Comparative Study of Inference Methods for Interpolative Decomposition
This work addresses the challenge of improving ID methods for data analysis in domains like genomics, though it appears incremental as it builds on existing Bayesian ID algorithms.
The authors tackled the problem of learning interpolative decomposition (ID) for low-rank approximation and feature selection by proposing a probabilistic model with automatic relevance determination (ARD) and Bayesian inference via Gibbs sampling. They showed that this approach leads to smaller reconstructive errors compared to vanilla Bayesian ID algorithms on real-world datasets like CCLE EC50, CCLE IC50, Gene Body Methylation, and Promoter Methylation.
In this paper, we propose a probabilistic model with automatic relevance determination (ARD) for learning interpolative decomposition (ID), which is commonly used for low-rank approximation, feature selection, 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 $IC50$, Gene Body Methylation, and Promoter Methylation datasets with different sizes, and dimensions, and show that the proposed Bayesian ID algorithms with automatic relevance determination lead to smaller reconstructive errors even compared to vanilla Bayesian ID algorithms with fixed latent dimension set to matrix rank.