Non-Asymptotic Performance Guarantees for Neural Estimation of $\mathsf{f}$-Divergences

• URL: http://arxiv.org/abs/2103.06923v1
• Date: Thu, 11 Mar 2021 19:47:30 GMT
• Title: Non-Asymptotic Performance Guarantees for Neural Estimation of $\mathsf{f}$-Divergences
• Authors: Sreejith Sreekumar, Zhengxin Zhang, Ziv Goldfeld
• Abstract summary: Statistical distances quantify the dissimilarity between probability distributions. A modern method for estimating such distances from data relies on parametrizing a variational form by a neural network (NN) and optimizing it. This paper explores this tradeoff by means of non-asymptotic error bounds, focusing on three popular choices of SDs.
• Score: 22.496696555768846
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Statistical distances (SDs), which quantify the dissimilarity between probability distributions, are central to machine learning and statistics. A modern method for estimating such distances from data relies on parametrizing a variational form by a neural network (NN) and optimizing it. These estimators are abundantly used in practice, but corresponding performance guarantees are partial and call for further exploration. In particular, there seems to be a fundamental tradeoff between the two sources of error involved: approximation and estimation. While the former needs the NN class to be rich and expressive, the latter relies on controlling complexity. This paper explores this tradeoff by means of non-asymptotic error bounds, focusing on three popular choices of SDs -- Kullback-Leibler divergence, chi-squared divergence, and squared Hellinger distance. Our analysis relies on non-asymptotic function approximation theorems and tools from empirical process theory. Numerical results validating the theory are also provided.

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