Denoising Fisher Training For Neural Implicit Samplers

• URL: http://arxiv.org/abs/2411.01453v1
• Date: Sun, 03 Nov 2024 06:21:59 GMT
• Title: Denoising Fisher Training For Neural Implicit Samplers
• Authors: Weijian Luo, Wei Deng,
• Abstract summary: We introduce Denoising Fisher Training (DFT), a novel training approach for neural implicit samplers with theoretical guarantees. DFT is empirically validated across diverse sampling benchmarks, including two-dimensional synthetic distribution, Bayesian logistic regression, and high-dimensional energy-based models (EBMs) In experiments with high-dimensional EBMs, our best one-step DFT neural sampler achieves results on par with MCMC methods with up to 200 sampling steps, leading to a substantially greater efficiency over 100 times higher.
• Score: 3.744818211876898
• License:
• Abstract: Efficient sampling from un-normalized target distributions is pivotal in scientific computing and machine learning. While neural samplers have demonstrated potential with a special emphasis on sampling efficiency, existing neural implicit samplers still have issues such as poor mode covering behavior, unstable training dynamics, and sub-optimal performances. To tackle these issues, in this paper, we introduce Denoising Fisher Training (DFT), a novel training approach for neural implicit samplers with theoretical guarantees. We frame the training problem as an objective of minimizing the Fisher divergence by deriving a tractable yet equivalent loss function, which marks a unique theoretical contribution to assessing the intractable Fisher divergences. DFT is empirically validated across diverse sampling benchmarks, including two-dimensional synthetic distribution, Bayesian logistic regression, and high-dimensional energy-based models (EBMs). Notably, in experiments with high-dimensional EBMs, our best one-step DFT neural sampler achieves results on par with MCMC methods with up to 200 sampling steps, leading to a substantially greater efficiency over 100 times higher. This result not only demonstrates the superior performance of DFT in handling complex high-dimensional sampling but also sheds light on efficient sampling methodologies across broader applications.

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