Normalized Latent Measure Factor Models

TL;DR

This paper introduces a Bayesian nonparametric model that combines latent traits with random measures to compare distributions, validated on simulated and real-world data for insightful population analysis.

Contribution

It develops a novel methodology using dependent normalized random measures with post-processing for identified inference, employing Riemannian optimization over Lie groups.

Findings

Effective in modeling complex distributions

Provides interpretable insights into population data

Validated on real-world datasets with promising results

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