Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference

• URL: http://arxiv.org/abs/2105.05489v1
• Date: Wed, 12 May 2021 07:51:47 GMT
• Title: Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference
• Authors: Shumao Zhang, Pengchuan Zhang, Thomas Y. Hou
• Abstract summary: We propose a Multiscale Invertible Generative Network (MsIGN) to solve high-dimensional Bayesian inference. MsIGN exploits the low-dimensional nature of the posterior, and generates samples from coarse to fine scale. On the natural image synthesis task, MsIGN achieves superior performance in bits-per-dimension over baseline models.
• Score: 9.953855915186352
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a Multiscale Invertible Generative Network (MsIGN) and associated training algorithm that leverages multiscale structure to solve high-dimensional Bayesian inference. To address the curse of dimensionality, MsIGN exploits the low-dimensional nature of the posterior, and generates samples from coarse to fine scale (low to high dimension) by iteratively upsampling and refining samples. MsIGN is trained in a multi-stage manner to minimize the Jeffreys divergence, which avoids mode dropping in high-dimensional cases. On two high-dimensional Bayesian inverse problems, we show superior performance of MsIGN over previous approaches in posterior approximation and multiple mode capture. On the natural image synthesis task, MsIGN achieves superior performance in bits-per-dimension over baseline models and yields great interpret-ability of its neurons in intermediate layers.

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