Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation

TL;DR

This paper introduces ACNML, a scalable method for uncertainty estimation and calibration in deep neural networks, especially effective under distribution shifts, by approximating the theoretically optimal CNML scheme.

Contribution

The paper proposes ACNML, a novel scalable approach that combines approximate Bayesian inference with CNML principles for improved out-of-distribution uncertainty estimation.

Findings

ACNML outperforms prior methods in calibration on OOD data

It provides a scalable and general-purpose uncertainty estimation framework

ACNML demonstrates robustness under distribution shift

Abstract

While deep neural networks provide good performance for a range of challenging tasks, calibration and uncertainty estimation remain major challenges, especially under distribution shift. In this paper, we propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation, calibration, and out-of-distribution robustness with deep networks. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle, but is computationally intractable to evaluate exactly for all but the simplest of model classes. We propose to use approximate Bayesian inference technqiues to produce a tractable approximation to the CNML distribution. Our approach can be combined with any approximate inference algorithm that provides tractable posterior densities over model parameters. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.