Robust Bayesian Nonnegative Matrix Factorization with Implicit Regularizers
This is an incremental improvement for researchers and practitioners using NMF in domains like genomics, offering more robust predictions.
The paper tackled the problem of robust nonnegative matrix factorization for predicting missing values and finding hidden patterns by introducing a probabilistic model with implicit norm regularization, showing that the proposed Bayesian NMF models lead to robust predictions and avoid overfitting compared to competitive approaches on real-world datasets like Genomics of Drug Sensitivity in Cancer.
We introduce a probabilistic model with implicit norm regularization 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, e.g., exponential density or distribution based on exponential function. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real-world datasets including Genomics of Drug Sensitivity in Cancer (GDSC $IC_{50}$) and Gene body methylation with different sizes and dimensions, and show that the proposed Bayesian NMF GL$_2^2$ and GL$_\infty$ models lead to robust predictions for different data values and avoid overfitting compared with competitive Bayesian NMF approaches.