Bayesian Low-Rank Interpolative Decomposition for Complex Datasets
This work addresses the need for improved low-rank decomposition methods in data analysis, but it appears incremental as it builds on existing interpolative decomposition techniques with a Bayesian approach.
The paper tackles the problem of learning interpolative decomposition for low-rank approximation and feature selection by introducing a probabilistic model with Bayesian inference, and shows that it achieves smaller reconstructive errors on real-world datasets like CCLE EC50 and MovieLens 100K compared to existing randomized methods.
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.