Posterior Ratio Estimation for Latent Variables

Abstract

Density Ratio Estimation has attracted attention from machine learning community due to its ability of comparing the underlying distributions of two datasets. However, in some applications, we want to compare distributions of emphlatent random variables that can be only inferred from observations. In this paper, we study the problem of estimating the ratio between two posterior probability density functions of a latent variable. Particularly, we assume the posterior ratio function can be well-approximated by a parametric model, which is then estimated using observed datasets and synthetic prior samples. We prove consistency of our estimator and the asymptotic normality of the estimated parameters as the number of prior samples tending to infinity. Finally, we validate our theories using numerical experiments and demonstrate the usefulness of the proposed method through some real-world applications.

Mladen Kolar

Associate Professor of Econometrics and Statistics

Mladen Kolar is an Associate Professor of Econometrics and Statistics at the University of Chicago Booth School of Business. His research is focused on high-dimensional statistical methods, graphical models, varying-coefficient models and data mining, driven by the need to uncover interesting and scientifically meaningful structures from observational data.