Conditional sampling of variational autoencoders (VAEs) is needed in various
applications, such as missing data imputation, but is computationally
intractable. A principled choice for asymptotically exact conditional sampling
is Metropolis-within-Gibbs (MWG). However, we observe that the tendency of VAEs
to learn a structured latent space, a commonly desired property, can cause the
MWG sampler to get "stuck" far from the target distribution. This paper
mitigates the limitations of MWG: we systematically outline the pitfalls in the
context of VAEs, propose two original methods that address these pitfalls, and
demonstrate an improved performance of the proposed methods on a set of
sampling tasks.

用于缺失数据填补等多种应用中需要条件抽样的变分自动编码器 (VAEs) 是计算不可行的。本文解决了 Metropolis-within-Gibbs (MWG) 在 VAEs 中存在的问题，提出了两种解决方法，并在一组抽样任务上展示了改进的性能。

通过迭代近似祖先采样实现变分自动编码器的条件抽样

Conditional Sampling of Variational Autoencoders via Iterated  Approximate Ancestral Sampling

Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability
distributions and offer guarantees of exact sampling. However, in the
continuous case, unfavorable geometry of the target distribution can greatly
limit the efficiency of MCMC methods. Augmenting samplers with neural networks
can potentially improve their efficiency. Previous neural network based
samplers were trained with objectives that either did not explicitly encourage
exploration, or used a L2 jump objective which could only be applied to well
structured distributions. Thus it seems promising to instead maximize the
proposal entropy for adapting the proposal to distributions of any shape. To
allow direct optimization of the proposal entropy, we propose a neural network
MCMC sampler that has a flexible and tractable proposal distribution.
Specifically, our network architecture utilizes the gradient of the target
distribution for generating proposals. Our model achieves significantly higher
efficiency than previous neural network MCMC techniques in a variety of
sampling tasks. Further, the sampler is applied on training of a convergent
energy-based model of natural images. The adaptive sampler achieves unbiased
sampling with significantly higher proposal entropy than Langevin dynamics
sampler.

本文提出了一种基于神经网络的自适应 MCMC 采样器，它利用目标分布的梯度生成提案，通过最大化建议熵来实现对建议熵的直接优化，从而提高了在各种采样任务中的效率。