Feature Selection for Latent Factor Models

Weighted sums of random kitchen sinks (W-RKS) is a commonly used feature extraction technique for supervised learning tasks. A major drawback of this method is the redundancy and ineffectiveness of many extracted random features. This paper investigates efficient methods for reducing such redundancy in multi-class classification problems. We specifically formulate feature selection as a variant of the sequentially nested model selection problem and introduce the Successive Empirical Excess Risk Difference Maximization (SEED-MAX) algorithm. It recursively computes empirical risks to identify the most parsimonious yet informative set of features. We derive an analytical lower bound for the probability of correct feature selection by the SEED-MAX algorithm. This lower bound on the probability of correct feature selection can be made arbitrarily close to one by increasing the training dataset size. To further enhance the rate of pruning, we evaluate the features retained by SEED-MAX using the Fisher test (F-Test). Empirical evaluations on UCR time-series classification datasets show that the sequential application of SEED-MAX with the Fisher test achieves approximately 92 percent rate of pruning with negligible degradation in classification accuracy. Implementations of the SEED-MAX and SEED-MAX-F-Test methods are available at https://github.com/OmidiAmin/seed-max-ftest.

Feature rankings are widely used in supervised feature selection because they are simple, scalable and easy to interpret. Variables are first ranked by a relevance score, and a subset is then obtained by retaining the top-ranked variables. Although the first stage has been extensively studied, the second is often governed by an arbitrary cardinality, an empirical threshold or cross-validation, without a direct interpretation. This raises a basic question: given a feature ranking, when is there enough accumulated class-separation evidence to stop selecting features? This paper develops a distributional framework for transforming supervised feature rankings into class-independent subsets through an explicit risk-calibrated stopping rule. For each variable and each pair of classes, marginal separation is measured by the Bhattacharyya coefficient between the corresponding class-conditional distributions. The proposed method selects a single global subset shared by all classes by retaining the shortest prefix of a ranking whose residual product overlap falls below a prescribed threshold for every relevant class contrast. We derive binary and multiclass Bayes-risk bounds for the labelled product marginal problem, and obtain prior-dependent and prior-free calibrations of the residual-overlap threshold from a target all-pairs risk level. An empirical comparison on high-dimensional genomic datasets illustrates that the rule can reduce tens of thousands of variables to a few dozen while maintaining predictive performance statistically comparable to the all-features baseline. As the stopping rule only requires one-dimensional marginal overlap estimates and scans a precomputed ranking, it is well suited to very high-dimensional settings where exhaustive subset search is infeasible and interpretable truncation of feature rankings is essential.

Selecting the most relevant or informative features is a key issue in actual machine learning problems. Since an exhaustive search is not feasible even for a moderate number of features, an intelligent search strategy must be employed for finding an optimal subset, which implies considering how features interact with each other in promoting class separability. Balancing feature subset size and classification accuracy constitutes a multi-objective optimization challenge. Here we propose MOELIGA, a multi-objective genetic algorithm incorporating an evolutionary local improvement strategy that evolves subordinate populations to refine feature subsets. MOELIGA employs a crowding-based fitness sharing mechanism and a sigmoid transformation to enhance diversity and guide compactness, alongside a geometry-based objective promoting classifier independence. Experimental evaluation on 14 diverse datasets demonstrates MOELIGA's ability to identify smaller feature subsets with superior or comparable classification performance relative to 11 state-of-the-art methods. These findings suggest MOELIGA effectively addresses the accuracy-dimensionality trade-off, offering a robust and adaptable approach for multi-objective feature selection in complex, high-dimensional scenarios.