Low-Discrepancy Points via Energetic Variational Inference

• URL: http://arxiv.org/abs/2111.10722v1
• Date: Sun, 21 Nov 2021 03:09:07 GMT
• Title: Low-Discrepancy Points via Energetic Variational Inference
• Authors: Yindong Chen, Yiwei Wang, Lulu Kang, Chun Liu
• Abstract summary: We propose a deterministic variational inference approach and generate low-discrepancy points by minimizing the kernel discrepancy. We name the resulting algorithm EVI-MMD and demonstrate it through examples in which the target distribution is fully specified. Its performances are satisfactory compared to alternative methods in the applications of distribution approximation, numerical integration, and generative learning.
• Score: 5.936959130012709
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we propose a deterministic variational inference approach and generate low-discrepancy points by minimizing the kernel discrepancy, also known as the Maximum Mean Discrepancy or MMD. Based on the general energetic variational inference framework by Wang et. al. (2021), minimizing the kernel discrepancy is transformed to solving a dynamic ODE system via the explicit Euler scheme. We name the resulting algorithm EVI-MMD and demonstrate it through examples in which the target distribution is fully specified, partially specified up to the normalizing constant, and empirically known in the form of training data. Its performances are satisfactory compared to alternative methods in the applications of distribution approximation, numerical integration, and generative learning. The EVI-MMD algorithm overcomes the bottleneck of the existing MMD-descent algorithms, which are mostly applicable to two-sample problems. Algorithms with more sophisticated structures and potential advantages can be developed under the EVI framework.

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