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 |
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41,901 | James-Stein Estimator with unequal variances (Ch. 2) | The calculation of the $\hat A_i$ and $\hat B_i$ columns in Table 3 follows the development in Section 8 of the 1973 paper Stein's Estimation Rule and Its Competitors--An Empirical Bayes Approach, which is reference [8] in the 1975 paper. Let $n=36$ be the number of observations. For row $i$ in the table we define the... | James-Stein Estimator with unequal variances (Ch. 2) | The calculation of the $\hat A_i$ and $\hat B_i$ columns in Table 3 follows the development in Section 8 of the 1973 paper Stein's Estimation Rule and Its Competitors--An Empirical Bayes Approach, whi | James-Stein Estimator with unequal variances (Ch. 2)
The calculation of the $\hat A_i$ and $\hat B_i$ columns in Table 3 follows the development in Section 8 of the 1973 paper Stein's Estimation Rule and Its Competitors--An Empirical Bayes Approach, which is reference [8] in the 1975 paper. Let $n=36$ be the number of... | James-Stein Estimator with unequal variances (Ch. 2)
The calculation of the $\hat A_i$ and $\hat B_i$ columns in Table 3 follows the development in Section 8 of the 1973 paper Stein's Estimation Rule and Its Competitors--An Empirical Bayes Approach, whi |
41,902 | Is there any point in using MSE loss in modern deep neural networks? | Suppose you want an unbiased prediction and that the conditional distribution of your dependent data is asymmetric. Then you want to minimize the squared error, or $L^2$ loss.
Minimizing the absolute error, or $L^1$ loss, is equivalent to finding the median of the conditional distribution (Hanley et al., 2001, The Amer... | Is there any point in using MSE loss in modern deep neural networks? | Suppose you want an unbiased prediction and that the conditional distribution of your dependent data is asymmetric. Then you want to minimize the squared error, or $L^2$ loss.
Minimizing the absolute | Is there any point in using MSE loss in modern deep neural networks?
Suppose you want an unbiased prediction and that the conditional distribution of your dependent data is asymmetric. Then you want to minimize the squared error, or $L^2$ loss.
Minimizing the absolute error, or $L^1$ loss, is equivalent to finding the ... | Is there any point in using MSE loss in modern deep neural networks?
Suppose you want an unbiased prediction and that the conditional distribution of your dependent data is asymmetric. Then you want to minimize the squared error, or $L^2$ loss.
Minimizing the absolute |
41,903 | UMVUE of $e^{-\lambda}$ from poisson distribution | Yes, Lehman Scheffe gives you the sufficiency of $\bar{X}$ for $e^{-\lambda}$. The problem is that $\bar{Y}$ does not actually condition on the sufficient statistic. Although the $Y$ are a function of the $X$, $\bar{Y}$ is not a function of the $\bar{X}$. The problem is that your expression isn't reduced. What, in fact... | UMVUE of $e^{-\lambda}$ from poisson distribution | Yes, Lehman Scheffe gives you the sufficiency of $\bar{X}$ for $e^{-\lambda}$. The problem is that $\bar{Y}$ does not actually condition on the sufficient statistic. Although the $Y$ are a function of | UMVUE of $e^{-\lambda}$ from poisson distribution
Yes, Lehman Scheffe gives you the sufficiency of $\bar{X}$ for $e^{-\lambda}$. The problem is that $\bar{Y}$ does not actually condition on the sufficient statistic. Although the $Y$ are a function of the $X$, $\bar{Y}$ is not a function of the $\bar{X}$. The problem is... | UMVUE of $e^{-\lambda}$ from poisson distribution
Yes, Lehman Scheffe gives you the sufficiency of $\bar{X}$ for $e^{-\lambda}$. The problem is that $\bar{Y}$ does not actually condition on the sufficient statistic. Although the $Y$ are a function of |
41,904 | Difference Between Linear Regression in Machine Learning and Statistical Model | Unfortunately, the dichotomy you describe is invalid. ML models (almost always) define a response distribution. For example, the extremely popular gradient boosting machine library XGBoost defines particular learning objectives (e.g. linear, logistic, Poisson, Cox, etc.).
The implementation of linear regression and GL... | Difference Between Linear Regression in Machine Learning and Statistical Model | Unfortunately, the dichotomy you describe is invalid. ML models (almost always) define a response distribution. For example, the extremely popular gradient boosting machine library XGBoost defines par | Difference Between Linear Regression in Machine Learning and Statistical Model
Unfortunately, the dichotomy you describe is invalid. ML models (almost always) define a response distribution. For example, the extremely popular gradient boosting machine library XGBoost defines particular learning objectives (e.g. linear,... | Difference Between Linear Regression in Machine Learning and Statistical Model
Unfortunately, the dichotomy you describe is invalid. ML models (almost always) define a response distribution. For example, the extremely popular gradient boosting machine library XGBoost defines par |
41,905 | learning rate in Adaboost sklearn | The official documentation states that "The learning rate shrinks the contribution of each regressor by learning_rate.". Thus, basically we need to understand three concepts:
1. Weak Classifier
A model whose error rate is only slightly better than random guessing, that is to say, 50% accuracy.
2. Boosting
This techniqu... | learning rate in Adaboost sklearn | The official documentation states that "The learning rate shrinks the contribution of each regressor by learning_rate.". Thus, basically we need to understand three concepts:
1. Weak Classifier
A mode | learning rate in Adaboost sklearn
The official documentation states that "The learning rate shrinks the contribution of each regressor by learning_rate.". Thus, basically we need to understand three concepts:
1. Weak Classifier
A model whose error rate is only slightly better than random guessing, that is to say, 50% a... | learning rate in Adaboost sklearn
The official documentation states that "The learning rate shrinks the contribution of each regressor by learning_rate.". Thus, basically we need to understand three concepts:
1. Weak Classifier
A mode |
41,906 | learning rate in Adaboost sklearn | It looks to me that this is mainly the problem with sklearn docs. Observe in a 2021 GitHub issue about this exact question, not one person has referenced a paper that is actually implemented, and entire discussion is purely about style.
I think @XavierBourretSicotte's answer above should be the accepted one, because it... | learning rate in Adaboost sklearn | It looks to me that this is mainly the problem with sklearn docs. Observe in a 2021 GitHub issue about this exact question, not one person has referenced a paper that is actually implemented, and enti | learning rate in Adaboost sklearn
It looks to me that this is mainly the problem with sklearn docs. Observe in a 2021 GitHub issue about this exact question, not one person has referenced a paper that is actually implemented, and entire discussion is purely about style.
I think @XavierBourretSicotte's answer above shou... | learning rate in Adaboost sklearn
It looks to me that this is mainly the problem with sklearn docs. Observe in a 2021 GitHub issue about this exact question, not one person has referenced a paper that is actually implemented, and enti |
41,907 | Fitting a distribution to match known points on the CDF | I think you are accidentally trying to maximize the squared errors. The default for optim() is to minimize the function, so the negative sign in your beta_func() results in searching for a max.
If you modify your function like so you get values closer to your guess:
beta_func2 <- function(par, x) sum( (pbeta( x, par[1... | Fitting a distribution to match known points on the CDF | I think you are accidentally trying to maximize the squared errors. The default for optim() is to minimize the function, so the negative sign in your beta_func() results in searching for a max.
If yo | Fitting a distribution to match known points on the CDF
I think you are accidentally trying to maximize the squared errors. The default for optim() is to minimize the function, so the negative sign in your beta_func() results in searching for a max.
If you modify your function like so you get values closer to your gue... | Fitting a distribution to match known points on the CDF
I think you are accidentally trying to maximize the squared errors. The default for optim() is to minimize the function, so the negative sign in your beta_func() results in searching for a max.
If yo |
41,908 | Is $R^2_{adjusted}$ both unbiased and consistent under the alternative in simple regression? | As a preliminary result, $R^2_{adjusted}$ is indeed unbiased under the null, at least under error normality.
From this question we have that
$$
R^2\sim Beta(1/2,(n-2)/2)
$$
under the null in the present setting of a simple regression ($k=2$). Hence, its mean is
$$
E(R^2)=\frac{1}{n-1}
$$
so that, from
$$
R^2_{adjuste... | Is $R^2_{adjusted}$ both unbiased and consistent under the alternative in simple regression? | As a preliminary result, $R^2_{adjusted}$ is indeed unbiased under the null, at least under error normality.
From this question we have that
$$
R^2\sim Beta(1/2,(n-2)/2)
$$
under the null in the pres | Is $R^2_{adjusted}$ both unbiased and consistent under the alternative in simple regression?
As a preliminary result, $R^2_{adjusted}$ is indeed unbiased under the null, at least under error normality.
From this question we have that
$$
R^2\sim Beta(1/2,(n-2)/2)
$$
under the null in the present setting of a simple reg... | Is $R^2_{adjusted}$ both unbiased and consistent under the alternative in simple regression?
As a preliminary result, $R^2_{adjusted}$ is indeed unbiased under the null, at least under error normality.
From this question we have that
$$
R^2\sim Beta(1/2,(n-2)/2)
$$
under the null in the pres |
41,909 | What constitutes a large KL divergence? | As commented by W. Huber, this is a fairly interesting question, even though I doubt there is a clear absolute answer. To quote a few generic references,
"...the K-L divergence represents the number of extra bits necessary to
code a source whose symbols were drawn from the distribution P, given
that the coder was ... | What constitutes a large KL divergence? | As commented by W. Huber, this is a fairly interesting question, even though I doubt there is a clear absolute answer. To quote a few generic references,
"...the K-L divergence represents the number | What constitutes a large KL divergence?
As commented by W. Huber, this is a fairly interesting question, even though I doubt there is a clear absolute answer. To quote a few generic references,
"...the K-L divergence represents the number of extra bits necessary to
code a source whose symbols were drawn from the dis... | What constitutes a large KL divergence?
As commented by W. Huber, this is a fairly interesting question, even though I doubt there is a clear absolute answer. To quote a few generic references,
"...the K-L divergence represents the number |
41,910 | How well does $Q(z|X)$ match $N(0,I)$ in variational autoencoders? | It's ok for $Q(z|X)$ to be different from $\mathcal{N}(0, I)$, because when we sample from the VAE, we're not trying to reconstruct $X$ anymore. Instead, we're trying to sample some $X \sim \mathcal{X}$ where $\mathcal{X}$ is the distribution of all images in the dataset.
Imagine of the latent space were actually a uni... | How well does $Q(z|X)$ match $N(0,I)$ in variational autoencoders? | It's ok for $Q(z|X)$ to be different from $\mathcal{N}(0, I)$, because when we sample from the VAE, we're not trying to reconstruct $X$ anymore. Instead, we're trying to sample some $X \sim \mathcal{X | How well does $Q(z|X)$ match $N(0,I)$ in variational autoencoders?
It's ok for $Q(z|X)$ to be different from $\mathcal{N}(0, I)$, because when we sample from the VAE, we're not trying to reconstruct $X$ anymore. Instead, we're trying to sample some $X \sim \mathcal{X}$ where $\mathcal{X}$ is the distribution of all ima... | How well does $Q(z|X)$ match $N(0,I)$ in variational autoencoders?
It's ok for $Q(z|X)$ to be different from $\mathcal{N}(0, I)$, because when we sample from the VAE, we're not trying to reconstruct $X$ anymore. Instead, we're trying to sample some $X \sim \mathcal{X |
41,911 | How well does $Q(z|X)$ match $N(0,I)$ in variational autoencoders? | The answer is two-fold:
(1) The encoder network needs to be expressive enough (wide enough and deep enough) to be able to map the nonlinear input space to something close to $\mathcal{N}(0,I)$.
(2) In addition to (1) (I added a 3rd hidden layer to the MNIST example I described in the question), when I increase the numb... | How well does $Q(z|X)$ match $N(0,I)$ in variational autoencoders? | The answer is two-fold:
(1) The encoder network needs to be expressive enough (wide enough and deep enough) to be able to map the nonlinear input space to something close to $\mathcal{N}(0,I)$.
(2) In | How well does $Q(z|X)$ match $N(0,I)$ in variational autoencoders?
The answer is two-fold:
(1) The encoder network needs to be expressive enough (wide enough and deep enough) to be able to map the nonlinear input space to something close to $\mathcal{N}(0,I)$.
(2) In addition to (1) (I added a 3rd hidden layer to the M... | How well does $Q(z|X)$ match $N(0,I)$ in variational autoencoders?
The answer is two-fold:
(1) The encoder network needs to be expressive enough (wide enough and deep enough) to be able to map the nonlinear input space to something close to $\mathcal{N}(0,I)$.
(2) In |
41,912 | How well does $Q(z|X)$ match $N(0,I)$ in variational autoencoders? | Also, we sample $z$ from the prior and decode it because we made the assumption that $p_{\theta}(x) = \int p_{\theta}(x|z)p(z) dz$. Therefore, sampling from $p_{\theta}(x)$ is equivalent to sampling from the joint $p_{\theta}(x,z)$ then discarding $z$. | How well does $Q(z|X)$ match $N(0,I)$ in variational autoencoders? | Also, we sample $z$ from the prior and decode it because we made the assumption that $p_{\theta}(x) = \int p_{\theta}(x|z)p(z) dz$. Therefore, sampling from $p_{\theta}(x)$ is equivalent to sampling f | How well does $Q(z|X)$ match $N(0,I)$ in variational autoencoders?
Also, we sample $z$ from the prior and decode it because we made the assumption that $p_{\theta}(x) = \int p_{\theta}(x|z)p(z) dz$. Therefore, sampling from $p_{\theta}(x)$ is equivalent to sampling from the joint $p_{\theta}(x,z)$ then discarding $z$. | How well does $Q(z|X)$ match $N(0,I)$ in variational autoencoders?
Also, we sample $z$ from the prior and decode it because we made the assumption that $p_{\theta}(x) = \int p_{\theta}(x|z)p(z) dz$. Therefore, sampling from $p_{\theta}(x)$ is equivalent to sampling f |
41,913 | What are LS means useful for? | I disagree strongly with the "only situation" in the OP. EMMs (estimated marginal means, more restrictively known as least-squares means) are very useful for heading off a Simpson's paradox situation in evaluating the effects of a factor. In your example, consider a scenario where these three things are true:
When $x_... | What are LS means useful for? | I disagree strongly with the "only situation" in the OP. EMMs (estimated marginal means, more restrictively known as least-squares means) are very useful for heading off a Simpson's paradox situation | What are LS means useful for?
I disagree strongly with the "only situation" in the OP. EMMs (estimated marginal means, more restrictively known as least-squares means) are very useful for heading off a Simpson's paradox situation in evaluating the effects of a factor. In your example, consider a scenario where these th... | What are LS means useful for?
I disagree strongly with the "only situation" in the OP. EMMs (estimated marginal means, more restrictively known as least-squares means) are very useful for heading off a Simpson's paradox situation |
41,914 | Reporting the effect of a predictor in a logistic regression fitted with a restricted cubic spline | My course notes describe the components of a restricted cubic spline function, and provides ways to interpret the model when general smooth effects are included. You can compute an odds ratio at two selected points for age (default in the summary.rms function is quartiles), or better: show the partial effect plots to ... | Reporting the effect of a predictor in a logistic regression fitted with a restricted cubic spline | My course notes describe the components of a restricted cubic spline function, and provides ways to interpret the model when general smooth effects are included. You can compute an odds ratio at two | Reporting the effect of a predictor in a logistic regression fitted with a restricted cubic spline
My course notes describe the components of a restricted cubic spline function, and provides ways to interpret the model when general smooth effects are included. You can compute an odds ratio at two selected points for a... | Reporting the effect of a predictor in a logistic regression fitted with a restricted cubic spline
My course notes describe the components of a restricted cubic spline function, and provides ways to interpret the model when general smooth effects are included. You can compute an odds ratio at two |
41,915 | Cross-validation for elastic net regression: squared error vs. correlation on the test set | I think I figured out what was happening here.
Note that the value of correlation does not depend on the length of $\hat\beta$. So if the test correlation keeps increasing while the test R-squared drops, it might indicate that $\lVert\hat\beta\rVert$ is not optimal and scaling $\hat\beta$ up or down by a scalar factor ... | Cross-validation for elastic net regression: squared error vs. correlation on the test set | I think I figured out what was happening here.
Note that the value of correlation does not depend on the length of $\hat\beta$. So if the test correlation keeps increasing while the test R-squared dro | Cross-validation for elastic net regression: squared error vs. correlation on the test set
I think I figured out what was happening here.
Note that the value of correlation does not depend on the length of $\hat\beta$. So if the test correlation keeps increasing while the test R-squared drops, it might indicate that $\... | Cross-validation for elastic net regression: squared error vs. correlation on the test set
I think I figured out what was happening here.
Note that the value of correlation does not depend on the length of $\hat\beta$. So if the test correlation keeps increasing while the test R-squared dro |
41,916 | What is the nugget effect? | In the context of estimating a variogram, a nugget allows for the variogram to assume a non-zero value for two observations having a distance of zero. The implication also is that the correlation between adjacent observations is reduced slightly.
I might say a nugget is a more general concept than measurement error, a... | What is the nugget effect? | In the context of estimating a variogram, a nugget allows for the variogram to assume a non-zero value for two observations having a distance of zero. The implication also is that the correlation betw | What is the nugget effect?
In the context of estimating a variogram, a nugget allows for the variogram to assume a non-zero value for two observations having a distance of zero. The implication also is that the correlation between adjacent observations is reduced slightly.
I might say a nugget is a more general concep... | What is the nugget effect?
In the context of estimating a variogram, a nugget allows for the variogram to assume a non-zero value for two observations having a distance of zero. The implication also is that the correlation betw |
41,917 | What is the nugget effect? | The nugget effect is like the random noise. It's just the small scale variability that you can't estimate with your large scale variability model.
The nugget effect is made of the measurement error and of the microscope variation, two types of variances.
This might be useful: Statistics or geostatistics? Sampling err... | What is the nugget effect? | The nugget effect is like the random noise. It's just the small scale variability that you can't estimate with your large scale variability model.
The nugget effect is made of the measurement error a | What is the nugget effect?
The nugget effect is like the random noise. It's just the small scale variability that you can't estimate with your large scale variability model.
The nugget effect is made of the measurement error and of the microscope variation, two types of variances.
This might be useful: Statistics or ... | What is the nugget effect?
The nugget effect is like the random noise. It's just the small scale variability that you can't estimate with your large scale variability model.
The nugget effect is made of the measurement error a |
41,918 | What does it mean to sample a data point from or according to a distribution? [duplicate] | 1) Whether humans can sample without bias is a question entirely different from whether random sampling can be done. Yes, random sampling can be done, and though some will argue that random seeds are partially deterministic, for all intents and purposes a computer generated random sample is random enough.
2) What does... | What does it mean to sample a data point from or according to a distribution? [duplicate] | 1) Whether humans can sample without bias is a question entirely different from whether random sampling can be done. Yes, random sampling can be done, and though some will argue that random seeds are | What does it mean to sample a data point from or according to a distribution? [duplicate]
1) Whether humans can sample without bias is a question entirely different from whether random sampling can be done. Yes, random sampling can be done, and though some will argue that random seeds are partially deterministic, for ... | What does it mean to sample a data point from or according to a distribution? [duplicate]
1) Whether humans can sample without bias is a question entirely different from whether random sampling can be done. Yes, random sampling can be done, and though some will argue that random seeds are |
41,919 | What does it mean to sample a data point from or according to a distribution? [duplicate] | This could really be answered by taking a course in Monte Carlo simulation, which goes into this topic in depth. Here's a good set of slides that cover common approaches to generating samples from specific distributions. There are also more complicated approaches like Markov Chain Monte Carlo and copula methods for ver... | What does it mean to sample a data point from or according to a distribution? [duplicate] | This could really be answered by taking a course in Monte Carlo simulation, which goes into this topic in depth. Here's a good set of slides that cover common approaches to generating samples from spe | What does it mean to sample a data point from or according to a distribution? [duplicate]
This could really be answered by taking a course in Monte Carlo simulation, which goes into this topic in depth. Here's a good set of slides that cover common approaches to generating samples from specific distributions. There are... | What does it mean to sample a data point from or according to a distribution? [duplicate]
This could really be answered by taking a course in Monte Carlo simulation, which goes into this topic in depth. Here's a good set of slides that cover common approaches to generating samples from spe |
41,920 | Is applying the CLT to the sum of random variables a good approximation? | Going the other way around, if the Z-score were truly a standard normal distribution, then your subsequent approximations would be exact. The degree of error should roughly scale with some measure of distance between the Z-score distribution and the standard Gaussian.
We can use K-S distance as our metric in the space ... | Is applying the CLT to the sum of random variables a good approximation? | Going the other way around, if the Z-score were truly a standard normal distribution, then your subsequent approximations would be exact. The degree of error should roughly scale with some measure of | Is applying the CLT to the sum of random variables a good approximation?
Going the other way around, if the Z-score were truly a standard normal distribution, then your subsequent approximations would be exact. The degree of error should roughly scale with some measure of distance between the Z-score distribution and t... | Is applying the CLT to the sum of random variables a good approximation?
Going the other way around, if the Z-score were truly a standard normal distribution, then your subsequent approximations would be exact. The degree of error should roughly scale with some measure of |
41,921 | Is kernel ridge regression the same as kernel regression? | Yeah, you are right. You practically replace the square matrix $X^TX$ with a Kernel $K$ when you estimate your coefficients. | Is kernel ridge regression the same as kernel regression? | Yeah, you are right. You practically replace the square matrix $X^TX$ with a Kernel $K$ when you estimate your coefficients. | Is kernel ridge regression the same as kernel regression?
Yeah, you are right. You practically replace the square matrix $X^TX$ with a Kernel $K$ when you estimate your coefficients. | Is kernel ridge regression the same as kernel regression?
Yeah, you are right. You practically replace the square matrix $X^TX$ with a Kernel $K$ when you estimate your coefficients. |
41,922 | Is kernel ridge regression the same as kernel regression? | No, they are not the same as algorithms, though you might be able to find pairs of kernel where they give the same answer (model) in terms of predictors.
Kernel Regression (simplest form) is a density estimator with mean prediction:
$$
\begin{align*}
\mu_{\text{kernel-regression}} &= \sum_i w_i y_i, \quad w_i = \frac{K... | Is kernel ridge regression the same as kernel regression? | No, they are not the same as algorithms, though you might be able to find pairs of kernel where they give the same answer (model) in terms of predictors.
Kernel Regression (simplest form) is a density | Is kernel ridge regression the same as kernel regression?
No, they are not the same as algorithms, though you might be able to find pairs of kernel where they give the same answer (model) in terms of predictors.
Kernel Regression (simplest form) is a density estimator with mean prediction:
$$
\begin{align*}
\mu_{\text{... | Is kernel ridge regression the same as kernel regression?
No, they are not the same as algorithms, though you might be able to find pairs of kernel where they give the same answer (model) in terms of predictors.
Kernel Regression (simplest form) is a density |
41,923 | Combining False Discovery Rates (FDR)? | You are not testing hypotheses, but fishing for interesting findings. There is nothing wrong with that. Do not do things that are often demanded by those who cannot tell the difference between a preliminary scientific investigation and bad statistics. See my commentary on the ASA's statement on P-values for more detail... | Combining False Discovery Rates (FDR)? | You are not testing hypotheses, but fishing for interesting findings. There is nothing wrong with that. Do not do things that are often demanded by those who cannot tell the difference between a preli | Combining False Discovery Rates (FDR)?
You are not testing hypotheses, but fishing for interesting findings. There is nothing wrong with that. Do not do things that are often demanded by those who cannot tell the difference between a preliminary scientific investigation and bad statistics. See my commentary on the ASA'... | Combining False Discovery Rates (FDR)?
You are not testing hypotheses, but fishing for interesting findings. There is nothing wrong with that. Do not do things that are often demanded by those who cannot tell the difference between a preli |
41,924 | What are the downsides of bayesian neural networks? | There are still many disadvantages of BNN compared with NN as listed below:
The computational cost is heavier. In here I am not just referring to the cost of training, i.e. getting the posterior distribution of all parameters. This part is in fact OK if you use variational inference with a simple distribution family f... | What are the downsides of bayesian neural networks? | There are still many disadvantages of BNN compared with NN as listed below:
The computational cost is heavier. In here I am not just referring to the cost of training, i.e. getting the posterior dist | What are the downsides of bayesian neural networks?
There are still many disadvantages of BNN compared with NN as listed below:
The computational cost is heavier. In here I am not just referring to the cost of training, i.e. getting the posterior distribution of all parameters. This part is in fact OK if you use varia... | What are the downsides of bayesian neural networks?
There are still many disadvantages of BNN compared with NN as listed below:
The computational cost is heavier. In here I am not just referring to the cost of training, i.e. getting the posterior dist |
41,925 | What are the downsides of bayesian neural networks? | BNN is not capable to recognize posterior distribution. It returns expectation and variance (confidence interval in the assumption of normal distribution). It is overkill to build a stochastic model for modelling expectation and variance. You can find backup experiments on ezcodesample.com proving that it is completely... | What are the downsides of bayesian neural networks? | BNN is not capable to recognize posterior distribution. It returns expectation and variance (confidence interval in the assumption of normal distribution). It is overkill to build a stochastic model f | What are the downsides of bayesian neural networks?
BNN is not capable to recognize posterior distribution. It returns expectation and variance (confidence interval in the assumption of normal distribution). It is overkill to build a stochastic model for modelling expectation and variance. You can find backup experimen... | What are the downsides of bayesian neural networks?
BNN is not capable to recognize posterior distribution. It returns expectation and variance (confidence interval in the assumption of normal distribution). It is overkill to build a stochastic model f |
41,926 | Negative Binomial distribution | Use a Chi-squared test as explained at https://stats.stackexchange.com/a/17148/919. The R code below implements such a test, with defaults appropriate for calving data.
The Chi-squared test is appropriate for such discrete datasets, as explained at that link. To see that it might work to decide whether a particular d... | Negative Binomial distribution | Use a Chi-squared test as explained at https://stats.stackexchange.com/a/17148/919. The R code below implements such a test, with defaults appropriate for calving data.
The Chi-squared test is approp | Negative Binomial distribution
Use a Chi-squared test as explained at https://stats.stackexchange.com/a/17148/919. The R code below implements such a test, with defaults appropriate for calving data.
The Chi-squared test is appropriate for such discrete datasets, as explained at that link. To see that it might work t... | Negative Binomial distribution
Use a Chi-squared test as explained at https://stats.stackexchange.com/a/17148/919. The R code below implements such a test, with defaults appropriate for calving data.
The Chi-squared test is approp |
41,927 | Negative Binomial distribution | I don't think that negative binomial is a reasonable first choice of the distribution for this variable. Yes, the number of days is a discrete number, but the true interval between the events is continuous: cows do not give birth exactly at given hour of the day. It just happens so that you measure the interval in days... | Negative Binomial distribution | I don't think that negative binomial is a reasonable first choice of the distribution for this variable. Yes, the number of days is a discrete number, but the true interval between the events is conti | Negative Binomial distribution
I don't think that negative binomial is a reasonable first choice of the distribution for this variable. Yes, the number of days is a discrete number, but the true interval between the events is continuous: cows do not give birth exactly at given hour of the day. It just happens so that y... | Negative Binomial distribution
I don't think that negative binomial is a reasonable first choice of the distribution for this variable. Yes, the number of days is a discrete number, but the true interval between the events is conti |
41,928 | Negative Binomial distribution | If you are set on using a discrete distribution then think of the days as a count variable and try a Poisson instead of a negative binomial. Then you can just use a glm in R. (I know people will get angry and say use a continuous, but maybe running both you can see why).
so do something like this
modp<- glm(Y ~ X1 + X2... | Negative Binomial distribution | If you are set on using a discrete distribution then think of the days as a count variable and try a Poisson instead of a negative binomial. Then you can just use a glm in R. (I know people will get a | Negative Binomial distribution
If you are set on using a discrete distribution then think of the days as a count variable and try a Poisson instead of a negative binomial. Then you can just use a glm in R. (I know people will get angry and say use a continuous, but maybe running both you can see why).
so do something l... | Negative Binomial distribution
If you are set on using a discrete distribution then think of the days as a count variable and try a Poisson instead of a negative binomial. Then you can just use a glm in R. (I know people will get a |
41,929 | Why is MCMC not reliable when compared to stochastic gradient descent? | In practice, the reliability of both methods will depend on the situation. But, here are a few points to consider:
MCMC must sample the space in a way that's representative of the distribution. This can require a large number of points, particularly in high dimensions. In contrast, SGD doesn't care about the overall st... | Why is MCMC not reliable when compared to stochastic gradient descent? | In practice, the reliability of both methods will depend on the situation. But, here are a few points to consider:
MCMC must sample the space in a way that's representative of the distribution. This c | Why is MCMC not reliable when compared to stochastic gradient descent?
In practice, the reliability of both methods will depend on the situation. But, here are a few points to consider:
MCMC must sample the space in a way that's representative of the distribution. This can require a large number of points, particularly... | Why is MCMC not reliable when compared to stochastic gradient descent?
In practice, the reliability of both methods will depend on the situation. But, here are a few points to consider:
MCMC must sample the space in a way that's representative of the distribution. This c |
41,930 | How to make a LSTM to predict next word | The most widely-used method for predicting the probability of a categorical output is to use softmax activation in the final layer and cross-entropy loss for training. This is because you're modeling the probability that each word in your dictionary comes next. Full softmax can be expensive, though, so sampled softmax ... | How to make a LSTM to predict next word | The most widely-used method for predicting the probability of a categorical output is to use softmax activation in the final layer and cross-entropy loss for training. This is because you're modeling | How to make a LSTM to predict next word
The most widely-used method for predicting the probability of a categorical output is to use softmax activation in the final layer and cross-entropy loss for training. This is because you're modeling the probability that each word in your dictionary comes next. Full softmax can b... | How to make a LSTM to predict next word
The most widely-used method for predicting the probability of a categorical output is to use softmax activation in the final layer and cross-entropy loss for training. This is because you're modeling |
41,931 | Probability of k zeros give the sum of n Poisson random variables is t? | Let $Y:=X_1+\ldots+X_n$. Observe that the distribution of $(X_1,\ldots,X_n)$ conditional on $Y = t$ is multinomial (exercise). This gives a conceptually easier way to think about the problem- you have $n$ boxes and throw $t$ balls in them at random. What is the probability that $k$ are empty?
Well, first of all, the... | Probability of k zeros give the sum of n Poisson random variables is t? | Let $Y:=X_1+\ldots+X_n$. Observe that the distribution of $(X_1,\ldots,X_n)$ conditional on $Y = t$ is multinomial (exercise). This gives a conceptually easier way to think about the problem- you ha | Probability of k zeros give the sum of n Poisson random variables is t?
Let $Y:=X_1+\ldots+X_n$. Observe that the distribution of $(X_1,\ldots,X_n)$ conditional on $Y = t$ is multinomial (exercise). This gives a conceptually easier way to think about the problem- you have $n$ boxes and throw $t$ balls in them at rand... | Probability of k zeros give the sum of n Poisson random variables is t?
Let $Y:=X_1+\ldots+X_n$. Observe that the distribution of $(X_1,\ldots,X_n)$ conditional on $Y = t$ is multinomial (exercise). This gives a conceptually easier way to think about the problem- you ha |
41,932 | Probability of k zeros give the sum of n Poisson random variables is t? | $Y = X_1+X_2+\cdots + X_n$ is a Poisson random variable with parameter $n\lambda$. So you can write down an expression for $P(Y=t)$.
There are $\binom{n}{k}$ choices for a set of $k$ variables that are zero. Pick a specific set. Then, the sum of the complementary set of variables is a Poisson random variable $Z$ with p... | Probability of k zeros give the sum of n Poisson random variables is t? | $Y = X_1+X_2+\cdots + X_n$ is a Poisson random variable with parameter $n\lambda$. So you can write down an expression for $P(Y=t)$.
There are $\binom{n}{k}$ choices for a set of $k$ variables that ar | Probability of k zeros give the sum of n Poisson random variables is t?
$Y = X_1+X_2+\cdots + X_n$ is a Poisson random variable with parameter $n\lambda$. So you can write down an expression for $P(Y=t)$.
There are $\binom{n}{k}$ choices for a set of $k$ variables that are zero. Pick a specific set. Then, the sum of th... | Probability of k zeros give the sum of n Poisson random variables is t?
$Y = X_1+X_2+\cdots + X_n$ is a Poisson random variable with parameter $n\lambda$. So you can write down an expression for $P(Y=t)$.
There are $\binom{n}{k}$ choices for a set of $k$ variables that ar |
41,933 | Confused about the realizability assumption and equations of upper bound | Let's formulate the problem in a clearer way.
ASSUMPTIONS:
$h_s = \underset{h\in\mathcal{H}}{\arg\min} \, L_{S}(h) \qquad$ (definition of ERM)
$\exists h^{*} \in \mathcal{H}: L_{(\mathcal{D}, f)}(h^{*}) = 0 \qquad$ (realizability assumption)
$\mathcal{H}_B = \{ h \in \mathcal{H}: L_{(\mathcal{D}, f)}(h) > \epsilon \}$... | Confused about the realizability assumption and equations of upper bound | Let's formulate the problem in a clearer way.
ASSUMPTIONS:
$h_s = \underset{h\in\mathcal{H}}{\arg\min} \, L_{S}(h) \qquad$ (definition of ERM)
$\exists h^{*} \in \mathcal{H}: L_{(\mathcal{D}, f)}(h^{ | Confused about the realizability assumption and equations of upper bound
Let's formulate the problem in a clearer way.
ASSUMPTIONS:
$h_s = \underset{h\in\mathcal{H}}{\arg\min} \, L_{S}(h) \qquad$ (definition of ERM)
$\exists h^{*} \in \mathcal{H}: L_{(\mathcal{D}, f)}(h^{*}) = 0 \qquad$ (realizability assumption)
$\ma... | Confused about the realizability assumption and equations of upper bound
Let's formulate the problem in a clearer way.
ASSUMPTIONS:
$h_s = \underset{h\in\mathcal{H}}{\arg\min} \, L_{S}(h) \qquad$ (definition of ERM)
$\exists h^{*} \in \mathcal{H}: L_{(\mathcal{D}, f)}(h^{ |
41,934 | Confused about the realizability assumption and equations of upper bound | I actually got stuck on this for a bit too ...
Remember how $h_S$ is defined:
$$h_S \in \underset{h\in H}{\mathrm{argmin}} (L_S(h))$$
The realizability assumption will tell you there's a perfect $h^*$. (Very strong assumption). This $h^*$ will have $L_S(h^*)=0$ by definition.
So when $h_S$ is defined as the argmin - ... | Confused about the realizability assumption and equations of upper bound | I actually got stuck on this for a bit too ...
Remember how $h_S$ is defined:
$$h_S \in \underset{h\in H}{\mathrm{argmin}} (L_S(h))$$
The realizability assumption will tell you there's a perfect $h^* | Confused about the realizability assumption and equations of upper bound
I actually got stuck on this for a bit too ...
Remember how $h_S$ is defined:
$$h_S \in \underset{h\in H}{\mathrm{argmin}} (L_S(h))$$
The realizability assumption will tell you there's a perfect $h^*$. (Very strong assumption). This $h^*$ will ha... | Confused about the realizability assumption and equations of upper bound
I actually got stuck on this for a bit too ...
Remember how $h_S$ is defined:
$$h_S \in \underset{h\in H}{\mathrm{argmin}} (L_S(h))$$
The realizability assumption will tell you there's a perfect $h^* |
41,935 | Is is possible for a gradient boosting regression to predict values outside of the range seen in its training data? | In the comment you ask for an example. You can find it here (links to most informative comment, but please read entire thread for clarity).
In the above example, the most intriguing part for me is the value of -666. It is the score on the 2nd tree (the one with variable V2). Note that score falls outside of assumed dis... | Is is possible for a gradient boosting regression to predict values outside of the range seen in its | In the comment you ask for an example. You can find it here (links to most informative comment, but please read entire thread for clarity).
In the above example, the most intriguing part for me is the | Is is possible for a gradient boosting regression to predict values outside of the range seen in its training data?
In the comment you ask for an example. You can find it here (links to most informative comment, but please read entire thread for clarity).
In the above example, the most intriguing part for me is the val... | Is is possible for a gradient boosting regression to predict values outside of the range seen in its
In the comment you ask for an example. You can find it here (links to most informative comment, but please read entire thread for clarity).
In the above example, the most intriguing part for me is the |
41,936 | Normally sampling from the standard simplex | These papers describe how to sample from a multivariate normal truncated on a (p - 1) simplex ([http://ieeexplore.ieee.org/abstract/document/6884588/], [dobigeon.perso.enseeiht.fr/papers/Dobigeon_TechReport_2007b.pdf]). Sampling is done via Gibbs sampling or HMC. In short, it uses ideas from the (conditional) multivari... | Normally sampling from the standard simplex | These papers describe how to sample from a multivariate normal truncated on a (p - 1) simplex ([http://ieeexplore.ieee.org/abstract/document/6884588/], [dobigeon.perso.enseeiht.fr/papers/Dobigeon_Tech | Normally sampling from the standard simplex
These papers describe how to sample from a multivariate normal truncated on a (p - 1) simplex ([http://ieeexplore.ieee.org/abstract/document/6884588/], [dobigeon.perso.enseeiht.fr/papers/Dobigeon_TechReport_2007b.pdf]). Sampling is done via Gibbs sampling or HMC. In short, it... | Normally sampling from the standard simplex
These papers describe how to sample from a multivariate normal truncated on a (p - 1) simplex ([http://ieeexplore.ieee.org/abstract/document/6884588/], [dobigeon.perso.enseeiht.fr/papers/Dobigeon_Tech |
41,937 | Normally sampling from the standard simplex | It sounds like you want the logit-normal distribution. This distribution shows up a lot in Compositional Data Analysis (CDA). CDA is often used in geology to measure the composition of minerals within soil or rock samples. The logit-normal takes a logit tranform of your random variable and this logit-transformed random... | Normally sampling from the standard simplex | It sounds like you want the logit-normal distribution. This distribution shows up a lot in Compositional Data Analysis (CDA). CDA is often used in geology to measure the composition of minerals within | Normally sampling from the standard simplex
It sounds like you want the logit-normal distribution. This distribution shows up a lot in Compositional Data Analysis (CDA). CDA is often used in geology to measure the composition of minerals within soil or rock samples. The logit-normal takes a logit tranform of your rando... | Normally sampling from the standard simplex
It sounds like you want the logit-normal distribution. This distribution shows up a lot in Compositional Data Analysis (CDA). CDA is often used in geology to measure the composition of minerals within |
41,938 | Independent Bernoulli trials vs markov chain | As a general rule, if you want to test a hypothesis $H_0$ against $H_A$, you must specify a model that encapsulates both possibilities and then use that model to try to infer which of the hypotheses is correct. So if you think your observed time-series data might have some form of auto-correlation, and you want to tes... | Independent Bernoulli trials vs markov chain | As a general rule, if you want to test a hypothesis $H_0$ against $H_A$, you must specify a model that encapsulates both possibilities and then use that model to try to infer which of the hypotheses i | Independent Bernoulli trials vs markov chain
As a general rule, if you want to test a hypothesis $H_0$ against $H_A$, you must specify a model that encapsulates both possibilities and then use that model to try to infer which of the hypotheses is correct. So if you think your observed time-series data might have some ... | Independent Bernoulli trials vs markov chain
As a general rule, if you want to test a hypothesis $H_0$ against $H_A$, you must specify a model that encapsulates both possibilities and then use that model to try to infer which of the hypotheses i |
41,939 | OLS asymptotic results | This comes up a lot in various contexts and therefore deserves a general answer. The question concerns pairs of random variables, so let's simply call them $X$ and $Y$. Think of them as the components of a bivariate random variable $(X,Y)$ with some distribution $F$. The properties of $F$ won't matter: the following... | OLS asymptotic results | This comes up a lot in various contexts and therefore deserves a general answer. The question concerns pairs of random variables, so let's simply call them $X$ and $Y$. Think of them as the componen | OLS asymptotic results
This comes up a lot in various contexts and therefore deserves a general answer. The question concerns pairs of random variables, so let's simply call them $X$ and $Y$. Think of them as the components of a bivariate random variable $(X,Y)$ with some distribution $F$. The properties of $F$ won'... | OLS asymptotic results
This comes up a lot in various contexts and therefore deserves a general answer. The question concerns pairs of random variables, so let's simply call them $X$ and $Y$. Think of them as the componen |
41,940 | What's the skewed-t distribution? | I have found the definition of the skewed distribution. Here the "skewed parameter" is not skewness. | What's the skewed-t distribution? | I have found the definition of the skewed distribution. Here the "skewed parameter" is not skewness. | What's the skewed-t distribution?
I have found the definition of the skewed distribution. Here the "skewed parameter" is not skewness. | What's the skewed-t distribution?
I have found the definition of the skewed distribution. Here the "skewed parameter" is not skewness. |
41,941 | What's the skewed-t distribution? | It seems like skew-t is used as name for different distributions. The mostly used one (I believe) is in https://en.wikipedia.org/wiki/Skewed_generalized_t_distribution, while the answer by @Monier is another one.
A Azallini introduced a general way of "skewing" a distribution, start with some density function $f$ (suc... | What's the skewed-t distribution? | It seems like skew-t is used as name for different distributions. The mostly used one (I believe) is in https://en.wikipedia.org/wiki/Skewed_generalized_t_distribution, while the answer by @Monier is | What's the skewed-t distribution?
It seems like skew-t is used as name for different distributions. The mostly used one (I believe) is in https://en.wikipedia.org/wiki/Skewed_generalized_t_distribution, while the answer by @Monier is another one.
A Azallini introduced a general way of "skewing" a distribution, start w... | What's the skewed-t distribution?
It seems like skew-t is used as name for different distributions. The mostly used one (I believe) is in https://en.wikipedia.org/wiki/Skewed_generalized_t_distribution, while the answer by @Monier is |
41,942 | If a random sample all came out positive, what can be inferred about the population? [duplicate] | 20 of 1000 are good. For rest 980, number of good ones can be from 0 to 980.
Calculate the probabilities that a random sample of 20 products from a manufacturing batch of 1000 and they all tested good, when # of good ones are 20, 21, ..., 1000 among 1000. (totally 981 probabilities). Add them together as denominator, a... | If a random sample all came out positive, what can be inferred about the population? [duplicate] | 20 of 1000 are good. For rest 980, number of good ones can be from 0 to 980.
Calculate the probabilities that a random sample of 20 products from a manufacturing batch of 1000 and they all tested good | If a random sample all came out positive, what can be inferred about the population? [duplicate]
20 of 1000 are good. For rest 980, number of good ones can be from 0 to 980.
Calculate the probabilities that a random sample of 20 products from a manufacturing batch of 1000 and they all tested good, when # of good ones a... | If a random sample all came out positive, what can be inferred about the population? [duplicate]
20 of 1000 are good. For rest 980, number of good ones can be from 0 to 980.
Calculate the probabilities that a random sample of 20 products from a manufacturing batch of 1000 and they all tested good |
41,943 | If a random sample all came out positive, what can be inferred about the population? [duplicate] | You can construct a confidence interval for the proportion $p$ of not defectives. The interval will be one-sided $[p_c, 1]$ say 95% this gives you an idea based on the width of the interval $([1-p_c,1])$ how confident you are that the proportion is close to 100%. This would be based on the hypergeometric distribution.... | If a random sample all came out positive, what can be inferred about the population? [duplicate] | You can construct a confidence interval for the proportion $p$ of not defectives. The interval will be one-sided $[p_c, 1]$ say 95% this gives you an idea based on the width of the interval $([1-p_c, | If a random sample all came out positive, what can be inferred about the population? [duplicate]
You can construct a confidence interval for the proportion $p$ of not defectives. The interval will be one-sided $[p_c, 1]$ say 95% this gives you an idea based on the width of the interval $([1-p_c,1])$ how confident you ... | If a random sample all came out positive, what can be inferred about the population? [duplicate]
You can construct a confidence interval for the proportion $p$ of not defectives. The interval will be one-sided $[p_c, 1]$ say 95% this gives you an idea based on the width of the interval $([1-p_c, |
41,944 | What is the maximum likelihood/GLM version of least absolute deviations for robust linear regression? | There's no GLM (no natural exponential family model) that corresponds to L1 (Least absolute value) regression.*
Note that if you're doing MLE then a density of form $\frac{c}{\phi}\exp(-g(\frac{y-\mathbf{x}\beta}{\phi}))$ with have log-likelihood $-n\log(\phi)-\sum_i g(\frac{y_i-\mathbf{x}_i\beta}{\phi})$.
Now maximi... | What is the maximum likelihood/GLM version of least absolute deviations for robust linear regression | There's no GLM (no natural exponential family model) that corresponds to L1 (Least absolute value) regression.*
Note that if you're doing MLE then a density of form $\frac{c}{\phi}\exp(-g(\frac{y-\mat | What is the maximum likelihood/GLM version of least absolute deviations for robust linear regression?
There's no GLM (no natural exponential family model) that corresponds to L1 (Least absolute value) regression.*
Note that if you're doing MLE then a density of form $\frac{c}{\phi}\exp(-g(\frac{y-\mathbf{x}\beta}{\phi}... | What is the maximum likelihood/GLM version of least absolute deviations for robust linear regression
There's no GLM (no natural exponential family model) that corresponds to L1 (Least absolute value) regression.*
Note that if you're doing MLE then a density of form $\frac{c}{\phi}\exp(-g(\frac{y-\mat |
41,945 | Why is it a big problem to have sparsity issues in Natural Language processing (NLP)? | There are two kinds of sparsity: data sparsity and model sparsity. Model sparsity can be good because it means that there is a concise explanation for the effect that we are modeling. Data sparsity is usually bad because it means that we are missing information that might be important. That slide is talking about data ... | Why is it a big problem to have sparsity issues in Natural Language processing (NLP)? | There are two kinds of sparsity: data sparsity and model sparsity. Model sparsity can be good because it means that there is a concise explanation for the effect that we are modeling. Data sparsity is | Why is it a big problem to have sparsity issues in Natural Language processing (NLP)?
There are two kinds of sparsity: data sparsity and model sparsity. Model sparsity can be good because it means that there is a concise explanation for the effect that we are modeling. Data sparsity is usually bad because it means that... | Why is it a big problem to have sparsity issues in Natural Language processing (NLP)?
There are two kinds of sparsity: data sparsity and model sparsity. Model sparsity can be good because it means that there is a concise explanation for the effect that we are modeling. Data sparsity is |
41,946 | Why is it a big problem to have sparsity issues in Natural Language processing (NLP)? | A 1 hot word vector in a large dictionary or a co-occurrence matrix in a large corpus are both usually very sparse matrices. This is a problem because a one hot vector, [0 0 1 0 .. 0] vector cannot compute relations to another one hot vector, i.e. dot product. So this would cause two words such as hotel and motel to ha... | Why is it a big problem to have sparsity issues in Natural Language processing (NLP)? | A 1 hot word vector in a large dictionary or a co-occurrence matrix in a large corpus are both usually very sparse matrices. This is a problem because a one hot vector, [0 0 1 0 .. 0] vector cannot co | Why is it a big problem to have sparsity issues in Natural Language processing (NLP)?
A 1 hot word vector in a large dictionary or a co-occurrence matrix in a large corpus are both usually very sparse matrices. This is a problem because a one hot vector, [0 0 1 0 .. 0] vector cannot compute relations to another one hot... | Why is it a big problem to have sparsity issues in Natural Language processing (NLP)?
A 1 hot word vector in a large dictionary or a co-occurrence matrix in a large corpus are both usually very sparse matrices. This is a problem because a one hot vector, [0 0 1 0 .. 0] vector cannot co |
41,947 | Why is it a big problem to have sparsity issues in Natural Language processing (NLP)? | In my opinion, the slide here is just stating that the co-occurrence matrix will have a lot of zeros in it. This is a bad thing because it is very CPU- and memory-inefficient. Imagine having to compute 0 times something 90% of the time and always get 0 as the answer. Also imagine having to store a lot of 0s in order to... | Why is it a big problem to have sparsity issues in Natural Language processing (NLP)? | In my opinion, the slide here is just stating that the co-occurrence matrix will have a lot of zeros in it. This is a bad thing because it is very CPU- and memory-inefficient. Imagine having to comput | Why is it a big problem to have sparsity issues in Natural Language processing (NLP)?
In my opinion, the slide here is just stating that the co-occurrence matrix will have a lot of zeros in it. This is a bad thing because it is very CPU- and memory-inefficient. Imagine having to compute 0 times something 90% of the tim... | Why is it a big problem to have sparsity issues in Natural Language processing (NLP)?
In my opinion, the slide here is just stating that the co-occurrence matrix will have a lot of zeros in it. This is a bad thing because it is very CPU- and memory-inefficient. Imagine having to comput |
41,948 | Covariance of Kronecker product? | Example 1:
Assuming without loss of generality your vectors are centered, or that $E[\mathbf{a}] = E[\mathbf{b}] = \mathbf{0}$, the covariance matrix is
\begin{align*}
E[\mathbf{c}\mathbf{c}^T] &= E[(\mathbf{a}\otimes \mathbf{b})(\mathbf{a} \otimes \mathbf{b})^T] \\
&= E\left\{
\left[ \begin{array}{c}
a_1\mathbf{b} \\
... | Covariance of Kronecker product? | Example 1:
Assuming without loss of generality your vectors are centered, or that $E[\mathbf{a}] = E[\mathbf{b}] = \mathbf{0}$, the covariance matrix is
\begin{align*}
E[\mathbf{c}\mathbf{c}^T] &= E[( | Covariance of Kronecker product?
Example 1:
Assuming without loss of generality your vectors are centered, or that $E[\mathbf{a}] = E[\mathbf{b}] = \mathbf{0}$, the covariance matrix is
\begin{align*}
E[\mathbf{c}\mathbf{c}^T] &= E[(\mathbf{a}\otimes \mathbf{b})(\mathbf{a} \otimes \mathbf{b})^T] \\
&= E\left\{
\left[ \... | Covariance of Kronecker product?
Example 1:
Assuming without loss of generality your vectors are centered, or that $E[\mathbf{a}] = E[\mathbf{b}] = \mathbf{0}$, the covariance matrix is
\begin{align*}
E[\mathbf{c}\mathbf{c}^T] &= E[( |
41,949 | Algorithm for generating a multi-level fractional factorial design | Since the purpose of the design is to "cover" the input space of the program to search for bugs, not to optimize or fit some model, it is not clear that statistical design of experiments is useful. See https://cran.r-project.org/web/views/ExperimentalDesign.html for an overview of what is available in R, especially ... | Algorithm for generating a multi-level fractional factorial design | Since the purpose of the design is to "cover" the input space of the program to search for bugs, not to optimize or fit some model, it is not clear that statistical design of experiments is useful. S | Algorithm for generating a multi-level fractional factorial design
Since the purpose of the design is to "cover" the input space of the program to search for bugs, not to optimize or fit some model, it is not clear that statistical design of experiments is useful. See https://cran.r-project.org/web/views/ExperimentalD... | Algorithm for generating a multi-level fractional factorial design
Since the purpose of the design is to "cover" the input space of the program to search for bugs, not to optimize or fit some model, it is not clear that statistical design of experiments is useful. S |
41,950 | Is inference based on full (global) regression model appropriate? | All depends on your study aims:
A) Exploratory study: Your aim is to screen a number of potentially interesting predictors for relationships. You want to to build a testable model based on these exploratory results. No inferences (in a null-hypothesis-significance-testing sense), or other important decisions are drawn ... | Is inference based on full (global) regression model appropriate? | All depends on your study aims:
A) Exploratory study: Your aim is to screen a number of potentially interesting predictors for relationships. You want to to build a testable model based on these explo | Is inference based on full (global) regression model appropriate?
All depends on your study aims:
A) Exploratory study: Your aim is to screen a number of potentially interesting predictors for relationships. You want to to build a testable model based on these exploratory results. No inferences (in a null-hypothesis-si... | Is inference based on full (global) regression model appropriate?
All depends on your study aims:
A) Exploratory study: Your aim is to screen a number of potentially interesting predictors for relationships. You want to to build a testable model based on these explo |
41,951 | Squared Loss for Multilabel Classification | This scheme is called the Brier loss. It is a proper scoring rule, and hence only the optimal classifier is correct, etc. It corresponds, of course, to the $L_2$ distance between the predictive label distribution and the true label distribution (which is a point mass).
Deep learning types these days strongly prefer the... | Squared Loss for Multilabel Classification | This scheme is called the Brier loss. It is a proper scoring rule, and hence only the optimal classifier is correct, etc. It corresponds, of course, to the $L_2$ distance between the predictive label | Squared Loss for Multilabel Classification
This scheme is called the Brier loss. It is a proper scoring rule, and hence only the optimal classifier is correct, etc. It corresponds, of course, to the $L_2$ distance between the predictive label distribution and the true label distribution (which is a point mass).
Deep le... | Squared Loss for Multilabel Classification
This scheme is called the Brier loss. It is a proper scoring rule, and hence only the optimal classifier is correct, etc. It corresponds, of course, to the $L_2$ distance between the predictive label |
41,952 | Squared Loss for Multilabel Classification | Thank @djs for the great answer. Agreeing majority of it, but maybe not the last part. (Had to post another answer due to lack of reputation to comment directly.)
Another interesting property: suppose that there are three categories, with the first one being correct. Cross-entropy would value the predictions $(.8, .2,... | Squared Loss for Multilabel Classification | Thank @djs for the great answer. Agreeing majority of it, but maybe not the last part. (Had to post another answer due to lack of reputation to comment directly.)
Another interesting property: suppos | Squared Loss for Multilabel Classification
Thank @djs for the great answer. Agreeing majority of it, but maybe not the last part. (Had to post another answer due to lack of reputation to comment directly.)
Another interesting property: suppose that there are three categories, with the first one being correct. Cross-en... | Squared Loss for Multilabel Classification
Thank @djs for the great answer. Agreeing majority of it, but maybe not the last part. (Had to post another answer due to lack of reputation to comment directly.)
Another interesting property: suppos |
41,953 | Scores are still correlated after PCA | Remember how PCA works: It starts by finding the single dimension (direction) of greatest variation in your dataset. That becomes PC1. Then it finds the direction of greatest variation that is at right angles to that. It becomes PC2. Etc.
The important thing to recognize is that if your data aren't centered, the ... | Scores are still correlated after PCA | Remember how PCA works: It starts by finding the single dimension (direction) of greatest variation in your dataset. That becomes PC1. Then it finds the direction of greatest variation that is at ri | Scores are still correlated after PCA
Remember how PCA works: It starts by finding the single dimension (direction) of greatest variation in your dataset. That becomes PC1. Then it finds the direction of greatest variation that is at right angles to that. It becomes PC2. Etc.
The important thing to recognize is t... | Scores are still correlated after PCA
Remember how PCA works: It starts by finding the single dimension (direction) of greatest variation in your dataset. That becomes PC1. Then it finds the direction of greatest variation that is at ri |
41,954 | Statistical approach to compare the calibration between models | As you know the Brier score measures calibration and is the mean square error, $\bar B = n^{-1} \sum (\hat y_i - y_i)^2$, between the predictions, $\hat y,$ and the responses, $y$. Since the Brier score is a mean, comparing two Brier scores is basically a comparison of means and you can go as fancy with it as you like.... | Statistical approach to compare the calibration between models | As you know the Brier score measures calibration and is the mean square error, $\bar B = n^{-1} \sum (\hat y_i - y_i)^2$, between the predictions, $\hat y,$ and the responses, $y$. Since the Brier sco | Statistical approach to compare the calibration between models
As you know the Brier score measures calibration and is the mean square error, $\bar B = n^{-1} \sum (\hat y_i - y_i)^2$, between the predictions, $\hat y,$ and the responses, $y$. Since the Brier score is a mean, comparing two Brier scores is basically a c... | Statistical approach to compare the calibration between models
As you know the Brier score measures calibration and is the mean square error, $\bar B = n^{-1} \sum (\hat y_i - y_i)^2$, between the predictions, $\hat y,$ and the responses, $y$. Since the Brier sco |
41,955 | Statistical approach to compare the calibration between models | For future reference, IMO the first answer does not address the calibration issue.
Consider predictions $ \hat{y}_1,\hat{y}_2 ..., \hat{y}_n $ made by a reasonable, well calibrated, model for input values $x_1, x_2,..., x_n$. Now consider a second set of predictions $\tilde{y}_1, \tilde{y}_2, ..., \tilde{y}_n$ that are... | Statistical approach to compare the calibration between models | For future reference, IMO the first answer does not address the calibration issue.
Consider predictions $ \hat{y}_1,\hat{y}_2 ..., \hat{y}_n $ made by a reasonable, well calibrated, model for input va | Statistical approach to compare the calibration between models
For future reference, IMO the first answer does not address the calibration issue.
Consider predictions $ \hat{y}_1,\hat{y}_2 ..., \hat{y}_n $ made by a reasonable, well calibrated, model for input values $x_1, x_2,..., x_n$. Now consider a second set of pr... | Statistical approach to compare the calibration between models
For future reference, IMO the first answer does not address the calibration issue.
Consider predictions $ \hat{y}_1,\hat{y}_2 ..., \hat{y}_n $ made by a reasonable, well calibrated, model for input va |
41,956 | How do you optimize a classification model, when you only care about the top 5% of the ROC Curve? | The general topic of binary classification with strongly unbalanced classes has been cover to a certain extent in the thread with the same name. In very short: caret does allow for more imbalance-appropriate metrics like Cohen's kappa or Precision-Recall AUC; the PRAUC is relatively new, you can find it using the prSum... | How do you optimize a classification model, when you only care about the top 5% of the ROC Curve? | The general topic of binary classification with strongly unbalanced classes has been cover to a certain extent in the thread with the same name. In very short: caret does allow for more imbalance-appr | How do you optimize a classification model, when you only care about the top 5% of the ROC Curve?
The general topic of binary classification with strongly unbalanced classes has been cover to a certain extent in the thread with the same name. In very short: caret does allow for more imbalance-appropriate metrics like C... | How do you optimize a classification model, when you only care about the top 5% of the ROC Curve?
The general topic of binary classification with strongly unbalanced classes has been cover to a certain extent in the thread with the same name. In very short: caret does allow for more imbalance-appr |
41,957 | MCMC Metropolis Hastings - Normalised distribution | $Z$ would be the integral of $\pi^\prime$ (i.e. the integral of the unnormalized density). The integral of $\pi$ would be 1.
Evaluating the integral accurately would often be difficult (or where it's not difficult, at least time consuming). | MCMC Metropolis Hastings - Normalised distribution | $Z$ would be the integral of $\pi^\prime$ (i.e. the integral of the unnormalized density). The integral of $\pi$ would be 1.
Evaluating the integral accurately would often be difficult (or where it's | MCMC Metropolis Hastings - Normalised distribution
$Z$ would be the integral of $\pi^\prime$ (i.e. the integral of the unnormalized density). The integral of $\pi$ would be 1.
Evaluating the integral accurately would often be difficult (or where it's not difficult, at least time consuming). | MCMC Metropolis Hastings - Normalised distribution
$Z$ would be the integral of $\pi^\prime$ (i.e. the integral of the unnormalized density). The integral of $\pi$ would be 1.
Evaluating the integral accurately would often be difficult (or where it's |
41,958 | Mean centering or not in the context of Partial Least Squares | There are mainly two algorithms for PLSR namely NIPALS and SIMPLS.
SIMPLS algorithm is generally faster yet numerically less stable(in most cases the difference is very small). The original article of SIMPLS provides the steps which starts with mean centering both X and Y. The maintainer of the package probably relies ... | Mean centering or not in the context of Partial Least Squares | There are mainly two algorithms for PLSR namely NIPALS and SIMPLS.
SIMPLS algorithm is generally faster yet numerically less stable(in most cases the difference is very small). The original article of | Mean centering or not in the context of Partial Least Squares
There are mainly two algorithms for PLSR namely NIPALS and SIMPLS.
SIMPLS algorithm is generally faster yet numerically less stable(in most cases the difference is very small). The original article of SIMPLS provides the steps which starts with mean centerin... | Mean centering or not in the context of Partial Least Squares
There are mainly two algorithms for PLSR namely NIPALS and SIMPLS.
SIMPLS algorithm is generally faster yet numerically less stable(in most cases the difference is very small). The original article of |
41,959 | Why is F-test not possible for comparing non-nested models | With nested models, it's possible to conceive of a saturated model. This provides a theoretical upper bound to the likelihood and parameter space. When you have this, you know for a fact that the long-range behavior of the log likelihood ratio is a $\chi^2_{p-q}$ random variable. This is necessary for conducting formal... | Why is F-test not possible for comparing non-nested models | With nested models, it's possible to conceive of a saturated model. This provides a theoretical upper bound to the likelihood and parameter space. When you have this, you know for a fact that the long | Why is F-test not possible for comparing non-nested models
With nested models, it's possible to conceive of a saturated model. This provides a theoretical upper bound to the likelihood and parameter space. When you have this, you know for a fact that the long-range behavior of the log likelihood ratio is a $\chi^2_{p-q... | Why is F-test not possible for comparing non-nested models
With nested models, it's possible to conceive of a saturated model. This provides a theoretical upper bound to the likelihood and parameter space. When you have this, you know for a fact that the long |
41,960 | Properties of the white noise process | Consider the i.i.d. process $\{x_t\}$ where $P(x_t=0)=P(x_t=2)=1/2$ for each integer $t$. This sequence satisfies $E(x_t)=1$ for each integer $t$. Now, construct the process $\{u_t\}=\{x_t^2(1-x_{t-1})\}$. For each integer $t$, then, we have \begin{align}E(u_t)&=E(x^2_t(1-x_{t-1}))\\ &=E(x_t^2)(1-E(x_{t-1}))\\ &=E(x_t^... | Properties of the white noise process | Consider the i.i.d. process $\{x_t\}$ where $P(x_t=0)=P(x_t=2)=1/2$ for each integer $t$. This sequence satisfies $E(x_t)=1$ for each integer $t$. Now, construct the process $\{u_t\}=\{x_t^2(1-x_{t-1} | Properties of the white noise process
Consider the i.i.d. process $\{x_t\}$ where $P(x_t=0)=P(x_t=2)=1/2$ for each integer $t$. This sequence satisfies $E(x_t)=1$ for each integer $t$. Now, construct the process $\{u_t\}=\{x_t^2(1-x_{t-1})\}$. For each integer $t$, then, we have \begin{align}E(u_t)&=E(x^2_t(1-x_{t-1}))... | Properties of the white noise process
Consider the i.i.d. process $\{x_t\}$ where $P(x_t=0)=P(x_t=2)=1/2$ for each integer $t$. This sequence satisfies $E(x_t)=1$ for each integer $t$. Now, construct the process $\{u_t\}=\{x_t^2(1-x_{t-1} |
41,961 | Tic Tac Toe AI with Machine Learning | Presumably you don't want an AI which looks ahead a few moves and brute-forces the best move. I guess you want an AI which will evaluate the strength of each possible move and choose the best.
One way you can approach this is to train an AI to take an input of the board and an input of where to play next and output a p... | Tic Tac Toe AI with Machine Learning | Presumably you don't want an AI which looks ahead a few moves and brute-forces the best move. I guess you want an AI which will evaluate the strength of each possible move and choose the best.
One way | Tic Tac Toe AI with Machine Learning
Presumably you don't want an AI which looks ahead a few moves and brute-forces the best move. I guess you want an AI which will evaluate the strength of each possible move and choose the best.
One way you can approach this is to train an AI to take an input of the board and an input... | Tic Tac Toe AI with Machine Learning
Presumably you don't want an AI which looks ahead a few moves and brute-forces the best move. I guess you want an AI which will evaluate the strength of each possible move and choose the best.
One way |
41,962 | Tic Tac Toe AI with Machine Learning | I am working on a very similar project to you, and I'm also doing it as an introduction to machine learning.
One of the best methods I've seen for getting a tic-tac-toe AI is a reinforcement learning method described in this paper and formally discussed in this book.
Basically, you have a program run through possible m... | Tic Tac Toe AI with Machine Learning | I am working on a very similar project to you, and I'm also doing it as an introduction to machine learning.
One of the best methods I've seen for getting a tic-tac-toe AI is a reinforcement learning | Tic Tac Toe AI with Machine Learning
I am working on a very similar project to you, and I'm also doing it as an introduction to machine learning.
One of the best methods I've seen for getting a tic-tac-toe AI is a reinforcement learning method described in this paper and formally discussed in this book.
Basically, you ... | Tic Tac Toe AI with Machine Learning
I am working on a very similar project to you, and I'm also doing it as an introduction to machine learning.
One of the best methods I've seen for getting a tic-tac-toe AI is a reinforcement learning |
41,963 | Tic Tac Toe AI with Machine Learning | I have just finished making a tictactoe bot.
The way I have set it up is that it learns from the moves that I make.
So, if I'm playing a PlayervsAI or PlayervsPlayer game, every move that the winner makes is recorded and saved in a file. So this data is essentially 'moves that lead up to a win'. The format of this da... | Tic Tac Toe AI with Machine Learning | I have just finished making a tictactoe bot.
The way I have set it up is that it learns from the moves that I make.
So, if I'm playing a PlayervsAI or PlayervsPlayer game, every move that the winner | Tic Tac Toe AI with Machine Learning
I have just finished making a tictactoe bot.
The way I have set it up is that it learns from the moves that I make.
So, if I'm playing a PlayervsAI or PlayervsPlayer game, every move that the winner makes is recorded and saved in a file. So this data is essentially 'moves that lea... | Tic Tac Toe AI with Machine Learning
I have just finished making a tictactoe bot.
The way I have set it up is that it learns from the moves that I make.
So, if I'm playing a PlayervsAI or PlayervsPlayer game, every move that the winner |
41,964 | word2vec neural network - bias units | It seems there are indeed no bias units at either layer. In his thesis on neural network based language models, Mikolov states that:
[...] biases are not used in the neural network, as no significant
improvement of performance was observed - following the Occam's razor,
the solution is as simple as it needs to be... | word2vec neural network - bias units | It seems there are indeed no bias units at either layer. In his thesis on neural network based language models, Mikolov states that:
[...] biases are not used in the neural network, as no significan | word2vec neural network - bias units
It seems there are indeed no bias units at either layer. In his thesis on neural network based language models, Mikolov states that:
[...] biases are not used in the neural network, as no significant
improvement of performance was observed - following the Occam's razor,
the so... | word2vec neural network - bias units
It seems there are indeed no bias units at either layer. In his thesis on neural network based language models, Mikolov states that:
[...] biases are not used in the neural network, as no significan |
41,965 | word2vec neural network - bias units | Bias is hidden in average vectors (take mean of all vectors; projection of a given vector on this mean effectively carries a bias). | word2vec neural network - bias units | Bias is hidden in average vectors (take mean of all vectors; projection of a given vector on this mean effectively carries a bias). | word2vec neural network - bias units
Bias is hidden in average vectors (take mean of all vectors; projection of a given vector on this mean effectively carries a bias). | word2vec neural network - bias units
Bias is hidden in average vectors (take mean of all vectors; projection of a given vector on this mean effectively carries a bias). |
41,966 | Can I treat a counting response variable as a continuous variable and run OLS? | A random variable is a counting variable does not only mean that it has natural number values. So, the number of sunny days in a year is not a counting random variable, because it is not the result of a counting process. Probably, a day is declared sunny if some burocratic criteria are fulfilled, like at least 5 hours... | Can I treat a counting response variable as a continuous variable and run OLS? | A random variable is a counting variable does not only mean that it has natural number values. So, the number of sunny days in a year is not a counting random variable, because it is not the result of | Can I treat a counting response variable as a continuous variable and run OLS?
A random variable is a counting variable does not only mean that it has natural number values. So, the number of sunny days in a year is not a counting random variable, because it is not the result of a counting process. Probably, a day is ... | Can I treat a counting response variable as a continuous variable and run OLS?
A random variable is a counting variable does not only mean that it has natural number values. So, the number of sunny days in a year is not a counting random variable, because it is not the result of |
41,967 | Can I treat a counting response variable as a continuous variable and run OLS? | At the fundamental level of chemistry and atomic theory, one could argue that the world is discrete rather than continuous. One might argue that continuous variables themselves are just very useful approximations to an underlying discrete reality. So clearly it is OK to treat counts as continuous variables. We do it al... | Can I treat a counting response variable as a continuous variable and run OLS? | At the fundamental level of chemistry and atomic theory, one could argue that the world is discrete rather than continuous. One might argue that continuous variables themselves are just very useful ap | Can I treat a counting response variable as a continuous variable and run OLS?
At the fundamental level of chemistry and atomic theory, one could argue that the world is discrete rather than continuous. One might argue that continuous variables themselves are just very useful approximations to an underlying discrete re... | Can I treat a counting response variable as a continuous variable and run OLS?
At the fundamental level of chemistry and atomic theory, one could argue that the world is discrete rather than continuous. One might argue that continuous variables themselves are just very useful ap |
41,968 | Is the decision boundary of a logistic classifier linear? | There are various different things that can be meant by "non-linear" (cf., this great answer: How to tell the difference between linear and non-linear regression models?) Part of the confusion behind questions like yours often resides in ambiguity about the term non-linear. It will help to get clearer on that (see th... | Is the decision boundary of a logistic classifier linear? | There are various different things that can be meant by "non-linear" (cf., this great answer: How to tell the difference between linear and non-linear regression models?) Part of the confusion behind | Is the decision boundary of a logistic classifier linear?
There are various different things that can be meant by "non-linear" (cf., this great answer: How to tell the difference between linear and non-linear regression models?) Part of the confusion behind questions like yours often resides in ambiguity about the ter... | Is the decision boundary of a logistic classifier linear?
There are various different things that can be meant by "non-linear" (cf., this great answer: How to tell the difference between linear and non-linear regression models?) Part of the confusion behind |
41,969 | Choosing Between Additive and Multiplicative Model? | I would go for additive too. As your apparent signal seems of low frequency, you can go a little beyond, at least empirically. You can check for instance the homoscedasticity of finite differences of the data (first or second order). This would act as a very crude high-pass filter, where you could expect the noise to... | Choosing Between Additive and Multiplicative Model? | I would go for additive too. As your apparent signal seems of low frequency, you can go a little beyond, at least empirically. You can check for instance the homoscedasticity of finite differences o | Choosing Between Additive and Multiplicative Model?
I would go for additive too. As your apparent signal seems of low frequency, you can go a little beyond, at least empirically. You can check for instance the homoscedasticity of finite differences of the data (first or second order). This would act as a very crude h... | Choosing Between Additive and Multiplicative Model?
I would go for additive too. As your apparent signal seems of low frequency, you can go a little beyond, at least empirically. You can check for instance the homoscedasticity of finite differences o |
41,970 | Choosing Between Additive and Multiplicative Model? | I took the 55 values and used AUTOBOX to automatically detect a hybrid model possibly including deterministic structure as well as ARIMA structure. The plot of the original data and the ACF plot of the original series is here. AUTOBOX concluded that a single trend and 3 seasonal dummies were more appropriate tham SARI... | Choosing Between Additive and Multiplicative Model? | I took the 55 values and used AUTOBOX to automatically detect a hybrid model possibly including deterministic structure as well as ARIMA structure. The plot of the original data and the ACF plot of th | Choosing Between Additive and Multiplicative Model?
I took the 55 values and used AUTOBOX to automatically detect a hybrid model possibly including deterministic structure as well as ARIMA structure. The plot of the original data and the ACF plot of the original series is here. AUTOBOX concluded that a single trend an... | Choosing Between Additive and Multiplicative Model?
I took the 55 values and used AUTOBOX to automatically detect a hybrid model possibly including deterministic structure as well as ARIMA structure. The plot of the original data and the ACF plot of th |
41,971 | LSTM: how to feed the Network with a mini batch? When to reset the LSTM state? | when should I reset the state of the LSTMs?
Typically, for each new input, i.e. for each sample.
how to feed the Network with a mini batch?
Typically, samples are padded so that all samples in a mini batch have the same length, for programming and performance reasons. | LSTM: how to feed the Network with a mini batch? When to reset the LSTM state? | when should I reset the state of the LSTMs?
Typically, for each new input, i.e. for each sample.
how to feed the Network with a mini batch?
Typically, samples are padded so that all samples in a m | LSTM: how to feed the Network with a mini batch? When to reset the LSTM state?
when should I reset the state of the LSTMs?
Typically, for each new input, i.e. for each sample.
how to feed the Network with a mini batch?
Typically, samples are padded so that all samples in a mini batch have the same length, for progr... | LSTM: how to feed the Network with a mini batch? When to reset the LSTM state?
when should I reset the state of the LSTMs?
Typically, for each new input, i.e. for each sample.
how to feed the Network with a mini batch?
Typically, samples are padded so that all samples in a m |
41,972 | Power and sample size in regression context? | There are two main approaches to power analysis:
When your design conforms to "classical standards" with regard to estimators used and distributional assumptions, then the formulae from Cohen (most of which are much older than that reference) are mathematically correct, provably so.
When your design starts to depart fr... | Power and sample size in regression context? | There are two main approaches to power analysis:
When your design conforms to "classical standards" with regard to estimators used and distributional assumptions, then the formulae from Cohen (most of | Power and sample size in regression context?
There are two main approaches to power analysis:
When your design conforms to "classical standards" with regard to estimators used and distributional assumptions, then the formulae from Cohen (most of which are much older than that reference) are mathematically correct, prov... | Power and sample size in regression context?
There are two main approaches to power analysis:
When your design conforms to "classical standards" with regard to estimators used and distributional assumptions, then the formulae from Cohen (most of |
41,973 | What is the difference between denoising autoencoder and contractive autoencoder? | No. The CAE tries to make the encoder (i.e. mapping from input to hidden layer) have the property of locality, i.e. small changes in input lead to small changes at hidden layer. This is a nice property because it means the mapping is not too sensitive, which should help it generalise beyond the training data.
(There is... | What is the difference between denoising autoencoder and contractive autoencoder? | No. The CAE tries to make the encoder (i.e. mapping from input to hidden layer) have the property of locality, i.e. small changes in input lead to small changes at hidden layer. This is a nice propert | What is the difference between denoising autoencoder and contractive autoencoder?
No. The CAE tries to make the encoder (i.e. mapping from input to hidden layer) have the property of locality, i.e. small changes in input lead to small changes at hidden layer. This is a nice property because it means the mapping is not ... | What is the difference between denoising autoencoder and contractive autoencoder?
No. The CAE tries to make the encoder (i.e. mapping from input to hidden layer) have the property of locality, i.e. small changes in input lead to small changes at hidden layer. This is a nice propert |
41,974 | How to properly do stacking/meta ensembling with cross validation | Only method 2 is valid i.e. without any leakage.
When doing stacking/ensembling, the golden rule is that the meta model must be trained on a separate dataset than the dataset(s) used to train the base models.
This is really important otherwise you risk to get poor generalization (test accuracy) because of target leakag... | How to properly do stacking/meta ensembling with cross validation | Only method 2 is valid i.e. without any leakage.
When doing stacking/ensembling, the golden rule is that the meta model must be trained on a separate dataset than the dataset(s) used to train the base | How to properly do stacking/meta ensembling with cross validation
Only method 2 is valid i.e. without any leakage.
When doing stacking/ensembling, the golden rule is that the meta model must be trained on a separate dataset than the dataset(s) used to train the base models.
This is really important otherwise you risk t... | How to properly do stacking/meta ensembling with cross validation
Only method 2 is valid i.e. without any leakage.
When doing stacking/ensembling, the golden rule is that the meta model must be trained on a separate dataset than the dataset(s) used to train the base |
41,975 | How to properly do stacking/meta ensembling with cross validation | I think the only way to really determine this is to experiment. I made a small one here. I split the dataset in two and trained a model and the stacking model with the same training data at the core. In the 2nd one I trained it on the other half of the data. The accuracy of the second was was higher slightly. However, ... | How to properly do stacking/meta ensembling with cross validation | I think the only way to really determine this is to experiment. I made a small one here. I split the dataset in two and trained a model and the stacking model with the same training data at the core. | How to properly do stacking/meta ensembling with cross validation
I think the only way to really determine this is to experiment. I made a small one here. I split the dataset in two and trained a model and the stacking model with the same training data at the core. In the 2nd one I trained it on the other half of the d... | How to properly do stacking/meta ensembling with cross validation
I think the only way to really determine this is to experiment. I made a small one here. I split the dataset in two and trained a model and the stacking model with the same training data at the core. |
41,976 | Determine the PMF of the multiplication of two discrete random variables | If $X,Y$ are independent discrete random variables with supports $\cal X, \cal Y$ (i.e. places where they are non-zero, then $$P(XY=c) = \sum_{x \in \cal X, ~~y \in \cal Y \\\text{ s.t. } xy=c} P(X=x,Y=y) = \sum_{x \in \cal X,~~ y \in \cal Y\\ \text{ s.t. } xy=c} P(X=x)P(Y=y)$$.
The first equality is true for any discr... | Determine the PMF of the multiplication of two discrete random variables | If $X,Y$ are independent discrete random variables with supports $\cal X, \cal Y$ (i.e. places where they are non-zero, then $$P(XY=c) = \sum_{x \in \cal X, ~~y \in \cal Y \\\text{ s.t. } xy=c} P(X=x, | Determine the PMF of the multiplication of two discrete random variables
If $X,Y$ are independent discrete random variables with supports $\cal X, \cal Y$ (i.e. places where they are non-zero, then $$P(XY=c) = \sum_{x \in \cal X, ~~y \in \cal Y \\\text{ s.t. } xy=c} P(X=x,Y=y) = \sum_{x \in \cal X,~~ y \in \cal Y\\ \te... | Determine the PMF of the multiplication of two discrete random variables
If $X,Y$ are independent discrete random variables with supports $\cal X, \cal Y$ (i.e. places where they are non-zero, then $$P(XY=c) = \sum_{x \in \cal X, ~~y \in \cal Y \\\text{ s.t. } xy=c} P(X=x, |
41,977 | The importance of the Gaussian copula | Now my question is, what exactly makes the Gaussian copula so important among all the possible choices of copulas?
Is it? What makes you say it's especially important?
suppose that their joint distribution is not a multivariate normal. Then my understanding is that since marginals are decoupled from the copula, that ... | The importance of the Gaussian copula | Now my question is, what exactly makes the Gaussian copula so important among all the possible choices of copulas?
Is it? What makes you say it's especially important?
suppose that their joint distr | The importance of the Gaussian copula
Now my question is, what exactly makes the Gaussian copula so important among all the possible choices of copulas?
Is it? What makes you say it's especially important?
suppose that their joint distribution is not a multivariate normal. Then my understanding is that since marginal... | The importance of the Gaussian copula
Now my question is, what exactly makes the Gaussian copula so important among all the possible choices of copulas?
Is it? What makes you say it's especially important?
suppose that their joint distr |
41,978 | Optimizing a "black box" function: Linear Regression or Bayesian Optimization... what's the difference? | Your understanding is correct.
BO inherently measures the uncertainty of regions of your search space. And the acquisition function governs the tradeoff between exploring a point in a region with high uncertainty versus exploring further in a region with lower uncertainty, but a higher value.
By contrast, vanilla regre... | Optimizing a "black box" function: Linear Regression or Bayesian Optimization... what's the differen | Your understanding is correct.
BO inherently measures the uncertainty of regions of your search space. And the acquisition function governs the tradeoff between exploring a point in a region with high | Optimizing a "black box" function: Linear Regression or Bayesian Optimization... what's the difference?
Your understanding is correct.
BO inherently measures the uncertainty of regions of your search space. And the acquisition function governs the tradeoff between exploring a point in a region with high uncertainty ver... | Optimizing a "black box" function: Linear Regression or Bayesian Optimization... what's the differen
Your understanding is correct.
BO inherently measures the uncertainty of regions of your search space. And the acquisition function governs the tradeoff between exploring a point in a region with high |
41,979 | How does numer.ai make predictions about the future? | If you sort the t_id column in the test dataset you will see that it goes from 1-36000. I would assume that it refers to "trade id". The way financial time series forecasting works is the you usually take lagged values of features at time t-1 and use them to predict the target value at time t, thus I would assume that ... | How does numer.ai make predictions about the future? | If you sort the t_id column in the test dataset you will see that it goes from 1-36000. I would assume that it refers to "trade id". The way financial time series forecasting works is the you usually | How does numer.ai make predictions about the future?
If you sort the t_id column in the test dataset you will see that it goes from 1-36000. I would assume that it refers to "trade id". The way financial time series forecasting works is the you usually take lagged values of features at time t-1 and use them to predict ... | How does numer.ai make predictions about the future?
If you sort the t_id column in the test dataset you will see that it goes from 1-36000. I would assume that it refers to "trade id". The way financial time series forecasting works is the you usually |
41,980 | How does numer.ai make predictions about the future? | You give them your predictions and not your classifier.
They're lowering the barrier to entry in one area, and not all of them. Sure, you could start up a fund of your own or sell your classifier to some other firm, but, (or so I think) goes their thought process and business model, the competition that they're prov... | How does numer.ai make predictions about the future? | You give them your predictions and not your classifier.
They're lowering the barrier to entry in one area, and not all of them. Sure, you could start up a fund of your own or sell your classifier t | How does numer.ai make predictions about the future?
You give them your predictions and not your classifier.
They're lowering the barrier to entry in one area, and not all of them. Sure, you could start up a fund of your own or sell your classifier to some other firm, but, (or so I think) goes their thought process ... | How does numer.ai make predictions about the future?
You give them your predictions and not your classifier.
They're lowering the barrier to entry in one area, and not all of them. Sure, you could start up a fund of your own or sell your classifier t |
41,981 | How to Find Confidence Level of Results | Since you are uncertain about what may be the true conversion rate of the ad, you should consider using bayesian approach:
Let $X$ be an r.v such that $X=1$ if the ad is successful. So $X \sim Be(p)$, where $p$ is the conversion rate of the ad and let's assume further that $p \sim U(0,1)$. So basically you have a no pr... | How to Find Confidence Level of Results | Since you are uncertain about what may be the true conversion rate of the ad, you should consider using bayesian approach:
Let $X$ be an r.v such that $X=1$ if the ad is successful. So $X \sim Be(p)$, | How to Find Confidence Level of Results
Since you are uncertain about what may be the true conversion rate of the ad, you should consider using bayesian approach:
Let $X$ be an r.v such that $X=1$ if the ad is successful. So $X \sim Be(p)$, where $p$ is the conversion rate of the ad and let's assume further that $p \si... | How to Find Confidence Level of Results
Since you are uncertain about what may be the true conversion rate of the ad, you should consider using bayesian approach:
Let $X$ be an r.v such that $X=1$ if the ad is successful. So $X \sim Be(p)$, |
41,982 | How to Find Confidence Level of Results | The classical parametric approach in frequentist statistics would be to model the situation as follows. Suppose all the people who see a certain advertisement are all independent of each other and have the same probability $p$ of clicking on the advertisement. We say these people form a Bernoulli population, i.e. a mem... | How to Find Confidence Level of Results | The classical parametric approach in frequentist statistics would be to model the situation as follows. Suppose all the people who see a certain advertisement are all independent of each other and hav | How to Find Confidence Level of Results
The classical parametric approach in frequentist statistics would be to model the situation as follows. Suppose all the people who see a certain advertisement are all independent of each other and have the same probability $p$ of clicking on the advertisement. We say these people... | How to Find Confidence Level of Results
The classical parametric approach in frequentist statistics would be to model the situation as follows. Suppose all the people who see a certain advertisement are all independent of each other and hav |
41,983 | How to Find Confidence Level of Results | Assuming that all people make independent choices, we can model the experiment as draws $X_i$ from a Bernoulli($p$) distribution with $E(X_i) = p$ and $\sigma^2(X_i) = p(1-p)$. For large $n$ ($n = 1000$ in your case) the independent draws from the Bernoulli distribution can be modelled as a Normal distribution accordin... | How to Find Confidence Level of Results | Assuming that all people make independent choices, we can model the experiment as draws $X_i$ from a Bernoulli($p$) distribution with $E(X_i) = p$ and $\sigma^2(X_i) = p(1-p)$. For large $n$ ($n = 100 | How to Find Confidence Level of Results
Assuming that all people make independent choices, we can model the experiment as draws $X_i$ from a Bernoulli($p$) distribution with $E(X_i) = p$ and $\sigma^2(X_i) = p(1-p)$. For large $n$ ($n = 1000$ in your case) the independent draws from the Bernoulli distribution can be mo... | How to Find Confidence Level of Results
Assuming that all people make independent choices, we can model the experiment as draws $X_i$ from a Bernoulli($p$) distribution with $E(X_i) = p$ and $\sigma^2(X_i) = p(1-p)$. For large $n$ ($n = 100 |
41,984 | How to combine/pool binomial confidence intervals after multiple imputation? | This is indeed an interesting problem. The issue is that the standard errors that are based on the central limit theorem for proportions are often undesirable because proportions are a computed quantity and for that reason exhibit skewed uncertainty over sampling. The Wilson score, such as you mentioned, gets around th... | How to combine/pool binomial confidence intervals after multiple imputation? | This is indeed an interesting problem. The issue is that the standard errors that are based on the central limit theorem for proportions are often undesirable because proportions are a computed quanti | How to combine/pool binomial confidence intervals after multiple imputation?
This is indeed an interesting problem. The issue is that the standard errors that are based on the central limit theorem for proportions are often undesirable because proportions are a computed quantity and for that reason exhibit skewed uncer... | How to combine/pool binomial confidence intervals after multiple imputation?
This is indeed an interesting problem. The issue is that the standard errors that are based on the central limit theorem for proportions are often undesirable because proportions are a computed quanti |
41,985 | Is the Brier Score appropriate for ordered categorical data? | In your case, the Brier score still "works" in that it incentivizes you to state the true forecast distribution (it is a proper scoring rule, see Gneiting and Raftery, 2007). For example, if the true probabilities were 0, 1/4, 1/4, 1/2, you would minimize your expected Brier score by actually stating these probabilitie... | Is the Brier Score appropriate for ordered categorical data? | In your case, the Brier score still "works" in that it incentivizes you to state the true forecast distribution (it is a proper scoring rule, see Gneiting and Raftery, 2007). For example, if the true | Is the Brier Score appropriate for ordered categorical data?
In your case, the Brier score still "works" in that it incentivizes you to state the true forecast distribution (it is a proper scoring rule, see Gneiting and Raftery, 2007). For example, if the true probabilities were 0, 1/4, 1/4, 1/2, you would minimize you... | Is the Brier Score appropriate for ordered categorical data?
In your case, the Brier score still "works" in that it incentivizes you to state the true forecast distribution (it is a proper scoring rule, see Gneiting and Raftery, 2007). For example, if the true |
41,986 | Intuition for near-decorrelation through centering | Here is a geometric argument that I think provides the required intuition.
Let us consider a $n\times p$ data matrix $\mathbf U$, where each row is one sample of your random variable $\mathbf u$. Usual "centering" refers to centering the columns of $\mathbf U$; as your $\mathbf u$ has zero mean, the data matrix $\mathb... | Intuition for near-decorrelation through centering | Here is a geometric argument that I think provides the required intuition.
Let us consider a $n\times p$ data matrix $\mathbf U$, where each row is one sample of your random variable $\mathbf u$. Usua | Intuition for near-decorrelation through centering
Here is a geometric argument that I think provides the required intuition.
Let us consider a $n\times p$ data matrix $\mathbf U$, where each row is one sample of your random variable $\mathbf u$. Usual "centering" refers to centering the columns of $\mathbf U$; as your... | Intuition for near-decorrelation through centering
Here is a geometric argument that I think provides the required intuition.
Let us consider a $n\times p$ data matrix $\mathbf U$, where each row is one sample of your random variable $\mathbf u$. Usua |
41,987 | Check uniformly distributed continuous random variable | Although it is meaningless to find a probability (unless you first specify a prior distribution of the endpoints), you can find the relative likelihood. A good basis for comparison would be the alternative hypothesis that the numbers are drawn from a uniform distribution between a lower bound $L$ and upper bound $U$.
... | Check uniformly distributed continuous random variable | Although it is meaningless to find a probability (unless you first specify a prior distribution of the endpoints), you can find the relative likelihood. A good basis for comparison would be the alter | Check uniformly distributed continuous random variable
Although it is meaningless to find a probability (unless you first specify a prior distribution of the endpoints), you can find the relative likelihood. A good basis for comparison would be the alternative hypothesis that the numbers are drawn from a uniform distr... | Check uniformly distributed continuous random variable
Although it is meaningless to find a probability (unless you first specify a prior distribution of the endpoints), you can find the relative likelihood. A good basis for comparison would be the alter |
41,988 | Check uniformly distributed continuous random variable | It's not clear exactly what you need, but let's first take a look at how to estimate the lower and upper boundaries. It is claimed on Wikipedia that the uniformly minimum variance unbiased estimators for the continuous uniform distribution on $(a,b)$ are the maximum spacing estimators $$ \hat{a}={{nx_{(1)}-x_{(n)}} \ov... | Check uniformly distributed continuous random variable | It's not clear exactly what you need, but let's first take a look at how to estimate the lower and upper boundaries. It is claimed on Wikipedia that the uniformly minimum variance unbiased estimators | Check uniformly distributed continuous random variable
It's not clear exactly what you need, but let's first take a look at how to estimate the lower and upper boundaries. It is claimed on Wikipedia that the uniformly minimum variance unbiased estimators for the continuous uniform distribution on $(a,b)$ are the maximu... | Check uniformly distributed continuous random variable
It's not clear exactly what you need, but let's first take a look at how to estimate the lower and upper boundaries. It is claimed on Wikipedia that the uniformly minimum variance unbiased estimators |
41,989 | Lay person's explanation of Sheather-Jones method for bandwidth selection? | Assuming it is indeed the preferred bandwidth estimator in Sheather and Jones' (1991) JRSS-B paper [1] that you mean (specifically, $\hat{h}_{2S}$), here's a brief discussion (as requested), but a brief discussion of a highly technical topic is necessarily a little vague and cryptic.
The basic issue of finding efficie... | Lay person's explanation of Sheather-Jones method for bandwidth selection? | Assuming it is indeed the preferred bandwidth estimator in Sheather and Jones' (1991) JRSS-B paper [1] that you mean (specifically, $\hat{h}_{2S}$), here's a brief discussion (as requested), but a bri | Lay person's explanation of Sheather-Jones method for bandwidth selection?
Assuming it is indeed the preferred bandwidth estimator in Sheather and Jones' (1991) JRSS-B paper [1] that you mean (specifically, $\hat{h}_{2S}$), here's a brief discussion (as requested), but a brief discussion of a highly technical topic is ... | Lay person's explanation of Sheather-Jones method for bandwidth selection?
Assuming it is indeed the preferred bandwidth estimator in Sheather and Jones' (1991) JRSS-B paper [1] that you mean (specifically, $\hat{h}_{2S}$), here's a brief discussion (as requested), but a bri |
41,990 | rigorous statistical-inference book recommendation | One book not mentioned above which I quite like is Theoretical Statistics, Topics for a Core Course by Keener. It is relatively rigorous but quite readable at the same time. Personally though, I think a subset of Theory of Point Estimation by Lehmann, Mathematical Statistics by Shao, and Keener should cover almost all ... | rigorous statistical-inference book recommendation | One book not mentioned above which I quite like is Theoretical Statistics, Topics for a Core Course by Keener. It is relatively rigorous but quite readable at the same time. Personally though, I think | rigorous statistical-inference book recommendation
One book not mentioned above which I quite like is Theoretical Statistics, Topics for a Core Course by Keener. It is relatively rigorous but quite readable at the same time. Personally though, I think a subset of Theory of Point Estimation by Lehmann, Mathematical Stat... | rigorous statistical-inference book recommendation
One book not mentioned above which I quite like is Theoretical Statistics, Topics for a Core Course by Keener. It is relatively rigorous but quite readable at the same time. Personally though, I think |
41,991 | rigorous statistical-inference book recommendation | Take a look at Testing Statistical Hypotheses by Erich Lehmann and Joseph Romano. I also like Statistical Inference by Casella and Berger. | rigorous statistical-inference book recommendation | Take a look at Testing Statistical Hypotheses by Erich Lehmann and Joseph Romano. I also like Statistical Inference by Casella and Berger. | rigorous statistical-inference book recommendation
Take a look at Testing Statistical Hypotheses by Erich Lehmann and Joseph Romano. I also like Statistical Inference by Casella and Berger. | rigorous statistical-inference book recommendation
Take a look at Testing Statistical Hypotheses by Erich Lehmann and Joseph Romano. I also like Statistical Inference by Casella and Berger. |
41,992 | rigorous statistical-inference book recommendation | I recommend the book Mathematical Statistics by Keith Knight, a very friendly introduction that covers all the basics you need to know to study statistics at a high level. | rigorous statistical-inference book recommendation | I recommend the book Mathematical Statistics by Keith Knight, a very friendly introduction that covers all the basics you need to know to study statistics at a high level. | rigorous statistical-inference book recommendation
I recommend the book Mathematical Statistics by Keith Knight, a very friendly introduction that covers all the basics you need to know to study statistics at a high level. | rigorous statistical-inference book recommendation
I recommend the book Mathematical Statistics by Keith Knight, a very friendly introduction that covers all the basics you need to know to study statistics at a high level. |
41,993 | Book recommendations for Design of Experiments? [duplicate] | There is a book by John Lawson Design and Analysis of Experiments with R and he has developed a companion library called daewr. It's easy to follow. Good luck | Book recommendations for Design of Experiments? [duplicate] | There is a book by John Lawson Design and Analysis of Experiments with R and he has developed a companion library called daewr. It's easy to follow. Good luck | Book recommendations for Design of Experiments? [duplicate]
There is a book by John Lawson Design and Analysis of Experiments with R and he has developed a companion library called daewr. It's easy to follow. Good luck | Book recommendations for Design of Experiments? [duplicate]
There is a book by John Lawson Design and Analysis of Experiments with R and he has developed a companion library called daewr. It's easy to follow. Good luck |
41,994 | Chi-squared test for continuous variables (averages) | The question you are asking could be answered by performing what is very often called a 2-way ANOVA (also called two factor analysis of variance in Zar's Biostatistical Analysis).
Side comment: What I find very interesting in the way you ask your question is that indeed there are striking similarities between a 2-way A... | Chi-squared test for continuous variables (averages) | The question you are asking could be answered by performing what is very often called a 2-way ANOVA (also called two factor analysis of variance in Zar's Biostatistical Analysis).
Side comment: What I | Chi-squared test for continuous variables (averages)
The question you are asking could be answered by performing what is very often called a 2-way ANOVA (also called two factor analysis of variance in Zar's Biostatistical Analysis).
Side comment: What I find very interesting in the way you ask your question is that ind... | Chi-squared test for continuous variables (averages)
The question you are asking could be answered by performing what is very often called a 2-way ANOVA (also called two factor analysis of variance in Zar's Biostatistical Analysis).
Side comment: What I |
41,995 | Chi-squared test for continuous variables (averages) | On the first part at least, I think it's wrong to say you can use the Chi2 test "to determine if the NUMBER of whales/sharks are independent to ocean location". One can use the Chi2 test to determine "whether observations of a big animal is whale or shark are independent to ocean location". And for this hypothesis, you... | Chi-squared test for continuous variables (averages) | On the first part at least, I think it's wrong to say you can use the Chi2 test "to determine if the NUMBER of whales/sharks are independent to ocean location". One can use the Chi2 test to determine | Chi-squared test for continuous variables (averages)
On the first part at least, I think it's wrong to say you can use the Chi2 test "to determine if the NUMBER of whales/sharks are independent to ocean location". One can use the Chi2 test to determine "whether observations of a big animal is whale or shark are indepen... | Chi-squared test for continuous variables (averages)
On the first part at least, I think it's wrong to say you can use the Chi2 test "to determine if the NUMBER of whales/sharks are independent to ocean location". One can use the Chi2 test to determine |
41,996 | Making simple simulation to confirm power of statistical test? | The test you used in your simulation isn't a t-test because you used 1.96 instead of a t-value and you used the true standard deviation instead of the sample standard deviation. Your simulation was approximating the power of the corresponding "z test":
> pwr.norm.test(d = 0.5, n = 25, power = NULL)
Mean power cal... | Making simple simulation to confirm power of statistical test? | The test you used in your simulation isn't a t-test because you used 1.96 instead of a t-value and you used the true standard deviation instead of the sample standard deviation. Your simulation was ap | Making simple simulation to confirm power of statistical test?
The test you used in your simulation isn't a t-test because you used 1.96 instead of a t-value and you used the true standard deviation instead of the sample standard deviation. Your simulation was approximating the power of the corresponding "z test":
> pw... | Making simple simulation to confirm power of statistical test?
The test you used in your simulation isn't a t-test because you used 1.96 instead of a t-value and you used the true standard deviation instead of the sample standard deviation. Your simulation was ap |
41,997 | How to test whether a time series of measurements have converged to an equilibrium | Calculate the root mean square deviation in a sliding window over the course of a time series. Set a threshold to define "Convergence". Stop when the root mean square value falls below the threshold. i.e.
$$WindowRMSD_j=\sqrt{\frac{\sum_{i=1}^n(x_i-\bar{x})^2 }{n-1}}$$
where $n$ is the window size, $j$ is the current ... | How to test whether a time series of measurements have converged to an equilibrium | Calculate the root mean square deviation in a sliding window over the course of a time series. Set a threshold to define "Convergence". Stop when the root mean square value falls below the threshold. | How to test whether a time series of measurements have converged to an equilibrium
Calculate the root mean square deviation in a sliding window over the course of a time series. Set a threshold to define "Convergence". Stop when the root mean square value falls below the threshold. i.e.
$$WindowRMSD_j=\sqrt{\frac{\sum... | How to test whether a time series of measurements have converged to an equilibrium
Calculate the root mean square deviation in a sliding window over the course of a time series. Set a threshold to define "Convergence". Stop when the root mean square value falls below the threshold. |
41,998 | practical implementation detail of Bayesian Optimization | The norm is to use any global optimizer you like. The problem is that the EI surface is highly multi-modal and disconnected; optimizing this acquisition function is a nontrivial problem in itself.
A common choice that I have seen in various papers is the DIRECT algorithm; sometimes I've seen CMA-ES which is a state-of-... | practical implementation detail of Bayesian Optimization | The norm is to use any global optimizer you like. The problem is that the EI surface is highly multi-modal and disconnected; optimizing this acquisition function is a nontrivial problem in itself.
A c | practical implementation detail of Bayesian Optimization
The norm is to use any global optimizer you like. The problem is that the EI surface is highly multi-modal and disconnected; optimizing this acquisition function is a nontrivial problem in itself.
A common choice that I have seen in various papers is the DIRECT a... | practical implementation detail of Bayesian Optimization
The norm is to use any global optimizer you like. The problem is that the EI surface is highly multi-modal and disconnected; optimizing this acquisition function is a nontrivial problem in itself.
A c |
41,999 | Why use quantile regression instead of splitting the data in quantiles and calculating multiple linear regressions? | You need to look at the difference between conditional and unconditional quantiles.
Your approach analyzes unconditional quantiles of $y$, and how they depend on $x$. That may be a worthwhile question to ask, but it is not the question that quantile regression discusses.
Quantile regression analyzes quantiles of $y$ co... | Why use quantile regression instead of splitting the data in quantiles and calculating multiple line | You need to look at the difference between conditional and unconditional quantiles.
Your approach analyzes unconditional quantiles of $y$, and how they depend on $x$. That may be a worthwhile question | Why use quantile regression instead of splitting the data in quantiles and calculating multiple linear regressions?
You need to look at the difference between conditional and unconditional quantiles.
Your approach analyzes unconditional quantiles of $y$, and how they depend on $x$. That may be a worthwhile question to ... | Why use quantile regression instead of splitting the data in quantiles and calculating multiple line
You need to look at the difference between conditional and unconditional quantiles.
Your approach analyzes unconditional quantiles of $y$, and how they depend on $x$. That may be a worthwhile question |
42,000 | What is the motivation for the entropy term in the proof of EM algorithm? | I would not say that the entropy is the most important piece of the proof. I will try to explain where the entropy term comes from in the following.
I will follow the notation used in the reference you provided. The goal of the EM algorithm is to maximize the log-likelihood function $l(D ; \theta)$ on a set of $n$ trai... | What is the motivation for the entropy term in the proof of EM algorithm? | I would not say that the entropy is the most important piece of the proof. I will try to explain where the entropy term comes from in the following.
I will follow the notation used in the reference yo | What is the motivation for the entropy term in the proof of EM algorithm?
I would not say that the entropy is the most important piece of the proof. I will try to explain where the entropy term comes from in the following.
I will follow the notation used in the reference you provided. The goal of the EM algorithm is to... | What is the motivation for the entropy term in the proof of EM algorithm?
I would not say that the entropy is the most important piece of the proof. I will try to explain where the entropy term comes from in the following.
I will follow the notation used in the reference yo |
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