Graphical Models & Probabilistic Inference

Graphical models combine graph theory and probability to represent complex relationships and enable efficient probabilistic inference.

Basics Of Graphical Models

Graphical models are used to represent joint probability distributions visually through graphs, enabling efficient probabilistic reasoning.

What Are Graphical Models?

Graphical models represent joint probability distributions over variables using graphs, facilitating efficient reasoning under uncertainty.

Key Concepts

This section introduces fundamental concepts in graphical models, including conditional independence, factorization, and the distinction between local and global semantics.

Types Of Graphical Models

This section discusses the different types of graphical models used to represent statistical relationships among variables, including Bayesian networks, Markov random fields, and factor graphs.

Bayesian Networks (Directed Graphical Models)

Bayesian Networks utilize directed acyclic graphs to represent conditional independence among variables, facilitating probabilistic inference.

Markov Random Fields (Mrfs) / Undirected Graphical Models

Markov Random Fields (MRFs) utilize undirected graphs to model the joint distribution of random variables, revealing dependencies through cliques.

Factor Graphs

Factor graphs are bipartite graphs that separate variables and factors, allowing for modular representation and facilitating message-passing algorithms.

Conditional Independence And D-Separation

This section introduces conditional independence and its significance in probabilistic reasoning, detailing how d-separation is used in Bayesian networks to determine independence among variables.

Conditional Independence

This section explores the concept of conditional independence, a crucial aspect in probabilistic reasoning and graphical models.

D-Separation In Bayesian Networks

d-Separation is a vital concept in Bayesian networks that allows us to determine whether a set of variables is conditionally independent.

Inference In Graphical Models

This section explores the techniques used for inference in graphical models, including both exact and approximate methods for computing probabilities and most probable explanations.

Exact Inference

This section discusses exact inference methods in graphical models, including variable elimination, belief propagation, and the junction tree algorithm to compute probabilities.

Variable Elimination

Variable elimination is a key exact inference method that systematically eliminates variables from probabilistic models through summation or maximization.

Belief Propagation (Message Passing)

Belief propagation is a method of performing inference on graphical models, relying on message passing between nodes to calculate beliefs over the variables.

Junction Tree Algorithm

The Junction Tree Algorithm is a method for performing exact inference in graphical models by converting the graph into a tree structure.

Approximate Inference

Approximate inference methods are utilized in graphical models when exact inference becomes infeasible due to complexities arising from cycles or high-dimensional data.

Sampling Methods

Sampling methods are techniques used to approximate probabilistic inference in graphical models.

Variational Inference

Variational inference is a method for approximating complex probability distributions using simpler ones.

Learning In Graphical Models

This section addresses learning in graphical models, focusing on parameter and structure learning techniques.

Parameter Learning

Parameter learning in graphical models involves estimating parameters from data using techniques like Maximum Likelihood Estimation (MLE) and Bayesian estimation.

Structure Learning

Structure learning involves discovering the graph structure of graphical models from data using various methods.

Applications Of Graphical Models

Graphical models are widely applicable across various domains, enhancing efficiency and accuracy in complex systems.