An Empirical Analysis of the Advantages of Finite- v.s. Infinite-Width Bayesian Neural Networks

Jiayu Yao; Yaniv Yacoby; Beau Coker; Weiwei Pan; Finale Doshi-Velez

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arXiv · 2211.09184

An Empirical Analysis of the Advantages of Finite- v.s. Infinite-Width Bayesian Neural Networks

Jiayu Yao·Yaniv Yacoby·Beau Coker·Weiwei Pan·Finale Doshi-Velez

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Abstract

Comparing Bayesian neural networks (BNNs) with different widths is challenging because, as the width increases, multiple model properties change simultaneously, and, inference in the finite-width case is intractable. In this work, we empirically compare finite- and infinite-width BNNs, and provide quantitative and qualitative explanations for their performance difference. We find that when the model is mis-specified, increasing width can hurt BNN performance. In these cases, we provide evidence that finite-width BNNs generalize better partially due to the properties of their frequency spectrum that allows them to adapt under model mismatch.

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Jiayu Yao, Yaniv Yacoby, Beau Coker, Weiwei Pan, Finale Doshi-Velez. 2022-11-16. An Empirical Analysis of the Advantages of Finite- v.s. Infinite-Width Bayesian Neural Networks. https://arxiv.org/abs/2211.09184

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