# Elements of Sequential Monte Carlo

## TL;DR

This tutorial provides a comprehensive overview of sequential Monte Carlo methods for approximate inference in probabilistic models, covering theory, practical design choices, and recent advances in learning proposals.

## Contribution

It reviews the fundamentals of SMC, discusses recent developments in learning proposals and target distributions, and illustrates applications in machine learning models.

## Key findings

- SMC effectively approximates intractable expectations in Bayesian inference.
- Recent methods improve proposal distributions using variational inference.
- SMC estimates of normalizing constants enable advanced inference techniques.

## Abstract

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as expectations with respect to the posterior distribution. The key challenge is to approximate these intractable expectations. In this tutorial, we review sequential Monte Carlo (SMC), a random-sampling-based class of methods for approximate inference. First, we explain the basics of SMC, discuss practical issues, and review theoretical results. We then examine two of the main user design choices: the proposal distributions and the so called intermediate target distributions. We review recent results on how variational inference and amortization can be used to learn efficient proposals and target distributions. Next, we discuss the SMC estimate of the normalizing constant, how this can be used for pseudo-marginal inference and inference evaluation. Throughout the tutorial we illustrate the use of SMC on various models commonly used in machine learning, such as stochastic recurrent neural networks, probabilistic graphical models, and probabilistic programs.