Reduced Rank Vector Generalized Linear Models for Feature Extraction

TL;DR

This paper introduces a novel framework for supervised feature extraction using reduced rank vector generalized linear models, emphasizing efficient computation and effective parameter tuning in high-dimensional settings.

Contribution

It develops a new approach for fitting singular value penalized models with rank constraints, enabling fast high-dimensional feature extraction with a novel cross-validation method.

Findings

Effective feature extraction demonstrated on real data

Fast computation with little performance loss in high dimensions

Proposed projective cross-validation improves parameter tuning

Abstract

Supervised linear feature extraction can be achieved by fitting a reduced rank multivariate model. This paper studies rank penalized and rank constrained vector generalized linear models. From the perspective of thresholding rules, we build a framework for fitting singular value penalized models and use it for feature extraction. Through solving the rank constraint form of the problem, we propose progressive feature space reduction for fast computation in high dimensions with little performance loss. A novel projective cross-validation is proposed for parameter tuning in such nonconvex setups. Real data applications are given to show the power of the methodology in supervised dimension reduction and feature extraction.