Latent Bayesian melding for integrating individual and population models

TL;DR

This paper introduces latent Bayesian melding, a method to integrate detailed individual models with coarse population models, improving prediction accuracy in applications like electricity disaggregation.

Contribution

The paper proposes a novel latent Bayesian melding approach that combines individual and population models using a logarithmic opinion pool framework.

Findings

Latent Bayesian melding outperforms generalized moment matching in prediction accuracy.

The method is demonstrated on electricity disaggregation, showing significant improvements.

It effectively integrates models at different granularities for better statistical inference.

Abstract

In many statistical problems, a more coarse-grained model may be suitable for population-level behaviour, whereas a more detailed model is appropriate for accurate modelling of individual behaviour. This raises the question of how to integrate both types of models. Methods such as posterior regularization follow the idea of generalized moment matching, in that they allow matching expectations between two models, but sometimes both models are most conveniently expressed as latent variable models. We propose latent Bayesian melding, which is motivated by averaging the distributions over populations statistics of both the individual-level and the population-level models under a logarithmic opinion pool framework. In a case study on electricity disaggregation, which is a type of single-channel blind source separation problem, we show that latent Bayesian melding leads to significantly more accurate predictions than an approach based solely on generalized moment matching.