Generative Modeling via Hierarchical Tensor Sketching

• URL: http://arxiv.org/abs/2304.05305v1
• Date: Tue, 11 Apr 2023 15:55:13 GMT
• Title: Generative Modeling via Hierarchical Tensor Sketching
• Authors: Yifan Peng, Yian Chen, E. Miles Stoudenmire, Yuehaw Khoo
• Abstract summary: We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. The complexity of the resulting algorithm scales linearly in the dimension of the high-dimensional density.
• Score: 12.005736675688917
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear equations for tensor cores in this tensor network. The complexity of the resulting algorithm scales linearly in the dimension of the high-dimensional density. An analysis of estimation error demonstrates the effectiveness of this method through several numerical experiments.

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