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.

翻译：从非归一化目标分布中高效采样是科学计算与机器学习中的一个基本问题。传统方法如马尔可夫链蒙特卡洛方法虽能保证从此类分布中获得渐近无偏样本，但在处理高维目标时存在计算效率低下的问题，尤其是在需要多次迭代以生成一批样本的情况下。本文提出了一种高效且可扩展的神经隐式采样器，克服了上述局限性。该采样器通过利用神经变换将易于采样的潜在向量直接映射至目标样本，无需迭代过程，从而能以较低计算成本生成大批量样本。为训练该神经隐式采样器，我们引入了两种新方法：KL训练法与Fisher训练法。前者最小化Kullback-Leibler散度，后者则最小化Fisher散度。通过采用这些训练方法，我们有效优化了神经隐式采样器以捕获所需的目标分布。为验证所提采样器的有效性、效率与可扩展性，我们在三个不同规模采样基准上进行了评估，包括：二维目标分布采样、贝叶斯推理及高维能量基模型采样。值得注意的是，在高维能量基模型实验中，我们的采样器生成的样本与基于MCMC的方法质量相当，但效率提升超过百倍，充分展示了神经隐式采样器的优越性。我们相信，本工作提供的理论与实证贡献将激励进一步研究，为本文未涉及的应用领域开发高效采样器。