# Comparative Study of Inference Methods for Interpolative Decomposition

arXiv: https://arxiv.org/abs/2206.14542 · HTML: https://mlsanity.com/paper/2206.14542/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 29 Jun 2022.

## Builds on (most cited first, 6 of 6)

- [A Survey of Methods for Low-Power Deep Learning and Computer Vision](https://mlsanity.com/paper/2003.11066/) (2020)
- [Matrix Decomposition and Applications](https://mlsanity.com/paper/2201.00145/) (2022)
- [Flexible and Hierarchical Prior for Bayesian Nonnegative Matrix Factorization](https://mlsanity.com/paper/2205.11025/) (2022)
- [A survey on Bayesian inference for Gaussian mixture model](https://mlsanity.com/paper/2108.11753/) (2021)
- [Prior and Likelihood Choices for Bayesian Matrix Factorisation on Small Datasets](https://mlsanity.com/paper/1712.00288/) (2017)
- [Bayesian Low-Rank Interpolative Decomposition for Complex Datasets](https://mlsanity.com/paper/2205.14825/) (2022)

## Built on by (most cited first, 2 of 2)

- [Robust Bayesian Nonnegative Matrix Factorization with Implicit Regularizers](https://mlsanity.com/paper/2208.10053/) (2022)
- [Feature Selection via the Intervened Interpolative Decomposition and its Application in Diversifying Quantitative Strategies](https://mlsanity.com/paper/2209.14532/) (2022)

## Abstract (arXiv)

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.