Examples of algorithms to get you started with WEKA: logistic regression, decision tree, neural network and support vector machine.

This is a tough task, I was in this precarious situation trying to explain to my younger son. I had a curated list of top 10 frequently used Machine Learning algorithms, but the key was to do a backward mapping of these Machine Learning techniques to solve problems which are of interest and relevance to my son. As a starting point to the conversation I asked him, list down your decision making points, meaning there may be many situations when you had to make decisions but you may not have all the information. I took those and matched it to the machine learning algorithms while explaining the core concept behind the problem solving. A classifier is a machine learning technique that takes a bunch of data and attempts to predict which class the new data belongs to. Sure, remember sometime back you were asking me who you want to invite to your birthday party and whether they will accept your invitation or not! Now, assume that you have got a data set about all the other 29 kids in your class. The information contains their hobby, kind of books they read, do they share their tiffin or not, are they friendly, in your last birthday did they come and did they bring nice gifts, etc. Now, given these information, you want to predict whether your classmates will accept your invitation or not.

We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process samples are assumed uncorrelated over time and having a time-varying marginal distribution. The selection method is based on testing conditional variances obtained for small subsets of process components. This allows to cope with the high-dimensional regime, where the sample size can be (drastically) smaller than the process dimension. We characterize the required sample size such that the proposed selection method is successful with high probability.

In this paper, we study the performance of extremum estimators from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. By adapting the classical concentration inequalities, we derive upper bounds on the empirical out-of-sample prediction errors as a function of the in-sample errors, in-sample data size, heaviness in the tails of the error distribution, and model complexity. We show that the error bounds may be used for tuning key estimation hyper-parameters, such as the number of folds K in cross-validation. We also show how K affects the bias-variance tradeoff for cross-validation. Simulations are used to demonstrate key results. We would also like to acknowledge participants at the 12th International Symposium on Econometric Theory and Applications and the 26th New Zealand Econometric Study Group as well as seminar participants at Utah, UNSW, and University of Melbourne for useful questions and comments. Fisher would like to acknowledge the financial support of the Australian Research Council, grant DP0663477. 1 1 Introduction Traditionally in econometrics, an estimation method is implemented on sample data in order to infer patterns in a population. Put another way, inference centers on generalizing to the population the pattern learned from the sample and evaluating how well the sample pattern fits the population. An alternative perspective is to consider how well a sample pattern fits another sample. In this paper, we study the ability of a model estimated from a given sample to fit new samples from the same population, referred to as the generalization ability (GA) of the model. As a way of evaluating the external validity of sample estimates, the concept of GA has been implemented in recent empirical research. For example, in the policy evaluation literature [Belloni et al., 2013, Gechter, 2015, Dolton, 2006, Blundell et al., 2004], the central question is whether any treatment effect estimated from a pilot program can be generalized to out-of-sample individuals.

We apply a novel spectral graph technique, that of locally-biased semi-supervised eigenvectors, to study the diversity of galaxies. This technique permits us to characterize empirically the natural variations in observed spectra data, and we illustrate how this approach can be used in an exploratory manner to highlight both large-scale global as well as small-scale local structure in Sloan Digital Sky Survey (SDSS) data. We use this method in a way that simultaneously takes into account the measurements of spectral lines as well as the continuum shape. Unlike Principal Component Analysis, this method does not assume that the Euclidean distance between galaxy spectra is a good global measure of similarity between all spectra, but instead it only assumes that local difference information between similar spectra is reliable. Moreover, unlike other nonlinear dimensionality methods, this method can be used to characterize very finely both small-scale local as well as large-scale global properties of realistic noisy data. The power of the method is demonstrated on the SDSS Main Galaxy Sample by illustrating that the derived embeddings of spectra carry an unprecedented amount of information. By using a straightforward global or unsupervised variant, we observe that the main features correlate strongly with star formation rate and that they clearly separate active galactic nuclei. Computed parameters of the method can be used to describe line strengths and their interdependencies. By using a locally-biased or semi-supervised variant, we are able to focus on typical variations around specific objects of astronomical interest. We present several examples illustrating that this approach can enable new discoveries in the data as well as a detailed understanding of very fine local structure that would otherwise be overwhelmed by large-scale noise and global trends in the data.

Information theoretic measures (e.g. the Kullback Liebler divergence and Shannon mutual information) have been used for exploring possibly nonlinear multivariate dependencies in high dimension. If these dependencies are assumed to follow a Markov factor graph model, this exploration process is called structure discovery. For discrete-valued samples, estimates of the information divergence over the parametric class of multinomial models lead to structure discovery methods whose mean squared error achieves parametric convergence rates as the sample size grows. However, a naive application of this method to continuous nonparametric multivariate models converges much more slowly. In this paper we introduce a new method for nonparametric structure discovery that uses weighted ensemble divergence estimators that achieve parametric convergence rates and obey an asymptotic central limit theorem that facilitates hypothesis testing and other types of statistical validation.

I don't think K-means clustering in R has any special meaning, whatever package you use the basic K-means algorithm remains the same.

Last week, we discussed Multi-class SVM loss; specifically, the hinge loss and squared hinge loss functions. A loss function, in the context of Machine Learning and Deep Learning, allows us to quantify how "good" or "bad" a given classification function (also called a "scoring function") is at correctly classifying data points in our dataset. In fact, if you have done previous work in Deep Learning, you have likely heard of this function before -- do the terms Softmax classifier and cross-entropy loss sound familiar? I'll go as far to say that if you do any work in Deep Learning (especially Convolutional Neural Networks) that you'll run into the term "Softmax": it's the final layer at the end of the network that yields your actual probability scores for each class label. To learn more about Softmax classifiers and the cross-entropy loss function, keep reading.

I happened to recently reread this article of mine from 2010, and I absolutely love it. I don't think it's been read by many people--it was published as one of three discussions of an article by Brad Efron in Statistical Science--so I wanted to share it with you again here. The information principle: the key to a good statistical method is not its underlying philosophy or mathematical reasoning, but rather what information the method allows us to use. Good methods make use of more information. The methodological attribution problem: the many useful contributions of a good statistical consultant, or collaborator, will often be attributed to the statistician's methods or philosophy rather than to the artful efforts of the statistician himself or herself.

The results are a little different to those obtained using RMSE as the objective function. The focus is still well and truly on the volatility indicators, but in this case the best cross validated performance occurred when selecting only 2 out of the 15 candidate variables. Here's a plot of the cross validated performance of the best feature set for various numbers of features: The model clearly performs better in terms of absolute return for a smaller number of predictors. Performance bottoms at 8 predictors and then improves, but never again achieves the performance obtained with 2-4 predictors. This is consistent with Aronson's assertion that we should stick with at most 3-4 variables otherwise overfitting is almost unavoidable.