NOMU: Neural Optimization-based Model Uncertainty
Jakob M Heiss, Jakob Weissteiner, Hanna S Wutte, Sven Seuken, Josef Teichmann
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.
BibTeX
@InProceedings{pmlr-v162-heiss22a,
title = {{NOMU}: Neural Optimization-based Model Uncertainty},
author = {Heiss, Jakob M and Weissteiner, Jakob and Wutte, Hanna S and Seuken, Sven and Teichmann, Josef},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {8708--8758},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/heiss22a/heiss22a.pdf},
url = {https://proceedings.mlr.press/v162/heiss22a.html},
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.}
}