Sparse Bilinear Logistic Regression

TL;DR

This paper presents a novel sparse bilinear logistic regression method tailored for decision problems with matrix-structured data, offering improved performance in fields like computer vision and brain-computer interfaces.

Contribution

It introduces the concept, formulates the bi-convex optimization problem, and develops an efficient block coordinate descent algorithm with theoretical convergence guarantees.

Findings

Outperforms existing methods in simulated data

Effective in real-world applications like computer vision

Provides theoretical convergence analysis

Abstract

In this paper, we introduce the concept of sparse bilinear logistic regression for decision problems involving explanatory variables that are two-dimensional matrices. Such problems are common in computer vision, brain-computer interfaces, style/content factorization, and parallel factor analysis. The underlying optimization problem is bi-convex; we study its solution and develop an efficient algorithm based on block coordinate descent. We provide a theoretical guarantee for global convergence and estimate the asymptotical convergence rate using the Kurdyka-{\L}ojasiewicz inequality. A range of experiments with simulated and real data demonstrate that sparse bilinear logistic regression outperforms current techniques in several important applications.