Bayesian Low-Rank Interpolative Decomposition for Complex Datasets

TL;DR

This paper presents a Bayesian probabilistic model for interpolative decomposition that improves feature selection and low-rank approximation accuracy on complex datasets using Gibbs sampling.

Contribution

It introduces a novel Bayesian framework for interpolative decomposition with latent variables and demonstrates superior performance over existing randomized methods.

Findings

Bayesian ID models achieve smaller reconstruction errors.

Models effectively identify hidden data patterns.

Demonstrated on diverse real-world datasets.

Abstract

In this paper, we introduce a probabilistic model for learning interpolative decomposition (ID), which is commonly used for feature selection, low-rank approximation, and identifying hidden patterns in data, where the matrix factors are latent variables associated with each data dimension. Prior densities with support on the specified subspace are used to address the constraint for the magnitude of the factored component of the observed matrix. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on a variety of real-world datasets including CCLE EC50, CCLE IC50, CTRP EC50,and MovieLens 100K datasets with different sizes, and dimensions, and show that the proposed Bayesian ID GBT and GBTN models lead to smaller reconstructive errors compared to existing randomized approaches.