论文标题
自动向后过滤前向Markov过程和图形模型进行前向指南
Automatic Backward Filtering Forward Guiding for Markov processes and graphical models
论文作者
论文摘要
我们将离散和连续的时间马尔可夫过程作为构建块结合到具有潜在和观察到的变量的概率图形模型中。我们介绍了自动向后滤波前向指导（BFFG）范式（Mider等，2021），以便对潜在状态和模型参数的可编程推断。我们的起点是生成模型，是对概率过程动态的正向描述。我们通过模型将观察结果提供的信息反向传播，以将生成（正向）模型转换为以数据为指导的条件前模型。它近似于两者之间的已知似然比近似实际条件模型。向后的过滤器和量度的正变化适合将其纳入概率编程环境中，因为它们可以作为一组转换规则进行配制。 可以将引导生成模型纳入不同的方法中，以有效地采样潜在状态和以观测为条件的参数。我们显示在各种设置中的适用性，包括具有离散状态空间的马尔可夫链，相互作用的粒子系统，状态空间模型，分支扩散和伽马过程。
We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.
