Given an unnormalized target distribution we want to obtain approximate
samples from it and a tight lower bound on its (log) normalization constant log
Z. Annealed Importance Sampling (AIS) with Hamiltonian MCMC is a powerful
method that can be used to do this. Its main drawback is that it uses
non-differentiable transition kernels, which makes tuning its many parameters
hard. We propose a framework to use an AIS-like procedure with Uncorrected
Hamiltonian MCMC, called Uncorrected Hamiltonian Annealing. Our method leads to
tight and differentiable lower bounds on log Z. We show empirically that our
method yields better performances than other competing approaches, and that the
ability to tune its parameters using reparameterization gradients may lead to
large performance improvements.

提出了一种使用类似于 AIS（Annealed Importance Sampling）的 Uncorrected Hamiltonian MCMC 过程的框架，称为 Uncorrected Hamiltonian Annealing，它能够在获得近似样本的同时，获得一个紧致、可微分的 logZ 的下界，相比其他竞争方法，我们的方法表现更好，并且使用重新参数化梯度调整参数能够显著提高性能。

基于未经校正的哈密顿退火的 MCMC 变分推断

MCMC Variational Inference via Uncorrected Hamiltonian Annealing

Black box variational inference (BBVI) with reparameterization gradients
triggered the exploration of divergence measures other than the
Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we
view BBVI with generalized divergences as a form of estimating the marginal
likelihood via biased importance sampling. The choice of divergence determines
a bias-variance trade-off between the tightness of a bound on the marginal
likelihood (low bias) and the variance of its gradient estimators. Drawing on
variational perturbation theory of statistical physics, we use these insights
to construct a family of new variational bounds. Enumerated by an odd integer
order $K$, this family captures the standard KL bound for $K=1$, and converges
to the exact marginal likelihood as $K\to\infty$. Compared to
alpha-divergences, our reparameterization gradients have a lower variance. We
show in experiments on Gaussian Processes and Variational Autoencoders that the
new bounds are more mass covering, and that the resulting posterior covariances
are closer to the true posterior and lead to higher likelihoods on held-out
data.

本文针对黑盒变分推断方法提出了基于广义差异度量的偏置重要性采样方法，并通过变分扰动理论构建了一族新的变分上界，对多个模型进行实验得出新的变分上界在数据拟合上更优

摄动黑盒变分推理

Perturbative Black Box Variational Inference

Optimization with noisy gradients has become ubiquitous in statistics and
machine learning. Reparameterization gradients, or gradient estimates computed
via the "reparameterization trick," represent a class of noisy gradients often
used in Monte Carlo variational inference (MCVI). However, when these gradient
estimators are too noisy, the optimization procedure can be slow or fail to
converge. One way to reduce noise is to use more samples for the gradient
estimate, but this can be computationally expensive. Instead, we view the noisy
gradient as a random variable, and form an inexpensive approximation of the
generating procedure for the gradient sample. This approximation has high
correlation with the noisy gradient by construction, making it a useful control
variate for variance reduction. We demonstrate our approach on non-conjugate
multi-level hierarchical models and a Bayesian neural net where we observed
gradient variance reductions of multiple orders of magnitude (20-2,000x).

本研究提出了一种基于控制变量（control variate）方法，通过估计梯度样本的生成过程近似减少噪声梯度的方差，取得了多个数量级（20-2,000 倍）的优化效果提升，在非共轭多级层次模型和贝叶斯神经网络实验中证明了其有效性。