Understanding Pathologies of Deep Heteroskedastic Regression

Eliot Wong-Toi, Alex James Boyd, Vincent Fortuin, Stephan Mandt

Keywords: heteroskedastic, regression

TL;DR: we provide a framework to explain why fitting heteroskedastic models is difficult and offer a solution

Abstract: Deep, overparameterized regression models are notorious for their tendency to overfit. This problem is exacerbated in heteroskedastic models, which predict both mean and residual noise for each data point. At one extreme, these models fit all training data perfectly, eliminating residual noise entirely; at the other, they overfit the residual noise while predicting a constant, uninformative mean. We observe a lack of middle ground, suggesting a phase transition dependent on model regularization strength. Empirical verification supports this conjecture by fitting numerous models with varying mean and variance regularization. To explain the transition, we develop a theoretical framework based on a statistical field theory, yielding qualitative agreement with experiments. As a practical consequence, our analysis simplifies hyperparameter tuning from a two-dimensional to a one-dimensional search, substantially reducing the computational burden. Experiments on diverse datasets, including UCI datasets and the large-scale ClimSim climate dataset, demonstrate significantly improved performance in various calibration tasks.

List Of Authors: Wong-Toi,Eliot and Boyd,Alex and Fortuin,Vincent and Mandt,Stephan

Code Url: https://github.com/ewongtoi/deep-heteroskedastic-regression

Submission Number: 570