Interpretability of linear regression models of glassy dynamics

TL;DR

This paper evaluates the interpretability of linear regression models for glassy dynamics, highlighting the challenges posed by multicollinearity and demonstrating how dimensional reduction can improve interpretability without sacrificing accuracy.

Contribution

It introduces a systematic analysis of structural descriptors in linear models of glassy dynamics, emphasizing the importance of dimensional reduction for interpretability.

Findings

Multicollinearity among descriptors hampers interpretability.

Ridge regression reduces multicollinearity but lacks physical clarity.

Dimensional reduction techniques improve model interpretability.

Abstract

Data-driven models can accurately describe and predict the dynamical properties of glass-forming liquids from structural data. Accurate predictions, however, do not guarantee an understanding of the underlying physical phenomena and the key factors that control them. In this paper, we illustrate the merits and limitations of linear regression models of glassy dynamics built on high-dimensional structural descriptors. By analyzing data for a two-dimensional glass model, we show that several descriptors commonly used in glass-transition studies display multicollinearity, which hinders the interpretability of linear models. Ridge regression suppresses some of the shortcomings of multicollinearity, but its solutions are not concise enough to be physically interpretable. Only by using dimensional reduction techniques we do eventually obtain linear models that strike a balance between prediction accuracy and interpretability. Our analysis points to a key role of local packing and composition fluctuations in the glass model under study.