NOMU: Neural Optimization-based Model Uncertainty

TL;DR

This paper introduces NOMU, a neural network architecture designed to reliably estimate model uncertainty in regression tasks, especially with scarce data, by satisfying key desiderata and outperforming existing methods in Bayesian optimization.

Contribution

NOMU is a novel modular neural network architecture that enforces key desiderata for model uncertainty, capable of providing uncertainty estimates for any trained neural network.

Findings

NOMU performs at least as well as state-of-the-art methods in regression.

NOMU outperforms benchmarks in noiseless Bayesian optimization.

NOMU can provide uncertainty estimates for previously trained neural networks.

Abstract

We study methods for estimating model uncertainty for neural networks (NNs) in regression. To isolate the effect of model uncertainty, we focus on a noiseless setting with scarce training data. We introduce five important desiderata regarding model uncertainty that any method should satisfy. However, we find that established benchmarks often fail to reliably capture some of these desiderata, even those that are required by Bayesian theory. To address this, we introduce a new approach for capturing model uncertainty for NNs, which we call Neural Optimization-based Model Uncertainty (NOMU). The main idea of NOMU is to design a network architecture consisting of two connected sub-NNs, one for model prediction and one for model uncertainty, and to train it using a carefully-designed loss function. Importantly, our design enforces that NOMU satisfies our five desiderata. Due to its modular architecture, NOMU can provide model uncertainty for any given (previously trained) NN if given access to its training data. We evaluate NOMU in various regressions tasks and noiseless Bayesian optimization (BO) with costly evaluations. In regression, NOMU performs at least as well as state-of-the-art methods. In BO, NOMU even outperforms all considered benchmarks.