Entropy-based Training Methods for Scalable Neural Implicit Sampler
Weijian Luo Boya Zhang Zhihua Zhang
Efficiently sampling from un-normalized target distributions is a fundamental
problem in scientific computing and machine learning. Traditional approaches
like Markov Chain Monte Carlo (MCMC) guarantee asymptotically unbiased samples
from such distributions but suffer from computational inefficiency,
particularly when dealing with high-dimensional targets, as they require
numerous iterations to generate a batch of samples. In this paper, we propose
an efficient and scalable neural implicit sampler that overcomes these
limitations. Our sampler can generate large batches of samples with low
computational costs by leveraging a neural transformation that directly maps
easily sampled latent vectors to target samples without the need for iterative
procedures. To train the neural implicit sampler, we introduce two novel
methods: the KL training method and the Fisher training method. The former
minimizes the Kullback-Leibler divergence, while the latter minimizes the
Fisher divergence. By employing these training methods, we effectively optimize
the neural implicit sampler to capture the desired target distribution. To
demonstrate the effectiveness, efficiency, and scalability of our proposed
samplers, we evaluate them on three sampling benchmarks with different scales.
These benchmarks include sampling from 2D targets, Bayesian inference, and
sampling from high-dimensional energy-based models (EBMs). Notably, in the
experiment involving high-dimensional EBMs, our sampler produces samples that
are comparable to those generated by MCMC-based methods while being more than
100 times more efficient, showcasing the efficiency of our neural sampler. We
believe that the theoretical and empirical contributions presented in this work
will stimulate further research on developing efficient samplers for various
applications beyond the ones explored in this study.