instruction
stringlengths
9
38.7k
As per answers to this question, there are shortcomings in the heuristics of deciding on the number of clusters. A more robust approach could be probability based clustering: from a probabilistic perspective, the goal of clustering is to find the most likely set of clusters given the data. Thus, we can never be "100% s...
The most well-known bandit algorithm is upper confidence bound (UCB) which popularized this class of algorithms. Since then I presume there are now better algorithms. What is the current best algorithm (in terms of either empirical performance or theoretical bounds)? Is this algorithm optimal in some sense?
I recently came across this work: http://cvlab.epfl.ch/alumni/oezuysal/ferns.html which is a balance between the full naive Bayes assumption (full independence between the features) and absolutely no independence assumption. This seems like a very appealing idea. Is there more work like this?
There seem to be many machine learning algorithms that rely on kernel functions. SVMs and NNs to name but two. So what is the definition of a kernel function and what are the requirements for it to be valid?
See also a similar question on stats.SE. In boosting algorithms such as AdaBoost and LPBoost it is known that the "weak" learners to be combined only have to perform better than chance to be useful, from Wikipedia: The classifiers it uses can be weak (i.e., display a substantial error rate), but as long as their perf...
How does a Support Vector Machine (SVM) work, and what differentiates it from other linear classifiers, such as the Linear Perceptron, Linear Discriminant Analysis, or Logistic Regression? * (* I'm thinking in terms of the underlying motivations for the algorithm, optimisation strategies, generalisation capabilities, a...
Canonical Correlation Analysis (CCA) (and its kernel equivalent (KCCA)) can be used to find linear (nonlinear) relationships between two aligned multivariate datasets (or views). Is there a way to extend this to more than two views? I suppose one way would be to apply CCA/KCCA recursively in a tree structure, but this ...
Pulsed or Spiking neural networks incorporate more of the membrane dynamics of biological neurons, where pulses carry information to the next layer. The neurons do not necessarily have to "fire" all at the same time, as they would in a backprop, for example. Yet, there seem to be barriers against employing these model...
Originally posted in stats.SE but never got an answer so reposting here. Is it ever a bad idea to normalise the kernel matrix? By this I mean the method described on page 113 of Shawe-Taylor & Cristianini's "Kernel Methods for Pattern Analysis" (matlab notation): % original kernel matrix stored in variable K % output u...
Basically, there are two common ways to learn against huge datasets (when you're confronted by time/space restrictions): Cheating :) - use just a "manageable" subset for training. The loss of accuracy may be negligible because of the law of diminishing returns - the predictive performance of the model often flattens o...
A common problem is ML is poor quality of the data: errors in feature values, misclassified instances, etc etc. One way of addressing this problem is to manually go through the data and check, but are there other techniques? (I bet there are!) Which ones are better and why?
As we saw in this question, the recommended strategy of building a decision tree is postpruning. The two methods for that are subtree replacement and subtree raising. At each node, an algorithm decides whether it should perform subtree replacement, subtree raising, or leave the subtree as is. Subtree replacement sele...
In reinforcement learning, what is the difference between dynamic programming and temporal difference learning?
By building the complete tree and pruning it afterward we are adopting a strategy of postpruning (or backward pruning) rather than prepruning (or forward pruning). Prepruning would involve trying to decide during the tree-building process when to stop developing subtrees. It's attractive because allows to avoid all the...
Possible Duplicate: How can I help ensure testing data does not leak into training data? Overfitting is obviously a significant problem in machine-learning...perhaps the most significant problem. I believe a main reason for that is that it is often easy to accidentally overfit in subtle ways, particularly with resp...
Suppose we measure the classifier error on a test set and obtain a certain success rate - say, 75%. Now, of course, this is only one measurement - how to calculate the "true" success rate? Sure it will be close to 75% but how close? I understand it's related to confidence intervals but now I'm lost in confidence inter...
A Recommender System would measure the correlation between ratings of different users and yield recommendations for a given user about the items which may be of interest to him. However, tastes change over time so old ratings might not reflect current preferences and vice versa. You may once have put "excellent" to a b...
A common pre-processing step for machine learning algorithms is whitening of data. It seems like it is always good to do whitening since it de-correlates the data, making it simpler to model. When is whitening not recommended? Note: I'm referring to de-correlation of the data.
I'm looking for a way to model and extract features from multivariate temporal data (e.g., multi-channel audio recordings). I'm specifically interested in deep learning methods such as RBM, sparse autoencoders and so on. Most methods I encountered consider only one dimension of the data, or maybe a 2D "block" in the da...
What is the best way to automatically select features for anomaly detection? I normally treat Anomaly Detection as an algorithm where the features are selected by human experts: what matters is the output range (as in "abnormal input - abnormal output") so even with many features you can come up with a much smaller sub...
I'm new to concept of HMMs. I have trained 2 HMMs separately. HMM1 is trained with symbols A, B, C. HMM2 is trained with symbols D, E, F. I have a set of observation symbols in the set V={A,B,C,D,E,F}. In testing phase, I'm extracting a symbol by trying to associate a test vector to one of the symbols in V (using eu...
When doing natural language processing, one can take a corpus and evaluate the probability of the next word occurring in a sequence of n. n is usually chosen as 2 or 3 (bigrams and trigrams). Is there a known point at which tracking the data for the nth chain becomes counterproductive, given the amount of time it ta...
I was looking at the Fiducial Inference page on wikipedia, which is an alternative to the traditional Frequentist and Bayesian standpoints. Although it was out of favour in mainstream statistics for many years, there seems to have been a resurgence in interest in recent years (see for example Jan Hannig's recent public...
A signal processing technique, the Mel frequency Cepstrum, is often used to extract information from a musical piece for use in a machine learning task. This method gives a short-term power spectrum, and the coefficients are used as input. In designing music retrieval systems, such coefficients are considered characte...
After playing way too much Angry Birds, I started to observe my own strategies. It turns out that I developed a very specific approach to getting 3 stars on each level. That made me wonder about the challenges of developing a machine learning system that would be able to play Angry Birds. Interacting with the game and ...
A limitations of standard neural net algorithms (like backprop) is that you have to make a design decision of how many hidden layers and neurons-per-layer you want. Usually, the learning rate and generalization is highly sensitive to these choices. This has been the reason, why neural net algorithms like cascade correl...
I encounter it in many books as well as web. Natural Language Processing and Machine Learning are said to be different subsets of Artificial Intelligence. Why is it? We can achieve results of Natural Language Processing by feeding sound patterns to Machine Learning algorithms. Then, what's the difference?
I am creating a Recommender System and want to incorporate both the ratings of "similar" users and the features of the items. The output is a predicted rating [0-1].I am considering a Neural Network (to start with). So, the inputs are a combination of the features of the items and the ratings of each user. For item A a...
As part of an assignment I'll have to write a genetic programming algorithm that does prediction of atmospheric pollutant levels. Since I have no experience, can anyone point me pointers to propositions of programming languages in which evolved programs will be written. Clarification: I'm not asking what will be the l...
Back in the 1990s, network topologies like Bidirectional Associative Memory and Hopfield Nets were all the rage. Largely, these were billed as having energy states and recurrents that would help them learn/store and recall specific patterns readily. These topologies are perhaps less pertinent now, but I'm wondering if...
What are some approaches for classifying data with a variable number of features? As an example, consider a problem where each data point is a vector of x and y points, and we don't have the same number of points for each instance. Can we treat each pair of x and y points as a feature? Or should we just summarize the p...
I found Project Euler http://projecteuler.net/ to be incredibly useful in learning programming languages. Is there a similar site for Machine Learning? I did see http://www.kaggle.com/, but it is not nearly as accessible to beginners as Project Euler.
Recently there was a ML-like question over on cstheory stackexchange, and I posted an answer recommending Powell's method, gradient descent, genetic algorithms, or other "approximation algorithms". In a comment someone told me these methods were "heuristics" and not "approximation algorithms" and frequently did not com...
I have a set of Observation Symbol Sequences which I have to test against a set of Trained HMM classifiers. I seem to understand the advantages of using Log Probability over regular probabilities. In the testing phase of a HMM classifier, I don't seem to get the motivation behind multiplying probabilities or adding log...
I've been reading a lot recently about the concept of joint regularization in computer vision. Joint regularization builds on the observation that when learning multiple related concepts, for example "cat" and "dog" the most of the useful features to classify something as "cat" should be useful to classify something as...
I'm trying to classify messages into different categories using an SVM. I've compiled a list of desirable words/symbols from the training set. For each vector, which represents a message, I set the corresponding row to 1 if the word is present: "corpus" is: [mary, little, lamb, star, twinkle] first message: "mary had...
We find the cluster centers and assign points to k different cluster bins in k-means clustering which is a very well known algorithm and is found almost in every machine learning package on the net. But the missing and most important part in my opinion is the choice of a correct k. What is the best value for it? And, ...
I wonder why do we use the Gaussian assumption when modelling the error. In Stanford's ML course, Prof. Ng describes it basically in two manners: It is mathematically convenient. (It's related to Least Squares fitting and easy to solve with pseudoinverse) Due to the Central Limit Theorem, we may assume that there are ...
A paper "Accurately computing running variance" at http://www.johndcook.com/standard_deviation.html shows how to compute running mean, variance and standard deviations. Are there algorithms where the parameters of a linear or logistic regression model can be similarly "dynamically" updated as each new training record i...
I have come across some basic ways to measure the complexity of neural networks: Naive and informal: count the number of neurons, hidden neurons, layers, or hidden layers VC-dimension (Eduardo D. Sontag [1998] "VC dimension of neural networks" [pdf].) A course grained and asymptotic computational complexity measure by...
There has been a recent interest in combining genetic algorithms and neural networks into a general neuroevolution framework. The basic idea, is that your genetic algorithm is evolving the parameters of many neural-network which are then used to solve your task at hand. A sort of genetic programming but instead of evol...
In Stanford's Machine Learning course Andrew Ng mentioned applying ML in IT. Some time later when I got moderate size(about 20k bots) DDoS on our site I decided to fight against it using simple Neural Network classifier. I've written this python script in about 30 minutes: https://github.com/SaveTheRbtz/junk/tree/maste...
Naive Bayes classifiers are a popular choice for classification problems. There are many reasons for this, including: "Zeitgeist" - widespread awareness after the success of spam filters about ten years ago Easy to write The classifier model is fast to build The model can be modified with new training data without hav...
Excuse me I'm not an English speaker and I have no idea whatsoever whether there is any standard naming scheme. And since I don't want to use names I have read in some books I will be overly descriptive. Let's suppose I want to describe a dataset containing data for prediction of weather pollutants. Each row of this d...
There are many situations where you may train several different classifiers, or use several different feature extraction methods. In the literature authors often give the mean classification error over a set of random splits of the data (i.e. after a doubly nested cross-validation), and sometimes give variances on the ...
Possible Duplicate: Bayesian and frequentist reasoning in plain English A very similar question was posed on stats.SE: Bayesian and frequentist reasoning in plain English, which provoked some interesting debate. However the debate is very focussed on how a statistician would behave, and doesn't really answer the que...
Feature engineering is often an important component to machine learning (it was used heavily to win the KDD Cup in 2010). However, I find that most feature engineering techniques either destroy any intuitive meaning of the underlying features or are very specific to a particular domain or even particular types of f...
Regarding Hawkins' HTM algorithm. Has anyone found a fruitful method to define the number of nodes in a layer and number of layers in a network?
I am intrigued by the concept of a Maximum Entropy Markov Model (MEMM), and I am thinking of using it for a Part of Speech (POS) tagger. At the moment, I am using a conventional Maximum Entropy (ME) classifier to tag each individual word. This uses a number of features, including the preceding two tags. MEMMs use the...
I am using SVM models to do short term forecasting of air pollutants. To train a new model I need to find appropriate metaparameters for an SVM model (I mean C, gamma and so on). Libsvm documentation (and many other books I have read) suggests using grid search to find these parameters - so I basically train model for...
I have collected responses from 85 people on their ability to undertake certain tasks. The responses are on a five point Likert scale: 5 = Very Good, 4 = Good, 3 = Average, 2 = Poor, 1 = Very Poor, The mean score is 2.8 and the standard deviation is 0.54. I understand what the mean and standard deviation stand for. M...
I am trying to estimate the following unobserved components model using the MARSS package $y_t = \mu_t + \varepsilon_t $ $\mu_t = \mu_{t-1} + \beta_{t-1}$ $\beta_t = \beta_{t-1} + \zeta_{t}$ with a restriction on the variance of the errors: $\sigma^2_{\zeta} = \frac{1}{\lambda}\sigma^2_{\varepsilon}$ for a given $\lam...
Let $\mathbb P(X=1) = \mathbb P(X=-1) = 1/2$. Define $$X_n = \begin {cases} X & \text{with probability } 1- \frac{1}{n}\\ e^n & \text{with probability } \frac{1}{n} \end {cases}$$ Does $X_n \leadsto X$ (i.e., converge in distribution)? Does $X_n \stackrel{P}{\rightarrow} X$? Does $\mathbb{E}[(X-X_n)^2] \to 0$? I...
How do I interpret this predictive model? S&P500 Next Week = Earnings Per Share * 0.25 + Dividends Per Share * -1.519 + Current S&P500* 1.018 + 5.409
Context In transportation planning, agent-based microsimulation is a method to deal with the complexity of the problem. Instead of computing aggregate flows (as in the classical four-step model), agents (persons, households, businesses, ...) are simulated on an individual basis. Results are obtained by aggregating afte...
I have percentile data (P10, P25, P75 and P90) for a variable. I also have the mean and median for each group: group mean median P10 P25 P75 P90 1 30100 26200 19900 22500 32800 44200 2 38700 36600 28000 31500 44000 52100 How do I: Create a probability density functio...
I am working on a determining why certain employees cause errors in a company's process and why others do not. I have the employee information, information about the errors they have made and the teams that the employees are in. All the employees in all the teams have caused errors at one point or another. What i want...
First, let's assume that we want to generated from a Dirichlet(1,1,1,1) distribution. Would the following method be correct?: generate three variates from a Uniform(0,1). Call them $x_1$, $x_2$, $x_3$. then, order these such that $0 \leq x_{(1)} \leq x_{(2)} \leq x_{(3)} \leq 1$ then, return the differences as our Dir...
One question I have carried around with me for a while is related to including quadratic terms for model specifications. I wonder why it is considered ok to include linear and quadratic terms into OLS analysis, despite the fact that the Variance Inflation Factor (VIF) gets high. A model specification that I was taught ...
I'm sure this is a simple problem, but I'm not sure how to search and find the answer. I have a set of parameters that I've estimated using 'fitdist': Fitting of the distribution ' gamma ' by matching moments Parameters: estimate shape 0.2018062 rate 3.1255336 Now I want to pull those parameters and store the...
Could someone please help explain how to calculate $P(A)$ given: $ P(B) = 0.2 $ $P(A|B) = 0.6$ $P(A|{\rm not} \ B) = 0.6$ Any explaination/help would be greatly appreciated.
I am applying Neural network and SVM to predict buy-hold - sell signals. I have trained nn and SVM in R. I used nnet function to train NN and svm to train SVM. I provided 20,000 data points to train and 2000 data points to test. training data set contain list of 10-15 technical indciators and buy-sell-hold signals. The...
I don't understand why predictions from lm.ridge() are so far out, when using the "best" lambda, based upon GCV. Can anyone help me to obtain better predictions? Or, at least, does anyone have a good ridge example with a simple explanation of the results? Below is my R code for wine quality data (from http://archive.ic...
Are there standard algorithms (as opposed to programs) for doing hierarchical linear regression? Do people usually just do MCMC or are there more specialized, perhaps partially closed form, algorithms?
I'm coming from a computer science domain with an estimation problem that I'm trying to address. My background isn't statistics, so I apologize if the terminology is bad. I've been reading various topics related to model estimation, but the area seems enormous. So, I'll describe the problem below, and it would be extre...
I posted the same question on math.stackexchange, but haven't got any reply. So I will try my luck here: In the context of robust statistics, there is the concept of breakdown point, which basically measures the proportion of outliers an estimator can handle before giving an arbitrary result: http://en.wikipedia.org/wi...
Whenever boosting is brought up, Adaboost is the first algorithm to be listed. What are the most popular boosting algorithms that aren't Adaboost?
Here is a block diagram which I'm using when I want to verify that my model is real. In each round a fold of 11/12 percent of the data is used to bulid the model (e.g. eigenvectors of the PCA) After 12 rounds I check that the models (e.g the eigenvectors of the PCA) from each round are not statistically different a...
This is a question I have posted here some while ago. and I would like to know if you think of more solutions for it from the ML perspective? Unfortunately, I can't use McNemar's test due to the small sample size (hence the values are not normally distributed) How can I compare whether a classifier's output is signif...
Functional principal component analysis (FPCA) is something I have stumbled upon and never got to understand. What is it all about? See "A survey of functional principal component analysis" by Shang, 2011, and I'm citing: PCA runs into serious difficulties in analyzing functional data because of the “curse of dimens...
Yesterday I asked this question in which I had 180 subjects with 500 features each. While I was sure that dimensional-reduction is a must in this case (500 features), most of the answers I got said that 500 are not too many. So, My question is: Is there any rule of thumb when one should use dimensional-reduction before...
In neuroscience it is very common to measure the reaction time (RT) of subjects. Based on the RT conclusions can be made about personal working memory capability, IQ etc. So I have such data, which came from some neuroscience experiment. In this data I have 180 subjects from two groups (90 subjects in each group) for...
This question is about using PCA as a dimension reduction method before feeding the data into a classifier. It's a common procedure to use PCA for a data set which contains a large number of features, and to only use the first several PCA-scores instead of the original features. My question is: After the PCA score has ...
The regret in a multi-arm bandit model is given by $$\underset{j}{\max}\sum_{t=1}^{T}x_j(t) -G_{A}$$ where $$G_A=\sum_{t=1}^{T}x_{it}(t)$$ is the total reward achieved by the learner, based on an action $i$, taken at each time interval $t$, i.e $i_{t}\in {1,2,...,K}$ and $x_j(t)$ is the reward assosciated with action ...
How would one go about testing an implementation of a Bayes Factor calculation? The analogue in Frequentist hypothesis testing is fairly straightforward: generate data according to the null hypothesis, use the code to generate a p-value, repeat thousands of times with different random seeds, and look for uniformity of ...
I am trying to implement Apriori algorithm. However I have a small doubt what to do when the same item appears more than once in the one basket,I have 2 transactions say T1 = {A,A,C} T2 = {A,X} What is the support of A ? Is it 3 or 2 ?
I am trying to introduce my data into SPSS. At the moment i am very confused. My questionnaire comprises 8 statements, where participants have ranked from strongly disagree to strongly agree their opinions. so far so simple. the only problem is, that for each of the 8 statements there are 8 characters that the particip...
I have likert scale responses (1-5 rating) of 20 respondents for a set of 25 questions. So that means that each respondent has answered 25 questions (with 1-5 rating). If I need to check the normality distribution of all the 25 questions together for a particular respondent, how do i do that?
ok i am not a statistician. I am doing paired comparison for several outcomes of cross validated interpolation results. I have to consider only the absolute value in my analysis and so although original data follows a normal distribution the resultant absolute values are only half normal. So is the t-test still valid a...
If I have a binomial maximum likelihood function $$ L(\theta | k) = \Pi_i^N p(\theta)^{k_i}(1-p(\theta))^{(n_i-k_i)}$$ I know that the index terms can be made into a sum, simplifying the expression for calculation purposes. I have a model which predicts the probability of success as a function of a variable (x) and a ...
When is is appropropriate to include or exclude the intercept from a regression model? SPSS provides this option in the GLM menu. I am assessing group difference (gender) on tasks performed (X) and income earned (Y). In this case, if no task is performed, then no income is earned. The SPSS guidelines states here: "I...
I am carrying out SVM and was interested in knowing the parameters that could be varied for each kernel. I am using 3 kernels: RBF, linear and polynominal. These are the parameters that i think can be changed: For Linear : C For RBF: C and gamma For Polynominal : C and gamma Would like to hear some feedback whether i ...
I use glm.nb from MASS package over many observations. I then extract the p-values for the interaction term. Due to multiple testing, I use BH method for correction for multiple testing, with FDR of 0.05. Sometimes, when I apply the negative binomial model to fit to the data, the model doesn't converge and ends up with...
Today, at the Cross Validated Journal Club (why weren't you there?), @mbq asked: Do you think we (modern data scientists) know what significance means? And how it relates to our confidence in our results? @Michelle replied as some (including me) usually do: I'm finding the concept of significance (based on p-values)...
I have n subjects observed over some time $t{\scriptscriptstyle n}<T$ . At several time points during $T$, I measure in each subject the value of an ordinal variable $V$ (which can take 5 values). Not every subject has measurements in every time point and there is censoring of the subjects during T. I would like to mod...
This is my first post on CV. I am wrapping my head around Maximum Likelihood Estimation (MLE), and ironically, I understand everything about the algorithm, except the starting point. What confuses me is the following: All the examples I have seen of course, start with some vector of observations, x1, x[2], ... x[N]. T...
My data is count data. What I did is identifying if embryos had (yes = 1) or not (no = 0) malformations or delay in their development, within samples of 15 embryos. In one type of experiment, I repeated this 6 times (6 independent replicates); in another type, I repeated this 9 times (9 independent replicates), so my ...
In a longitudinal study, two groups of subjects have been measured over a period of two years at 6 months intervals. During these measurements subjects have been assessed with a series of $k$ measures ($M_1$ to $M_k$). From other sources we expect to see a difference between the groups and a decline in the performance...
I have a data set, whose elements (say 1,000 elements) are numeric with values between 0 and 1. It is safe to think the elements are independent from each other, i.e, the order of these elements does not matter at all. Also, from the histogram of the data set, I can tell it does not follow any parametric distribution (...
I read on this exchange a heuristic method of estimating gamma for the rbf kernel in SVMs. I was wondering if someone might be able to explain it to me in a little more detail? I believe you select 1000 (or a large number) of pairs of datapoints from the dataset then calculate the norm for the difference of each pair. ...
Does rpart function require normalized data when using the "anova" method? Im assuming so, but I do not like to assume. I have looked and no where has it said it needs to be, but the method makes me think it does. Thanks Scott
This question is a follow-up on my previous question. Suppose I have a Brownian motion process that is defined as follows: at time $i=1$ random variable $X_1\sim\mathbf{N}(\mu,\sigma^2)$, and, for any subsequent random variables $X_i$ and $X_j$ such that $i<j$, $X_j-X_i\sim\mathcal{N}(0,(j-i)\sigma^2)$. I collect $n$...
I am trying to test the significance of the difference between two populations. Here is a link to the population 1 data: http://pastebin.com/914mCRqA and population 2 data: http://pastebin.com/PmDgLLAb Could someone tell me whether it is best to use median or mean and hence what test to use? I was thinking of using the...
I came across this nice illustration of the "Coefficient of determination" (source): Which leads me to ask two questions: How to do it with R? (I guess my main question would be how to deal with the opacity) Are there other interesting/useful visualizations of the "Coefficient of determination"? (and again, is there...
I would like to compute the Wilcoxon rank-sum test in Stata for two countries of my sample with the dummyvalue 3 and 6. Can anyone give the right code for Stata?
I have calculated the correlation between A and B for 10 different subjects. For averaging purposes, I've converted the r-values to z-values using Fisher's z-transformation. subj zvalue s1 -0.04 s2 -0.14 s3 -0.29 s4 -0.20 s5 -0.37 s6 -0.01 s7 -0.09 s8 0.20 s9 -0.15 s10 0.09 I want to test if the correlation between...
I'm hoping someone can explain this bit of R code for me related to glm(). I don't understand the diagnostic plot that has been suggested. It seems a more informative plot would be to plot against the fitted values, but maybe I don't understand something. Here's the code: result <- glm(survive~age, data=donner, family=...
In Poisson Regression, suppose we have the following regression equation: $\ln(E(Y_i|X_1)) = \beta_0+ \beta_{1}X_{1}$ where $Y$ is the number of heart attacks. Also suppose $X_1$ is a binary variable (e.g. smokers versus non-smokers). How would you interpret the coefficient $\beta_1$? Smokers, on average, have $\exp(\b...
I am confused how to interpret the result of performing a normalized correlation with a constant vector. Since you have to divide by the standard deviation of both vectors (reference: http://en.wikipedia.org/wiki/Cross-correlation ), if one of them is constant (say a vector of all 5's, which has standard deviation of z...
I'm reading the book "Collective Intelligence" and in one chapter they introduce how to measure similarity between users on a movie review website with euclidean distance. Now are the movies rated all on the scale from 1-5. But what if I want to find similar users based on features like - lets say body height, body wid...