We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic conditioning. However, in many real-life scenarios, the observations are given as marginal distributions, summary statistics, or samplers. Conventional probabilistic programming systems lack adequate means for modeling and inference in such scenarios. We propose a generalization of deterministic conditioning to stochastic conditioning, that is, conditioning on the marginal distribution of a variable taking a particular form. To this end, we first define the formal notion of stochastic conditioning and discuss its key properties. We then show how to perform inference in the presence of stochastic conditioning. We demonstrate potential usage of stochastic conditioning on several case studies which involve various kinds of stochastic conditioning and are difficult to solve otherwise. Although we present stochastic conditioning in the context of probabilistic programming, our formalization is general and applicable to other settings.

翻译：我们处理关于可观测变量分布的设定概率方案的问题。概率方案通常以联合数据分布的样本为条件,我们称之为确定性条件。然而,在许多现实生活中,观测被描述为边际分布、简要统计或取样器。常规概率方案系统缺乏在这些情景中进行建模和推断的充分手段。我们建议对确定性功能进行概括化,以随机调节为条件,即以特定形式的变量的边际分布为条件。为此,我们首先界定随机调节的正式概念,并讨论其关键特性。然后我们展示如何在有随机调节的情况下进行推断。我们展示了在涉及各种随机调节和难以解析的若干案例研究上使用随机调节的潜力。尽管我们在概率规划背景下采用了随机调节,但我们的正规化是一般性的,适用于其他环境。