# Flexible and Hierarchical Prior for Bayesian Nonnegative Matrix Factorization

arXiv: https://arxiv.org/abs/2205.11025 · HTML: https://mlsanity.com/paper/2205.11025/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 25 references that are in the map.
- First posted on arXiv 23 May 2022.

## Builds on (most cited first, 5 of 5)

- [Probabilistic Latent Semantic Analysis](https://mlsanity.com/paper/1301.6705/) (2013)
- [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)
- [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)

## Built on by (most cited first, 7 of 7)

- [Bayesian Low-Rank Interpolative Decomposition for Complex Datasets](https://mlsanity.com/paper/2205.14825/) (2022)
- [Autoencoding Conditional GAN for Portfolio Allocation Diversification](https://mlsanity.com/paper/2207.05701/) (2022)
- [Comparative Study of Inference Methods for Interpolative Decomposition](https://mlsanity.com/paper/2206.14542/) (2022)
- [Robust Bayesian Nonnegative Matrix Factorization with Implicit Regularizers](https://mlsanity.com/paper/2208.10053/) (2022)
- [Low-Rank Approximation, Adaptation, and Other Tales](https://mlsanity.com/paper/2408.05883/) (2024)
- [A Hybrid Approach on Conditional GAN for Portfolio Analysis](https://mlsanity.com/paper/2208.07159/) (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 introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent variables associated with each data dimension. The nonnegativity constraint for the latent factors is handled by choosing priors with support on the nonnegative subspace. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real-world datasets including MovieLens 100K and MovieLens 1M with different sizes and dimensions and show that the proposed Bayesian NMF GRRN model leads to better predictions and avoids overfitting compared to existing Bayesian NMF approaches.