Doubly Non-Central Beta Matrix Factorization for Stable Dimensionality Reduction of Bounded Support Matrix Data

TL;DR

This paper introduces a stable and interpretable matrix decomposition method for bounded support data, improving hyper-parameter stability while maintaining predictive performance, with applications in DNA methylation analysis.

Contribution

The paper develops a novel Tucker-based matrix factorization approach with an efficient sampling algorithm, specifically designed for bounded support matrices, enhancing stability over existing methods.

Findings

Comparable predictive accuracy to state-of-the-art methods

Significantly improved stability to hyper-parameter changes

Higher confidence in scientific hypothesis testing

Abstract

We consider the problem of developing interpretable and computationally efficient matrix decomposition methods for matrices whose entries have bounded support. Such matrices are found in large-scale DNA methylation studies and many other settings. Our approach decomposes the data matrix into a Tucker representation wherein the number of columns in the constituent factor matrices is not constrained. We derive a computationally efficient sampling algorithm to solve for the Tucker decomposition. We evaluate the performance of our method using three criteria: predictability, computability, and stability. Empirical results show that our method has similar performance as other state-of-the-art approaches in terms of held-out prediction and computational complexity, but has significantly better performance in terms of stability to changes in hyper-parameters. The improved stability results in higher confidence in the results in applications where the constituent factors are used to generate and test scientific hypotheses such as DNA methylation analysis of cancer samples.