Probabilistic Graphical Models: A Concise Tutorial

TL;DR

This tutorial introduces probabilistic graphical models, explaining their theoretical foundations, representations, and algorithms for learning and inference, serving as a comprehensive guide for understanding this key machine learning framework.

Contribution

It provides a concise, accessible overview of probabilistic graphical models, covering formalism, methods, and applications, bridging probability and graph theory.

Findings

Explains how graphs represent multivariate distributions

Describes algorithms for learning model parameters and structures

Details exact and approximate inference methods

Abstract

Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant body of theory that bridges two mathematical traditions: probability and graph theory. This framework provides compact yet expressive representations of joint probability distributions, yielding powerful generative models for probabilistic reasoning. This tutorial provides a concise introduction to the formalisms, methods, and applications of this modeling framework. After a review of basic probability and graph theory, we explore three dominant themes: (1) the representation of multivariate distributions in the intuitive visual language of graphs, (2) algorithms for learning model parameters and graphical structures from data, and (3) algorithms for inference, both exact and approximate.