text: We propose two novel samplers to produce high-quality samples from a given (un-normalized) probability density. The sampling is achieved by transforming a reference distribution to the target distribution with neural networks, which are trained separately by minimizing two kinds of Stein Discrepancies, and hence our method is named as Stein neural sampler. Theoretical and empirical results suggest that, compared with traditional sampling schemes, our samplers share the following three advantages: 1. Being asymptotically correct; 2. Experiencing less convergence issue in practice; 3. Generating samples instantaneously.
  @cite_0: Existing Markov Chain Monte Carlo (MCMC) methods are either based on general-purpose and domain-agnostic schemes which can lead to slow convergence, or hand-crafting of problem-specific proposals by an expert. We propose A-NICE-MC, a novel method to train flexible parametric Markov chain kernels to produce samples with desired properties. First, we propose an efficient likelihood-free adversarial training method to train a Markov chain and mimic a given data distribution. Then, we leverage flexible volume preserving flows to obtain parametric kernels for MCMC. Using a bootstrap approach, we show how to train efficient Markov chains to sample from a prescribed posterior distribution by iteratively improving the quality of both the model and the samples. A-NICE-MC provides the first framework to automatically design efficient domain-specific MCMC proposals. Empirical results demonstrate that A-NICE-MC combines the strong guarantees of MCMC with the expressiveness of deep neural networks, and is able to significantly outperform competing methods such as Hamiltonian Monte Carlo.
summary: The fusion of deep learning and sampling is not new. @cite_0 proposed A-NICE-MC, where the proposal distribution in MCMC is, instead of domain-agnostic, adversarially trained using neural networks. Stein GAN also proposes to train a neural network to draw samples from given target distributions for probabilistic inference. Their method is by iteratively adjusting the weights according to the SVGD updates. From a GAN perspective, in each iteration of Stein GAN, the discriminator is performing a two sample test between the currently generated samples and the one-step updated samples by SVGD. This method generalized SVGD to training neural networks and it is minimizing the Kullback-Leibler divergence between the sampling distribution and the target inside a RKHS.