Normalized Latent Measure Factor Models

Mario Beraha; Jim E. Griffin

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arXiv · 2205.15654

Normalized Latent Measure Factor Models

Mario Beraha·Jim E. Griffin

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Abstract

We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random measures where each measure is a linear combination of a set of latent measures, interpretable as characteristic traits shared by different distributions, with positive random weights. The model is non-identified and a method for post-processing posterior samples to achieve identified inference is developed. This uses Riemannian optimization to solve a non-trivial optimization problem over a Lie group of matrices. The effectiveness of our approach is validated on simulated data and in two applications to two real-world data sets: school student test scores and personal incomes in California. Our approach leads to interesting insights for populations and easily interpretable posterior inference

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Mario Beraha, Jim E. Griffin. 2022-05-31. Normalized Latent Measure Factor Models. https://arxiv.org/abs/2205.15654

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