Cadre Modeling: Simultaneously Discovering Subpopulations and Predictive Models

TL;DR

This paper introduces a discriminative model that simultaneously discovers subpopulations, called cadres, and builds predictive models for each, leading to better insights and predictions in regression tasks with unknown subgroups.

Contribution

The paper presents a novel method for joint subpopulation discovery and prediction modeling with interpretability and feature selection, outperforming separate approaches.

Findings

Significantly outperforms separate subpopulation and prediction methods in simulations.

Provides state-of-the-art prediction of polymer glass transition temperature.

Identifies meaningful, interpretable cadres with robust generalization.

Abstract

We consider the problem in regression analysis of identifying subpopulations that exhibit different patterns of response, where each subpopulation requires a different underlying model. Unlike statistical cohorts, these subpopulations are not known a priori; thus, we refer to them as cadres. When the cadres and their associated models are interpretable, modeling leads to insights about the subpopulations and their associations with the regression target. We introduce a discriminative model that simultaneously learns cadre assignment and target-prediction rules. Sparsity-inducing priors are placed on the model parameters, under which independent feature selection is performed for both the cadre assignment and target-prediction processes. We learn models using adaptive step size stochastic gradient descent, and we assess cadre quality with bootstrapped sample analysis. We present simulated results showing that, when the true clustering rule does not depend on the entire set of features, our method significantly outperforms methods that learn subpopulation-discovery and target-prediction rules separately. In a materials-by-design case study, our model provides state-of-the-art prediction of polymer glass transition temperature. Importantly, the method identifies cadres of polymers that respond differently to structural perturbations, thus providing design insight for targeting or avoiding specific transition temperature ranges. It identifies chemically meaningful cadres, each with interpretable models. Further experimental results show that cadre methods have generalization that is competitive with linear and nonlinear regression models and can identify robust subpopulations.