Discriminative Estimation of Total Variation Distance: A Fidelity Auditor for Generative Data

• URL: http://arxiv.org/abs/2405.15337v1
• Date: Fri, 24 May 2024 08:18:09 GMT
• Title: Discriminative Estimation of Total Variation Distance: A Fidelity Auditor for Generative Data
• Authors: Lan Tao, Shirong Xu, Chi-Hua Wang, Namjoon Suh, Guang Cheng,
• Abstract summary: We propose a discriminative approach to estimate the total variation (TV) distance between two distributions. Our method quantitatively characterizes the relation between the Bayes risk in classifying two distributions and their TV distance. We demonstrate that, with a specific choice of hypothesis class in classification, a fast convergence rate in estimating the TV distance can be achieved.
• Score: 10.678533056953784
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: With the proliferation of generative AI and the increasing volume of generative data (also called as synthetic data), assessing the fidelity of generative data has become a critical concern. In this paper, we propose a discriminative approach to estimate the total variation (TV) distance between two distributions as an effective measure of generative data fidelity. Our method quantitatively characterizes the relation between the Bayes risk in classifying two distributions and their TV distance. Therefore, the estimation of total variation distance reduces to that of the Bayes risk. In particular, this paper establishes theoretical results regarding the convergence rate of the estimation error of TV distance between two Gaussian distributions. We demonstrate that, with a specific choice of hypothesis class in classification, a fast convergence rate in estimating the TV distance can be achieved. Specifically, the estimation accuracy of the TV distance is proven to inherently depend on the separation of two Gaussian distributions: smaller estimation errors are achieved when the two Gaussian distributions are farther apart. This phenomenon is also validated empirically through extensive simulations. In the end, we apply this discriminative estimation method to rank fidelity of synthetic image data using the MNIST dataset.

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