Information-theoretic Feature Selection via Tensor Decomposition and Submodularity
This work addresses feature selection for machine learning practitioners, offering a more efficient method with performance guarantees, though it appears incremental as it builds on existing tensor decomposition and submodular optimization techniques.
The paper tackles the challenge of feature selection by maximizing high-order mutual information, which requires complex multivariate probability distributions and combinatorial optimization, by introducing a low-rank tensor model and indirect targeting to reduce complexity and improve classification performance. Numerical experiments on standard datasets show the proposed approach compares favorably to state-of-the-art methods.
Feature selection by maximizing high-order mutual information between the selected feature vector and a target variable is the gold standard in terms of selecting the best subset of relevant features that maximizes the performance of prediction models. However, such an approach typically requires knowledge of the multivariate probability distribution of all features and the target, and involves a challenging combinatorial optimization problem. Recent work has shown that any joint Probability Mass Function (PMF) can be represented as a naive Bayes model, via Canonical Polyadic (tensor rank) Decomposition. In this paper, we introduce a low-rank tensor model of the joint PMF of all variables and indirect targeting as a way of mitigating complexity and maximizing the classification performance for a given number of features. Through low-rank modeling of the joint PMF, it is possible to circumvent the curse of dimensionality by learning principal components of the joint distribution. By indirectly aiming to predict the latent variable of the naive Bayes model instead of the original target variable, it is possible to formulate the feature selection problem as maximization of a monotone submodular function subject to a cardinality constraint - which can be tackled using a greedy algorithm that comes with performance guarantees. Numerical experiments with several standard datasets suggest that the proposed approach compares favorably to the state-of-art for this important problem.