Let $\pi_{0}$ and $\pi_{1}$ be two distributions on the Borel space
$(\mathbb{R}^{d},\mathcal{B}(\mathbb{R}^{d}))$. Any measurable function
$T:\mathbb{R}^{d}\rightarrow\mathbb{R}^{d}$ such that $Y=T(X)\sim\pi_{1}$ if
$X\sim\pi_{0}$ is called a transport map from $\pi_{0}$ to $\pi_{1}$. For any
$\pi_{0}$ and $\pi_{1}$, if one could obtain an analytical expression for a
transport map from $\pi_{0}$ to $\pi_{1}$, then this could be straightforwardly
applied to sample from any distribution. One would map draws from an
easy-to-sample distribution $\pi_{0}$ to the target distribution $\pi_{1}$
using this transport map. Although it is usually impossible to obtain an
explicit transport map for complex target distributions, we show here how to
build a tractable approximation of a novel transport map. This is achieved by
moving samples from $\pi_{0}$ using an ordinary differential equation with a
velocity field that depends on the full conditional distributions of the
target. Even when this ordinary differential equation is time-discretized and
the full conditional distributions are numerically approximated, the resulting
distribution of mapped samples can be efficiently evaluated and used as a
proposal within sequential Monte Carlo samplers. We demonstrate significant
gains over state-of-the-art sequential Monte Carlo samplers at a fixed
computational complexity on a variety of applications.

本文介绍了一种通过数值逼近复杂目标分布的条件分布、迭代求解普通微分方程得到一个可行的传输映射，用于提高在多种应用中的随机抽样并展示出显著的优越性能。

应用于贝叶斯计算的近似转运的吉布斯流

Gibbs flow for approximate transport with applications to Bayesian  computation

Recent work by Bengio et al. (2013) proposes a sampling procedure for
denoising autoencoders which involves learning the transition operator of a
Markov chain. The transition operator is typically unimodal, which limits its
capacity to model complex data. In order to perform efficient sampling from
conditional distributions, we extend this work, both theoretically and
algorithmically, to gated autoencoders (Memisevic, 2013), The proposed model is
able to generate convincing class-conditional samples when trained on both the
MNIST and TFD datasets.

本文将 Bengio 等人提出的去噪自编码器的采样程序扩展到了 gated 自编码器，实现了在 MNIST 数据集中的分类条件采样。

生成类别有条件的自编码器

Generative Class-conditional Autoencoders

The subject of this paper is the elucidation of effects of actions from
causal assumptions represented as a directed graph, and statistical knowledge
given as a probability distribution. In particular, we are interested in
predicting conditional distributions resulting from performing an action on a
set of variables and, subsequently, taking measurements of another set. We
provide a necessary and sufficient graphical condition for the cases where such
distributions can be uniquely computed from the available information, as well
as an algorithm which performs this computation whenever the condition holds.
Furthermore, we use our results to prove completeness of do-calculus [Pearl,
1995] for the same identification problem.

本文研究了有向图表示的因果假设和以概率分布形式给出的统计知识对行为影响的阐明。在特定的情况下，我们感兴趣的是预测在一组变量上执行操作并随后对另一组变量进行测量所产生的条件分布。我们提供了一种必要且充分的图形条件，可用于唯一计算出这些分布的情况，同时还提供了一种算法。此外，我们使用我们的结果证明了对于相同的识别问题，do-calculus [Pearl, 1995] 是完备的。

条件干预分布的识别

Identification of Conditional Interventional Distributions

We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS)
embeddings of conditional distributions and vector-valued regressors. This
connection introduces a natural regularized loss function which the RKHS
embeddings minimise, providing an intuitive understanding of the embeddings and
a justification for their use. Furthermore, the equivalence allows the
application of vector-valued regression methods and results to the problem of
learning conditional distributions. Using this link we derive a sparse version
of the embedding by considering alternative formulations. Further, by applying
convergence results for vector-valued regression to the embedding problem we
derive minimax convergence rates which are O(\log(n)/n) -- compared to current
state of the art rates of O(n^{-1/4}) -- and are valid under milder and more
intuitive assumptions. These minimax upper rates coincide with lower rates up
to a logarithmic factor, showing that the embedding method achieves nearly
optimal rates. We study our sparse embedding algorithm in a reinforcement
learning task where the algorithm shows significant improvement in sparsity
over an incomplete Cholesky decomposition.

本文介绍了使用 reproducing kernel Hilbert space embeddings of conditional distributions 与 vector-valued regressors 之间的等价关系，从而引入了一个自然的正则化损失函数以更好地理解和使用这种嵌入方法，并且通过向量回归方法的应用和导出推导生成了嵌入算法的最小一致收敛率 O (log (n)/n)，并在强化学习任务中得出了一个稀疏嵌入算法。