Let ${\pi }_0$ and ${\pi }_1$ be two distributions on the Borel space $({\mathbb{R}}^d,\mathfrak{B}({\mathbb{R}}^d))$. Any measurable function $T:{\mathbb{R}}^d\to {\mathbb{R}}^d$ 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‐discretised 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.

中文翻译：

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Gibbs流量用于近似运输，并应用于贝叶斯计算

让 ${\pi }_0$ 和 ${\pi }_{\mathrm{1个}}$ 是Borel空间上的两个分布 $（{\mathbb{[R}}^d，\mathfrak{乙}（{\mathbb{[R}}^d））$。任何可测量的功能$Ť：{\mathbb{[R}}^d\to {\mathbb{[R}}^d$ 这样 $ÿ=Ť（X）〜{\pi }_{\mathrm{1个}}$ 如果 $X〜{\pi }_0$ 被称为从 ${\pi }_0$ 到 ${\pi }_{\mathrm{1个}}$。对于任何${\pi }_0$ 和 ${\pi }_{\mathrm{1个}}$，如果可以从中获得运输图的解析表达式 ${\pi }_0$ 到 ${\pi }_{\mathrm{1个}}$，则可以直接将其应用于任何分布的样本。一个人会从一个易于样本的分布中绘制地图${\pi }_0$ 到目标分布 ${\pi }_{\mathrm{1个}}$使用此运输地图。尽管通常不可能获得用于复杂目标分布的显式运输图，但我们在此处显示了如何构建新颖运输图的易处理近似。这是通过从${\pi }_0$使用常微分方程，其速度场取决于目标的全部条件分布。即使当该常微分方程在时间上离散并且对整个条件分布进行数值近似时，映射样本的所得分布也可以得到有效评估，并可以用作顺序蒙特卡洛采样器中的建议。在各种应用程序上，我们以固定的计算复杂度证明了与先进的顺序蒙特卡洛采样器相比所取得的显著成就。