Interpretable Model Summaries Using the Wasserstein Distance

TL;DR

This paper introduces a novel method using Wasserstein distance to create low-dimensional, interpretable summaries of complex statistical models, aiding understanding and communication of model parameters.

Contribution

The paper proposes a new approach for selecting interpretable parameter subsets in complex models using Wasserstein distance, applicable after model estimation.

Findings

Effective in reducing model complexity while maintaining fidelity

Demonstrated on cancer datasets with promising results

Provides a flexible tool for model interpretability

Abstract

Statistical models often include thousands of parameters. However, large models decrease the investigator's ability to interpret and communicate the estimated parameters. Reducing the dimensionality of the parameter space in the estimation phase is a commonly used approach, but less work has focused on selecting subsets of the parameters for interpreting the estimated model -- especially in settings such as Bayesian inference and model averaging. Importantly, many models do not have straightforward interpretations and create another layer of obfuscation. To solve this gap, we introduce a new method that uses the Wasserstein distance to identify a low-dimensional interpretable model projection. After the estimation of complex models, users can budget how many parameters they wish to interpret and the proposed generates a simplified model of the desired dimension minimizing the distance to the full model. We provide simulation results to illustrate the method and apply it to cancer datasets.