This paper describes a distributed MapReduce implementation of the minimum Redundancy Maximum Relevance algorithm, a popular feature selection method in bioinformatics and network inference problems. The proposed approach handles both tall/narrow and wide/short datasets. We further provide an open source implementation based on Hadoop/Spark, and illustrate its scalability on datasets involving millions of observations or features.
Feature selection is an important and challenging task in high dimensional clustering. For example, in genomics, there may only be a small number of genes that are differentially expressed, which are informative to the overall clustering structure. Existing feature selection methods, such as Sparse K-means, rarely tackle the problem of accounting features that can only separate a subset of clusters. In genomics, it is highly likely that a gene can only define one subtype against all the other subtypes or distinguish a pair of subtypes but not others. In this paper, we propose a K-means based clustering algorithm that discovers informative features as well as which cluster pairs are separable by each selected features. The method is essentially an EM algorithm, in which we introduce lasso-type constraints on each cluster pair in the M step, and make the E step possible by maximizing the raw cross-cluster distance instead of minimizing the intra-cluster distance. The results were demonstrated on simulated data and a leukemia gene expression dataset.
Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. Here, we introduce a new approach -- the Bayesian Ising Approximation (BIA) -- to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high dimensional regression by analyzing a gene expression dataset with nearly 30,000 features.
High-dimensional feature selection is a central problem in a variety of application domains such as machine learning, image analysis, and genomics. In this paper, we propose graph-based tests as a useful basis for feature selection. We describe an algorithm for selecting informative features in high-dimensional data, where each observation comes from one of $K$ different distributions. Our algorithm can be applied in a completely nonparametric setup without any distributional assumptions on the data, and it aims at outputting those features in the data, that contribute the most to the overall distributional variation. At the heart of our method is the recursive application of distribution-free graph-based tests on subsets of the feature set, located at different depths of a hierarchical clustering tree constructed from the data. Our algorithm recovers all truly contributing features with high probability, while ensuring optimal control on false-discovery. Finally, we show the superior performance of our method over other existing ones through synthetic data, and also demonstrate the utility of the method on a real-life dataset from the domain of climate change.
We introduce a new method of performing high dimensional discriminant analysis, which we call multiDA. We achieve this by constructing a hybrid model that seamlessly integrates a multiclass diagonal discriminant analysis model and feature selection components. Our feature selection component naturally simplifies to weights which are simple functions of likelihood ratio statistics allowing natural comparisons with traditional hypothesis testing methods. We provide heuristic arguments suggesting desirable asymptotic properties of our algorithm with regards to feature selection. We compare our method with several other approaches, showing marked improvements in regard to prediction accuracy, interpretability of chosen features, and algorithm run time. We demonstrate such strengths of our model by showing strong classification performance on publicly available high dimensional datasets, as well as through multiple simulation studies. We make an R package available implementing our approach.
Feature selection is an important tool to deal with high dimensional data. In unsupervised case, many popular algorithms aim at maintaining the structure of the original data. In this paper, we propose a simple and effective feature selection algorithm to enhance sample similarity preservation through a new perspective, topology preservation, which is represented by persistent diagrams from the context of computational topology. This method is designed upon a unified feature selection framework called IVFS, which is inspired by random subset method. The scheme is flexible and can handle cases where the problem is analytically intractable. The proposed algorithm is able to well preserve the pairwise distances, as well as topological patterns, of the full data. We demonstrate that our algorithm can provide satisfactory performance under a sharp sub-sampling rate, which supports efficient implementation of our proposed method to large scale datasets. Extensive experiments validate the effectiveness of the proposed feature selection scheme.