Non-negative Probabilistic Factorization

Ela Fallik, Nir Friedman

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Keywords: NMF, Probabilistic graphical models, unsupervised learning, molecular biology

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TL;DR: Probabilistic extension of NMF, extracting source distributions from mixed samples without direct observations

Abstract: Non-negative Matrix Factorization (NMF) is a powerful data-analysis tool to extract non-negative latent components from linearly mixed samples. It is particularly useful when the observed signal aggregates contributions from multiple sources. However, NMF only accounts for two types of variations between samples - disparities in the proportions of sources contribution and observation noise. Here, we present VarNMF, a probabilistic extension of NMF that introduces another type of variation between samples: a variation in the actual value a source contributes to the samples. We show that by modeling sources as distributions and applying an Expectation Maximization procedure, we can learn this type of variation directly from mixed samples without observing any source directly. We apply VarNMF to a dataset of genomic measurements from liquid biopsies and demonstrate its ability to extract cancer-associated source distributions that reflect inter-cancer variability directly from mixed samples and without prior knowledge. The proposed model provides a framework for learning source distributions from additive mixed samples without direct observations.

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Submission Number: 702