Robust priors for regularized regression

TL;DR

This paper introduces robust, non-zero priors for penalized regression that improve interpretability and performance across various tasks, inspired by human decision heuristics, and allows interpolation between models of different complexities.

Contribution

It presents a novel method for constructing priors based on decision heuristics, enabling more robust and interpretable regression models with a principled way to interpolate between model complexities.

Findings

Models with robust priors showed excellent worst-case performance.

The approach was successfully applied to decision, classification, and brain imaging data.

Solutions derived from the heuristics used to create the priors were consistent and interpretable.

Abstract

Induction benefits from useful priors. Penalized regression approaches, like ridge regression, shrink weights toward zero but zero association is usually not a sensible prior. Inspired by simple and robust decision heuristics humans use, we constructed non-zero priors for penalized regression models that provide robust and interpretable solutions across several tasks. Our approach enables estimates from a constrained model to serve as a prior for a more general model, yielding a principled way to interpolate between models of differing complexity. We successfully applied this approach to a number of decision and classification problems, as well as analyzing simulated brain imaging data. Models with robust priors had excellent worst-case performance. Solutions followed from the form of the heuristic that was used to derive the prior. These new algorithms can serve applications in data analysis and machine learning, as well as help in understanding how people transition from novice to expert performance.