Sparse Bilinear Logistic Regression
This work addresses a common problem in fields such as computer vision and brain-computer interfaces, but it appears incremental as it builds on existing logistic regression methods with a sparse bilinear extension.
The paper tackles the problem of decision-making with two-dimensional matrix variables by introducing sparse bilinear logistic regression, and it demonstrates through experiments that this method outperforms current techniques in applications like computer vision and brain-computer interfaces.
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-Łojasiewicz inequality. A range of experiments with simulated and real data demonstrate that sparse bilinear logistic regression outperforms current techniques in several important applications.