Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference
This addresses the curse of dimensionality in Bayesian inference for fields like computational science and image processing, representing an incremental improvement with a novel method for a known bottleneck.
The authors tackled high-dimensional Bayesian inference by proposing a Multiscale Invertible Generative Network (MsIGN) that generates samples from coarse to fine scales, showing superior performance in posterior approximation and mode capture on inverse problems and achieving better bits-per-dimension in natural image synthesis.
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.