this is true. That is, M-estimators are a type of robust statistics, and MLE's are a special case of M-estimators.
However, it's definitely not the case that M |
41,465 | Are maximum likelihood estimator robust estimators? | One way to look at it is that there is no strict distinction between robust and non-robust estimators, but rather they can be compared according to their robustness properties (as already pointed in the answer by @CliffAB.) Thus, M-estimators can be viewed as explicitly designed to resemble the maximum likelihood estim... | Are maximum likelihood estimator robust estimators? | One way to look at it is that there is no strict distinction between robust and non-robust estimators, but rather they can be compared according to their robustness properties (as already pointed in t | Are maximum likelihood estimator robust estimators?
One way to look at it is that there is no strict distinction between robust and non-robust estimators, but rather they can be compared according to their robustness properties (as already pointed in the answer by @CliffAB.) Thus, M-estimators can be viewed as explicit... | Are maximum likelihood estimator robust estimators?
One way to look at it is that there is no strict distinction between robust and non-robust estimators, but rather they can be compared according to their robustness properties (as already pointed in t |
41,466 | Propensity Score Matching implementation after multiple imputation | Update 1/4/20: A new package has been written for this purpose called MatchThem. It's on CRAN, and an article about how to use it is under review. It's compatible with version 4.0.0 of cobalt for balance checking. It has built-in functions for performing matching and estimating treatment effects from multiply imputed d... | Propensity Score Matching implementation after multiple imputation | Update 1/4/20: A new package has been written for this purpose called MatchThem. It's on CRAN, and an article about how to use it is under review. It's compatible with version 4.0.0 of cobalt for bala | Propensity Score Matching implementation after multiple imputation
Update 1/4/20: A new package has been written for this purpose called MatchThem. It's on CRAN, and an article about how to use it is under review. It's compatible with version 4.0.0 of cobalt for balance checking. It has built-in functions for performin... | Propensity Score Matching implementation after multiple imputation
Update 1/4/20: A new package has been written for this purpose called MatchThem. It's on CRAN, and an article about how to use it is under review. It's compatible with version 4.0.0 of cobalt for bala |
41,467 | Why do we care about Quasi-norm in Statistics and Machine Learning? | One common area where quasinorms are used involves dimension reduction and sparsity.
Consider Lasso, where the standard OLS problem is augmented by a penalty, or cost term:.
$$\min_{\beta}\dfrac{1}{N}\|Y-X\beta\|_2 \quad s.t. \|\beta\|_1\leq t$$
where $\|\cdot\|_p$ is the standard $L_p$ norm.
Why are we doing this aga... | Why do we care about Quasi-norm in Statistics and Machine Learning? | One common area where quasinorms are used involves dimension reduction and sparsity.
Consider Lasso, where the standard OLS problem is augmented by a penalty, or cost term:.
$$\min_{\beta}\dfrac{1}{N | Why do we care about Quasi-norm in Statistics and Machine Learning?
One common area where quasinorms are used involves dimension reduction and sparsity.
Consider Lasso, where the standard OLS problem is augmented by a penalty, or cost term:.
$$\min_{\beta}\dfrac{1}{N}\|Y-X\beta\|_2 \quad s.t. \|\beta\|_1\leq t$$
where... | Why do we care about Quasi-norm in Statistics and Machine Learning?
One common area where quasinorms are used involves dimension reduction and sparsity.
Consider Lasso, where the standard OLS problem is augmented by a penalty, or cost term:.
$$\min_{\beta}\dfrac{1}{N |
41,468 | Why is F-measure more popular than accuracy? | $F_1$ works better when you care most for classification of rare positives. $F_\beta$ is just a weighted harmonic mean of two positive focused measures, i.e. precision and recall. When $\beta=1$ precision and recall are equally weighted in $F_1$, which is used most in practice. When positive incidence rate is low in th... | Why is F-measure more popular than accuracy? | $F_1$ works better when you care most for classification of rare positives. $F_\beta$ is just a weighted harmonic mean of two positive focused measures, i.e. precision and recall. When $\beta=1$ preci | Why is F-measure more popular than accuracy?
$F_1$ works better when you care most for classification of rare positives. $F_\beta$ is just a weighted harmonic mean of two positive focused measures, i.e. precision and recall. When $\beta=1$ precision and recall are equally weighted in $F_1$, which is used most in practi... | Why is F-measure more popular than accuracy?
$F_1$ works better when you care most for classification of rare positives. $F_\beta$ is just a weighted harmonic mean of two positive focused measures, i.e. precision and recall. When $\beta=1$ preci |
41,469 | How to understand RandomForestExplainer output (R package) | At each node, a subset of the full set of predictors is evaluated for their strength of association with the dependent variable. The strength of association may be measured using a correlation coefficient, or some other metric (necessary if there are both categorical or continuous predictors). The most strongly associa... | How to understand RandomForestExplainer output (R package) | At each node, a subset of the full set of predictors is evaluated for their strength of association with the dependent variable. The strength of association may be measured using a correlation coeffic | How to understand RandomForestExplainer output (R package)
At each node, a subset of the full set of predictors is evaluated for their strength of association with the dependent variable. The strength of association may be measured using a correlation coefficient, or some other metric (necessary if there are both categ... | How to understand RandomForestExplainer output (R package)
At each node, a subset of the full set of predictors is evaluated for their strength of association with the dependent variable. The strength of association may be measured using a correlation coeffic |
41,470 | Is Monte Carlo cross-validation procedure valid? | Short answer: it is neither wrong nor new.
We've been discussing this validation scheme under the name "set validation" ≈ 15 a ago when preparing a paper*, but in the end never actually referred to it as we didn't find it used in practice.
Wikipedia refers to the same validation scheme as repeated random sub-sampli... | Is Monte Carlo cross-validation procedure valid? | Short answer: it is neither wrong nor new.
We've been discussing this validation scheme under the name "set validation" ≈ 15 a ago when preparing a paper*, but in the end never actually referred to | Is Monte Carlo cross-validation procedure valid?
Short answer: it is neither wrong nor new.
We've been discussing this validation scheme under the name "set validation" ≈ 15 a ago when preparing a paper*, but in the end never actually referred to it as we didn't find it used in practice.
Wikipedia refers to the sam... | Is Monte Carlo cross-validation procedure valid?
Short answer: it is neither wrong nor new.
We've been discussing this validation scheme under the name "set validation" ≈ 15 a ago when preparing a paper*, but in the end never actually referred to |
41,471 | In a Bayesian hierarchical model, if exchangeability doesn't hold, what exactly goes wrong? | Exchangeability is not necessary. There are Bayesian models in which observations are not exchangeable. For example, models for time-series analysis and forecast in weather prediction or finance. Generally speaking, in such models more recent observations are considered to be more relevant for inference about future on... | In a Bayesian hierarchical model, if exchangeability doesn't hold, what exactly goes wrong? | Exchangeability is not necessary. There are Bayesian models in which observations are not exchangeable. For example, models for time-series analysis and forecast in weather prediction or finance. Gene | In a Bayesian hierarchical model, if exchangeability doesn't hold, what exactly goes wrong?
Exchangeability is not necessary. There are Bayesian models in which observations are not exchangeable. For example, models for time-series analysis and forecast in weather prediction or finance. Generally speaking, in such mode... | In a Bayesian hierarchical model, if exchangeability doesn't hold, what exactly goes wrong?
Exchangeability is not necessary. There are Bayesian models in which observations are not exchangeable. For example, models for time-series analysis and forecast in weather prediction or finance. Gene |
41,472 | In a Bayesian hierarchical model, if exchangeability doesn't hold, what exactly goes wrong? | From the representation theorem, we know that exchangeability is essentially just an operational condition that is equivalent to the conditional IID form (which implies equicorrelation among the observable values). If this doesn't hold, it just means that there is some structure to the problem that is incompatible wit... | In a Bayesian hierarchical model, if exchangeability doesn't hold, what exactly goes wrong? | From the representation theorem, we know that exchangeability is essentially just an operational condition that is equivalent to the conditional IID form (which implies equicorrelation among the obser | In a Bayesian hierarchical model, if exchangeability doesn't hold, what exactly goes wrong?
From the representation theorem, we know that exchangeability is essentially just an operational condition that is equivalent to the conditional IID form (which implies equicorrelation among the observable values). If this does... | In a Bayesian hierarchical model, if exchangeability doesn't hold, what exactly goes wrong?
From the representation theorem, we know that exchangeability is essentially just an operational condition that is equivalent to the conditional IID form (which implies equicorrelation among the obser |
41,473 | How is PCA applied to new data? | I will answer each question:
$A$ is indeed the covariance matrix (so $X^TX$ assuming $X$ is standardized)
The output of PCA is 3 things: the vector of column means $\mu$ of $X$, the vector of column stddevs $\sigma$ of $X$ and the rotation matrix $R = [v_1 ... v_p]$. Therefore, for a new sample row $x_0^T$, to compute... | How is PCA applied to new data? | I will answer each question:
$A$ is indeed the covariance matrix (so $X^TX$ assuming $X$ is standardized)
The output of PCA is 3 things: the vector of column means $\mu$ of $X$, the vector of column | How is PCA applied to new data?
I will answer each question:
$A$ is indeed the covariance matrix (so $X^TX$ assuming $X$ is standardized)
The output of PCA is 3 things: the vector of column means $\mu$ of $X$, the vector of column stddevs $\sigma$ of $X$ and the rotation matrix $R = [v_1 ... v_p]$. Therefore, for a ne... | How is PCA applied to new data?
I will answer each question:
$A$ is indeed the covariance matrix (so $X^TX$ assuming $X$ is standardized)
The output of PCA is 3 things: the vector of column means $\mu$ of $X$, the vector of column |
41,474 | Lower Bound on $E[\frac{1}{X}]$ for positive symmetric distribution | Let's try the usual preliminaries: simplify by choosing appropriate units of measurement and exploiting the symmetry assumption.
Reframing the question
Change the units of $X$ so that its mean is $m=1$: this will not alter the truth of the inequality. Thus the distribution $F$ of $X$ is symmetric about $1$ and the ran... | Lower Bound on $E[\frac{1}{X}]$ for positive symmetric distribution | Let's try the usual preliminaries: simplify by choosing appropriate units of measurement and exploiting the symmetry assumption.
Reframing the question
Change the units of $X$ so that its mean is $m=1 | Lower Bound on $E[\frac{1}{X}]$ for positive symmetric distribution
Let's try the usual preliminaries: simplify by choosing appropriate units of measurement and exploiting the symmetry assumption.
Reframing the question
Change the units of $X$ so that its mean is $m=1$: this will not alter the truth of the inequality. ... | Lower Bound on $E[\frac{1}{X}]$ for positive symmetric distribution
Let's try the usual preliminaries: simplify by choosing appropriate units of measurement and exploiting the symmetry assumption.
Reframing the question
Change the units of $X$ so that its mean is $m=1 |
41,475 | In reinforcement learning, what is the formal definition of the symbols $S_t$ and $A_t$? | In the summary of notation (page xvi) of Sutton and Barto's book, they define $S_t$ as:
state at time $t$, typically due, stochastically, to $S_{t-1}$ and $A_{t-1}$
This is similar to what you observed:
However, what confuses me is that in order to properly define $S_t$ for $t>0$ it seems necessary to first define a... | In reinforcement learning, what is the formal definition of the symbols $S_t$ and $A_t$? | In the summary of notation (page xvi) of Sutton and Barto's book, they define $S_t$ as:
state at time $t$, typically due, stochastically, to $S_{t-1}$ and $A_{t-1}$
This is similar to what you obser | In reinforcement learning, what is the formal definition of the symbols $S_t$ and $A_t$?
In the summary of notation (page xvi) of Sutton and Barto's book, they define $S_t$ as:
state at time $t$, typically due, stochastically, to $S_{t-1}$ and $A_{t-1}$
This is similar to what you observed:
However, what confuses me... | In reinforcement learning, what is the formal definition of the symbols $S_t$ and $A_t$?
In the summary of notation (page xvi) of Sutton and Barto's book, they define $S_t$ as:
state at time $t$, typically due, stochastically, to $S_{t-1}$ and $A_{t-1}$
This is similar to what you obser |
41,476 | In reinforcement learning, what is the formal definition of the symbols $S_t$ and $A_t$? | I came up with one possible interpretation of these symbols that seem to be consistent with all the material I've seen so far in these courses.
As pointed out in Dennis Soemers' answer, Sutton's book define $S_t$ as:
state at time $t$, typically due, stochastically, to $S_{t−1}$ and $A_{t−1}$
The "typically due" led ... | In reinforcement learning, what is the formal definition of the symbols $S_t$ and $A_t$? | I came up with one possible interpretation of these symbols that seem to be consistent with all the material I've seen so far in these courses.
As pointed out in Dennis Soemers' answer, Sutton's book | In reinforcement learning, what is the formal definition of the symbols $S_t$ and $A_t$?
I came up with one possible interpretation of these symbols that seem to be consistent with all the material I've seen so far in these courses.
As pointed out in Dennis Soemers' answer, Sutton's book define $S_t$ as:
state at time... | In reinforcement learning, what is the formal definition of the symbols $S_t$ and $A_t$?
I came up with one possible interpretation of these symbols that seem to be consistent with all the material I've seen so far in these courses.
As pointed out in Dennis Soemers' answer, Sutton's book |
41,477 | In reinforcement learning, what is the formal definition of the symbols $S_t$ and $A_t$? | I am scratching my head about this as well... In principal what follows is more of a comment than an answer. Everything I say is just guessing because I have neither read a formal description yet.
I think that most applied statisticians have a very deep understanding what they are doing but the do not allow the rest of... | In reinforcement learning, what is the formal definition of the symbols $S_t$ and $A_t$? | I am scratching my head about this as well... In principal what follows is more of a comment than an answer. Everything I say is just guessing because I have neither read a formal description yet.
I t | In reinforcement learning, what is the formal definition of the symbols $S_t$ and $A_t$?
I am scratching my head about this as well... In principal what follows is more of a comment than an answer. Everything I say is just guessing because I have neither read a formal description yet.
I think that most applied statisti... | In reinforcement learning, what is the formal definition of the symbols $S_t$ and $A_t$?
I am scratching my head about this as well... In principal what follows is more of a comment than an answer. Everything I say is just guessing because I have neither read a formal description yet.
I t |
41,478 | Best approach for count prediction in time-series? | You have intermittent-time-series, i.e., your time series are integer-valued, nonnegative and "mostly" zero. You may want to search for "forecasting intermittent time series" or similar.
The classical approach for point forecasts in such a case is crostons-method. One alternative is a Poisson or Negative Binomial regre... | Best approach for count prediction in time-series? | You have intermittent-time-series, i.e., your time series are integer-valued, nonnegative and "mostly" zero. You may want to search for "forecasting intermittent time series" or similar.
The classical | Best approach for count prediction in time-series?
You have intermittent-time-series, i.e., your time series are integer-valued, nonnegative and "mostly" zero. You may want to search for "forecasting intermittent time series" or similar.
The classical approach for point forecasts in such a case is crostons-method. One ... | Best approach for count prediction in time-series?
You have intermittent-time-series, i.e., your time series are integer-valued, nonnegative and "mostly" zero. You may want to search for "forecasting intermittent time series" or similar.
The classical |
41,479 | Mathematical Machine Learning Theory "from scratch" textbook? | Per @Coffee's recommendation, I would recommend the text Machine Learning: A Bayesian and Optimization Perspective by Sergios Theodoridis along with Pattern Recognition by the same author.
These two texts combined are 2,000 pages total and cover everything from undergrad-level probability to linear models, and (as far... | Mathematical Machine Learning Theory "from scratch" textbook? | Per @Coffee's recommendation, I would recommend the text Machine Learning: A Bayesian and Optimization Perspective by Sergios Theodoridis along with Pattern Recognition by the same author.
These two | Mathematical Machine Learning Theory "from scratch" textbook?
Per @Coffee's recommendation, I would recommend the text Machine Learning: A Bayesian and Optimization Perspective by Sergios Theodoridis along with Pattern Recognition by the same author.
These two texts combined are 2,000 pages total and cover everything ... | Mathematical Machine Learning Theory "from scratch" textbook?
Per @Coffee's recommendation, I would recommend the text Machine Learning: A Bayesian and Optimization Perspective by Sergios Theodoridis along with Pattern Recognition by the same author.
These two |
41,480 | Q-learning vs. Value Iteration | I don't see anything in its update equation as to why it requires knowledge of rewards before hand and why it cannot be trained in an online way in the same way that Q-learning can?
The usual Value Iteration update rule is:
$$v(s) \leftarrow \text{max}_a[\sum_{r,s'} p(r, s'|s,a)(r + \gamma v(s')]$$
or it might be wri... | Q-learning vs. Value Iteration | I don't see anything in its update equation as to why it requires knowledge of rewards before hand and why it cannot be trained in an online way in the same way that Q-learning can?
The usual Value | Q-learning vs. Value Iteration
I don't see anything in its update equation as to why it requires knowledge of rewards before hand and why it cannot be trained in an online way in the same way that Q-learning can?
The usual Value Iteration update rule is:
$$v(s) \leftarrow \text{max}_a[\sum_{r,s'} p(r, s'|s,a)(r + \ga... | Q-learning vs. Value Iteration
I don't see anything in its update equation as to why it requires knowledge of rewards before hand and why it cannot be trained in an online way in the same way that Q-learning can?
The usual Value |
41,481 | Sampling distribution of sample variance of non-normal iid r.v.s | The asymptotic distribution for the sample variance (in the general non-normal case) can be found in O'Neill (2014) (Result 14, p. 285). As others have pointed out in the comments to your question, the more general result can be obtained via a combination of the CLT and Slutsky's theorem, working on an expansion for t... | Sampling distribution of sample variance of non-normal iid r.v.s | The asymptotic distribution for the sample variance (in the general non-normal case) can be found in O'Neill (2014) (Result 14, p. 285). As others have pointed out in the comments to your question, t | Sampling distribution of sample variance of non-normal iid r.v.s
The asymptotic distribution for the sample variance (in the general non-normal case) can be found in O'Neill (2014) (Result 14, p. 285). As others have pointed out in the comments to your question, the more general result can be obtained via a combinatio... | Sampling distribution of sample variance of non-normal iid r.v.s
The asymptotic distribution for the sample variance (in the general non-normal case) can be found in O'Neill (2014) (Result 14, p. 285). As others have pointed out in the comments to your question, t |
41,482 | Deep NNs, backpropagation and error calculation | "When we apply the transpose weight matrix, $(w^{l+1})^T$, we can think intuitively of this as moving the error backward through the network"
Is that the sentence you're confused about? Note that in this sentence he's not trying to provide intuition for ''applying the transpose operator'', he's trying to provide intuit... | Deep NNs, backpropagation and error calculation | "When we apply the transpose weight matrix, $(w^{l+1})^T$, we can think intuitively of this as moving the error backward through the network"
Is that the sentence you're confused about? Note that in t | Deep NNs, backpropagation and error calculation
"When we apply the transpose weight matrix, $(w^{l+1})^T$, we can think intuitively of this as moving the error backward through the network"
Is that the sentence you're confused about? Note that in this sentence he's not trying to provide intuition for ''applying the tra... | Deep NNs, backpropagation and error calculation
"When we apply the transpose weight matrix, $(w^{l+1})^T$, we can think intuitively of this as moving the error backward through the network"
Is that the sentence you're confused about? Note that in t |
41,483 | Generate a Gaussian and a binary random variables with predefined correlation | To generate such a pair $(B,Y)$ with $B$ Bernoulli (with parameter $p$) and $Y$ normal, why not begin with a suitable binormal variable $(X,Y)$ and define $B$ to be the indicator that $X$ exceeds its $1-p$ quantile? By centering $(X,Y)$ at the origin and standardizing its marginals, the only question concerns what cor... | Generate a Gaussian and a binary random variables with predefined correlation | To generate such a pair $(B,Y)$ with $B$ Bernoulli (with parameter $p$) and $Y$ normal, why not begin with a suitable binormal variable $(X,Y)$ and define $B$ to be the indicator that $X$ exceeds its | Generate a Gaussian and a binary random variables with predefined correlation
To generate such a pair $(B,Y)$ with $B$ Bernoulli (with parameter $p$) and $Y$ normal, why not begin with a suitable binormal variable $(X,Y)$ and define $B$ to be the indicator that $X$ exceeds its $1-p$ quantile? By centering $(X,Y)$ at t... | Generate a Gaussian and a binary random variables with predefined correlation
To generate such a pair $(B,Y)$ with $B$ Bernoulli (with parameter $p$) and $Y$ normal, why not begin with a suitable binormal variable $(X,Y)$ and define $B$ to be the indicator that $X$ exceeds its |
41,484 | Bayesian network vs. association rules | This question is similar to the question: what's the difference between parametric vs. non-parametric models.
Bayesian network can be viewed as parametric model. Where we have explicit assumptions on the random variables, and dependencies among random variables (assuming we only do parameter learning no structure lear... | Bayesian network vs. association rules | This question is similar to the question: what's the difference between parametric vs. non-parametric models.
Bayesian network can be viewed as parametric model. Where we have explicit assumptions on | Bayesian network vs. association rules
This question is similar to the question: what's the difference between parametric vs. non-parametric models.
Bayesian network can be viewed as parametric model. Where we have explicit assumptions on the random variables, and dependencies among random variables (assuming we only ... | Bayesian network vs. association rules
This question is similar to the question: what's the difference between parametric vs. non-parametric models.
Bayesian network can be viewed as parametric model. Where we have explicit assumptions on |
41,485 | Likelihood in Linear Regression | The key assumption to derive $f_{Y_i|X_i}$ is that the noise is independent from the input, that is $\epsilon_i$ is independent from $X_i$. You don't need to know or assume anything about the distribution of $X_i$.
You start with:
$$f_{Y_i|X_i}(x,y)=p(Y_i=y|X_i=x)=p(\beta_0x+\epsilon_i=y|X_i=x)=p(\epsilon_i=y-\beta_0x|... | Likelihood in Linear Regression | The key assumption to derive $f_{Y_i|X_i}$ is that the noise is independent from the input, that is $\epsilon_i$ is independent from $X_i$. You don't need to know or assume anything about the distribu | Likelihood in Linear Regression
The key assumption to derive $f_{Y_i|X_i}$ is that the noise is independent from the input, that is $\epsilon_i$ is independent from $X_i$. You don't need to know or assume anything about the distribution of $X_i$.
You start with:
$$f_{Y_i|X_i}(x,y)=p(Y_i=y|X_i=x)=p(\beta_0x+\epsilon_i=y... | Likelihood in Linear Regression
The key assumption to derive $f_{Y_i|X_i}$ is that the noise is independent from the input, that is $\epsilon_i$ is independent from $X_i$. You don't need to know or assume anything about the distribu |
41,486 | Likelihood in Linear Regression | Thanks to the answer of Benoit Sanchez I finally understood (but got hooked up on the wrong path of a replacement rule for conditional densities). The Answer is as follows:
One needs to assume that
The pairs $(x_i, y_i)$ come from random variables $(X_i, Y_i)$ such that the variables $Z_i = (X_i, Y_i)$ are independent... | Likelihood in Linear Regression | Thanks to the answer of Benoit Sanchez I finally understood (but got hooked up on the wrong path of a replacement rule for conditional densities). The Answer is as follows:
One needs to assume that
T | Likelihood in Linear Regression
Thanks to the answer of Benoit Sanchez I finally understood (but got hooked up on the wrong path of a replacement rule for conditional densities). The Answer is as follows:
One needs to assume that
The pairs $(x_i, y_i)$ come from random variables $(X_i, Y_i)$ such that the variables $Z... | Likelihood in Linear Regression
Thanks to the answer of Benoit Sanchez I finally understood (but got hooked up on the wrong path of a replacement rule for conditional densities). The Answer is as follows:
One needs to assume that
T |
41,487 | Why is softmax regression often written without the bias term? | If you use matrix notation, then
$$
\beta_0 + \beta_1 X_1 + \dots +\beta_k X_k
$$
can be defined in terms of design matrix that already contains a column of ones for the intercept
$$
\mathbf{X} =
\left[ \begin{array}{cccc}
1 & x_{1,1} & \dots & x_{1,k} \\
1 & x_{2,1} & \dots & x_{2,k} \\
\vdots & \vdots & \ddots & \v... | Why is softmax regression often written without the bias term? | If you use matrix notation, then
$$
\beta_0 + \beta_1 X_1 + \dots +\beta_k X_k
$$
can be defined in terms of design matrix that already contains a column of ones for the intercept
$$
\mathbf{X} =
\l | Why is softmax regression often written without the bias term?
If you use matrix notation, then
$$
\beta_0 + \beta_1 X_1 + \dots +\beta_k X_k
$$
can be defined in terms of design matrix that already contains a column of ones for the intercept
$$
\mathbf{X} =
\left[ \begin{array}{cccc}
1 & x_{1,1} & \dots & x_{1,k} \\... | Why is softmax regression often written without the bias term?
If you use matrix notation, then
$$
\beta_0 + \beta_1 X_1 + \dots +\beta_k X_k
$$
can be defined in terms of design matrix that already contains a column of ones for the intercept
$$
\mathbf{X} =
\l |
41,488 | Importance of choice of latent distribution in GAN's | A sufficiently powerful function approximator can map any probability distribution to any other probability distribution. In practice, this means that any for reasonable choice of latent distribution, you can train a generator to map that to the distribution of images in your dataset.
So it doesn't make any fundamental... | Importance of choice of latent distribution in GAN's | A sufficiently powerful function approximator can map any probability distribution to any other probability distribution. In practice, this means that any for reasonable choice of latent distribution, | Importance of choice of latent distribution in GAN's
A sufficiently powerful function approximator can map any probability distribution to any other probability distribution. In practice, this means that any for reasonable choice of latent distribution, you can train a generator to map that to the distribution of image... | Importance of choice of latent distribution in GAN's
A sufficiently powerful function approximator can map any probability distribution to any other probability distribution. In practice, this means that any for reasonable choice of latent distribution, |
41,489 | Importance of choice of latent distribution in GAN's | I partially disagree with what @shimano said
The variability of the samples generated which you mentioned in your question isn't really a function of the latent distribution
The sampling space is very crucial for the GANs results. For instance, sampling $z\sim\mathbb{N}(\mu, \sigma)$ where $\sigma=1$ or $\sigma=10$ ... | Importance of choice of latent distribution in GAN's | I partially disagree with what @shimano said
The variability of the samples generated which you mentioned in your question isn't really a function of the latent distribution
The sampling space is v | Importance of choice of latent distribution in GAN's
I partially disagree with what @shimano said
The variability of the samples generated which you mentioned in your question isn't really a function of the latent distribution
The sampling space is very crucial for the GANs results. For instance, sampling $z\sim\mat... | Importance of choice of latent distribution in GAN's
I partially disagree with what @shimano said
The variability of the samples generated which you mentioned in your question isn't really a function of the latent distribution
The sampling space is v |
41,490 | How to find the smallest $\lambda$ such that all Lasso / Elastic Net coefficients are zero? | A lasso solution $\widehat{\beta}(\lambda)$ solves
$$\min_\beta \frac{1}{2}||y-X\beta||_2^2 +\lambda||\beta||_1.$$
and it is well known that we have $\widehat{\beta}(\lambda)=0$ for all $\lambda \geq \lambda_1$ where $\lambda_1 = \max_j |X_j^Ty|$, which should give you the desired value.
Note that $\lambda_1$ may n... | How to find the smallest $\lambda$ such that all Lasso / Elastic Net coefficients are zero? | A lasso solution $\widehat{\beta}(\lambda)$ solves
$$\min_\beta \frac{1}{2}||y-X\beta||_2^2 +\lambda||\beta||_1.$$
and it is well known that we have $\widehat{\beta}(\lambda)=0$ for all $\lambda \g | How to find the smallest $\lambda$ such that all Lasso / Elastic Net coefficients are zero?
A lasso solution $\widehat{\beta}(\lambda)$ solves
$$\min_\beta \frac{1}{2}||y-X\beta||_2^2 +\lambda||\beta||_1.$$
and it is well known that we have $\widehat{\beta}(\lambda)=0$ for all $\lambda \geq \lambda_1$ where $\lambda... | How to find the smallest $\lambda$ such that all Lasso / Elastic Net coefficients are zero?
A lasso solution $\widehat{\beta}(\lambda)$ solves
$$\min_\beta \frac{1}{2}||y-X\beta||_2^2 +\lambda||\beta||_1.$$
and it is well known that we have $\widehat{\beta}(\lambda)=0$ for all $\lambda \g |
41,491 | How to find the smallest $\lambda$ such that all Lasso / Elastic Net coefficients are zero? | First, I think glmnet will start with a large $\lambda$ instead of a small $\lambda$. Here is the documentation: note, if we want to specify $\lambda$, it is better in decreasing order.
Typical usage is to have the program compute its own lambda sequence based on nlambda and lambda.min.ratio. Supplying a value of lam... | How to find the smallest $\lambda$ such that all Lasso / Elastic Net coefficients are zero? | First, I think glmnet will start with a large $\lambda$ instead of a small $\lambda$. Here is the documentation: note, if we want to specify $\lambda$, it is better in decreasing order.
Typical usag | How to find the smallest $\lambda$ such that all Lasso / Elastic Net coefficients are zero?
First, I think glmnet will start with a large $\lambda$ instead of a small $\lambda$. Here is the documentation: note, if we want to specify $\lambda$, it is better in decreasing order.
Typical usage is to have the program com... | How to find the smallest $\lambda$ such that all Lasso / Elastic Net coefficients are zero?
First, I think glmnet will start with a large $\lambda$ instead of a small $\lambda$. Here is the documentation: note, if we want to specify $\lambda$, it is better in decreasing order.
Typical usag |
41,492 | Poisson GLMM vs GLM in R (lme4) | There is probably something wrong with the question. The deviance for fit1 can be computed with
deviance(fit1)
# same as
sum(resid(fit1)^2)
But for the GLMM, the lme4 packages uses another method documented in ?llikAIC, which gives 1128 - higher than for the GLM.
Perhaps the question actually wants to test for the ... | Poisson GLMM vs GLM in R (lme4) | There is probably something wrong with the question. The deviance for fit1 can be computed with
deviance(fit1)
# same as
sum(resid(fit1)^2)
But for the GLMM, the lme4 packages uses another method | Poisson GLMM vs GLM in R (lme4)
There is probably something wrong with the question. The deviance for fit1 can be computed with
deviance(fit1)
# same as
sum(resid(fit1)^2)
But for the GLMM, the lme4 packages uses another method documented in ?llikAIC, which gives 1128 - higher than for the GLM.
Perhaps the question... | Poisson GLMM vs GLM in R (lme4)
There is probably something wrong with the question. The deviance for fit1 can be computed with
deviance(fit1)
# same as
sum(resid(fit1)^2)
But for the GLMM, the lme4 packages uses another method |
41,493 | Poisson GLMM vs GLM in R (lme4) | This is a tricky exercise. Let's break it down in two parts.
Specify a Poisson GLMM for the 1990 General Society Survey data. 1308 subjects responded to the question: Within the past 12 months, how many people have you known personally that were victims of homicide? The responses are broken down by race ("white" and "... | Poisson GLMM vs GLM in R (lme4) | This is a tricky exercise. Let's break it down in two parts.
Specify a Poisson GLMM for the 1990 General Society Survey data. 1308 subjects responded to the question: Within the past 12 months, how m | Poisson GLMM vs GLM in R (lme4)
This is a tricky exercise. Let's break it down in two parts.
Specify a Poisson GLMM for the 1990 General Society Survey data. 1308 subjects responded to the question: Within the past 12 months, how many people have you known personally that were victims of homicide? The responses are br... | Poisson GLMM vs GLM in R (lme4)
This is a tricky exercise. Let's break it down in two parts.
Specify a Poisson GLMM for the 1990 General Society Survey data. 1308 subjects responded to the question: Within the past 12 months, how m |
41,494 | How is the decision boundary's equation determined? | You need one additional piece of information to determine a decision boundary: a level to threshold the probabilities. Given a threshold $T$, we make positive decisions when
$$ g(\theta_0 + \theta_1 x_1 + \theta_2 x_2 + \theta_3 x_1^2 + \theta_4 x_2^2) \geq T $$
and negative decisions when
$$ g(\theta_0 + \theta_1 x_1... | How is the decision boundary's equation determined? | You need one additional piece of information to determine a decision boundary: a level to threshold the probabilities. Given a threshold $T$, we make positive decisions when
$$ g(\theta_0 + \theta_1 | How is the decision boundary's equation determined?
You need one additional piece of information to determine a decision boundary: a level to threshold the probabilities. Given a threshold $T$, we make positive decisions when
$$ g(\theta_0 + \theta_1 x_1 + \theta_2 x_2 + \theta_3 x_1^2 + \theta_4 x_2^2) \geq T $$
and ... | How is the decision boundary's equation determined?
You need one additional piece of information to determine a decision boundary: a level to threshold the probabilities. Given a threshold $T$, we make positive decisions when
$$ g(\theta_0 + \theta_1 |
41,495 | What is the chance that someone is dealt a suit in the game of Bridge? | The answer is a tiny number, but large enough to suggest someone has at sometime been dealt a suit in the US. This post shows how to find that chance (with a sequence of three simple calculations), provides an interpretation, and concludes by showing how to compute it accurately.
Let's begin with a small generalizati... | What is the chance that someone is dealt a suit in the game of Bridge? | The answer is a tiny number, but large enough to suggest someone has at sometime been dealt a suit in the US. This post shows how to find that chance (with a sequence of three simple calculations), p | What is the chance that someone is dealt a suit in the game of Bridge?
The answer is a tiny number, but large enough to suggest someone has at sometime been dealt a suit in the US. This post shows how to find that chance (with a sequence of three simple calculations), provides an interpretation, and concludes by showi... | What is the chance that someone is dealt a suit in the game of Bridge?
The answer is a tiny number, but large enough to suggest someone has at sometime been dealt a suit in the US. This post shows how to find that chance (with a sequence of three simple calculations), p |
41,496 | What is the chance that someone is dealt a suit in the game of Bridge? | Using the conditional probabilities, $P$ with a subscript $i$ $i=1, 2, \ldots, 13$ to denote the probability of getting the "right" card, we can use inductive reasoning to calculate the probability. We can assume WLOG that the player is dealt all 13 cards in sequence irrespective of what may be dealt to the other playe... | What is the chance that someone is dealt a suit in the game of Bridge? | Using the conditional probabilities, $P$ with a subscript $i$ $i=1, 2, \ldots, 13$ to denote the probability of getting the "right" card, we can use inductive reasoning to calculate the probability. W | What is the chance that someone is dealt a suit in the game of Bridge?
Using the conditional probabilities, $P$ with a subscript $i$ $i=1, 2, \ldots, 13$ to denote the probability of getting the "right" card, we can use inductive reasoning to calculate the probability. We can assume WLOG that the player is dealt all 13... | What is the chance that someone is dealt a suit in the game of Bridge?
Using the conditional probabilities, $P$ with a subscript $i$ $i=1, 2, \ldots, 13$ to denote the probability of getting the "right" card, we can use inductive reasoning to calculate the probability. W |
41,497 | What is the chance that someone is dealt a suit in the game of Bridge? | One player = $\frac {\binom{4}{1}} {\binom{52}{13}} = 6.29907808979643E-012$
One player not having it is 1 - 6.29907808979643E-012 so that to the 4th is none
Any player $1 - (1 - 6.29907808979643E-012)^4 = 2.5196289499263E-011$
One or more is one minus the chance of no player
This is a little odd because if 3 ar... | What is the chance that someone is dealt a suit in the game of Bridge? | One player = $\frac {\binom{4}{1}} {\binom{52}{13}} = 6.29907808979643E-012$
One player not having it is 1 - 6.29907808979643E-012 so that to the 4th is none
Any player $1 - (1 - 6.29907808979643E | What is the chance that someone is dealt a suit in the game of Bridge?
One player = $\frac {\binom{4}{1}} {\binom{52}{13}} = 6.29907808979643E-012$
One player not having it is 1 - 6.29907808979643E-012 so that to the 4th is none
Any player $1 - (1 - 6.29907808979643E-012)^4 = 2.5196289499263E-011$
One or more is on... | What is the chance that someone is dealt a suit in the game of Bridge?
One player = $\frac {\binom{4}{1}} {\binom{52}{13}} = 6.29907808979643E-012$
One player not having it is 1 - 6.29907808979643E-012 so that to the 4th is none
Any player $1 - (1 - 6.29907808979643E |
41,498 | What would the distribution of time spent per day on a given site look like? | For youtube I think the distribution depends on the distribution of video length. Most videos are about 8 to 10 minutes (this is the average span of the people attention). One might watch 0, 1, 2, or any other number of videos. A Poison distribution might be a good candidate to model the number of visits to a website o... | What would the distribution of time spent per day on a given site look like? | For youtube I think the distribution depends on the distribution of video length. Most videos are about 8 to 10 minutes (this is the average span of the people attention). One might watch 0, 1, 2, or | What would the distribution of time spent per day on a given site look like?
For youtube I think the distribution depends on the distribution of video length. Most videos are about 8 to 10 minutes (this is the average span of the people attention). One might watch 0, 1, 2, or any other number of videos. A Poison distri... | What would the distribution of time spent per day on a given site look like?
For youtube I think the distribution depends on the distribution of video length. Most videos are about 8 to 10 minutes (this is the average span of the people attention). One might watch 0, 1, 2, or |
41,499 | What would the distribution of time spent per day on a given site look like? | Having the vocabulary to describe a distribution is an important skill as a data scientist when it comes to communicating ideas to your peers. There are 4 important concepts, with supporting vocabulary, that you can use to structure your answer to a question like this. These are:
Center (mean, median, mode)
Spread (sta... | What would the distribution of time spent per day on a given site look like? | Having the vocabulary to describe a distribution is an important skill as a data scientist when it comes to communicating ideas to your peers. There are 4 important concepts, with supporting vocabular | What would the distribution of time spent per day on a given site look like?
Having the vocabulary to describe a distribution is an important skill as a data scientist when it comes to communicating ideas to your peers. There are 4 important concepts, with supporting vocabulary, that you can use to structure your answe... | What would the distribution of time spent per day on a given site look like?
Having the vocabulary to describe a distribution is an important skill as a data scientist when it comes to communicating ideas to your peers. There are 4 important concepts, with supporting vocabular |
41,500 | What would the distribution of time spent per day on a given site look like? | The answer is wrong in the sense that you do not explain how you arrived at this answer. The reason that they ask a question like this during in an interview is to see how you think.
One way to answer such a question would be to say that you don't know but that you can make an educated guess. Let's assume that if a pe... | What would the distribution of time spent per day on a given site look like? | The answer is wrong in the sense that you do not explain how you arrived at this answer. The reason that they ask a question like this during in an interview is to see how you think.
One way to answe | What would the distribution of time spent per day on a given site look like?
The answer is wrong in the sense that you do not explain how you arrived at this answer. The reason that they ask a question like this during in an interview is to see how you think.
One way to answer such a question would be to say that you ... | What would the distribution of time spent per day on a given site look like?
The answer is wrong in the sense that you do not explain how you arrived at this answer. The reason that they ask a question like this during in an interview is to see how you think.
One way to answe |
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