Machine Learning/Learning Center/Probabilistic Graphical Models

Probabilistic Graphical Models

Master graph-based probability models that simplify complex probabilistic computations. Learn how nodes and edges represent random variables and their dependencies for inference in speech recognition, image processing, and text analysis.

Fundamentals

Module 1

Understand the foundation of probabilistic graphical models. Learn graph structure definitions, directed vs undirected models, generative vs discriminative paradigms, and how graphs simplify probability computation through inference.

Topics Covered:

Graph Structure Definition

Directed vs Undirected Models

Generative vs Discriminative

Core Inference Goals

Medical Diagnosis Networks

Hidden Markov Models (HMM)

Module 2

Master sequential directed graph models with hidden states. Learn state and observation variables, three parameters (A, B, π), joint probability formulas, and three fundamental problems: evaluation, decoding (Viterbi), and learning (Baum-Welch).

Topics Covered:

State & Observation Variables

Transition & Emission Matrices

Forward/Backward Algorithms

Viterbi Algorithm

Baum-Welch Learning

Speech Recognition Examples

Markov Random Fields (MRF)

Module 3

Explore undirected graph probability models. Learn cliques and maximal cliques, potential functions (energy functions), joint distribution based on clique decomposition, and three Markov properties: global, local, and pairwise.

Topics Covered:

Cliques & Maximal Cliques

Potential Functions

Energy Functions

Three Markov Properties

Conditional Independence

Image Denoising Examples

Conditional Random Fields (CRF)

Module 4

Master discriminative undirected graph models for sequence labeling. Learn linear-chain CRF structure, transition and state feature functions, conditional probability formulas, and applications to part-of-speech tagging and named entity recognition.

Topics Covered:

Linear-Chain CRF

Feature Functions

Transition & State Features

Sequence Labeling

POS Tagging

Named Entity Recognition

Exact Inference

Module 5

Learn precise probability computation methods without approximation. Master variable elimination algorithms, belief propagation (message passing), marginal and conditional probability calculation, and when to use exact methods for acyclic graphs.

Topics Covered:

Variable Elimination

Belief Propagation

Message Passing

Marginal Probability

Conditional Probability

Tree Structure Inference

Approximate Inference

Module 6

Handle complex graphs and high-dimensional variables with approximation methods. Learn MCMC sampling (Metropolis-Hastings, Gibbs sampling), variational inference (ELBO, KL divergence, mean-field), and when to use each approach.

Topics Covered:

MCMC Sampling

Metropolis-Hastings

Gibbs Sampling

Variational Inference

ELBO & KL Divergence

Mean-Field Approximation

Topic Models (LDA)

Module 7

Master generative directed graph models for text analysis. Learn Latent Dirichlet Allocation (LDA), bag-of-words representation, Dirichlet distributions, document-topic and topic-word distributions, parameter estimation, and topic inference for document clustering.

Topics Covered:

LDA Model Structure

Bag-of-Words

Dirichlet Distribution

Document-Topic Distribution

Topic-Word Distribution

Text Topic Modeling

Suggested Learning Paths

Fundamentals Path

Start with core concepts

Fundamentals
Hidden Markov Models
Markov Random Fields

Inference Path

Master inference methods

Exact Inference
Approximate Inference

Applications Path

Focus on practical applications

Conditional Random Fields
Topic Models

Why Learn Probabilistic Graphical Models?

Simplify Complex Probability

Graph structures provide intuitive visualizations of probabilistic relationships, making complex joint distributions manageable through factorization.

Real-World Applications

Essential for speech recognition (HMM), image processing (MRF), natural language processing (CRF, LDA), and many other domains requiring structured probabilistic reasoning.

Foundation for Advanced ML

Understanding graphical models provides the foundation for deep learning, variational autoencoders, and other modern probabilistic machine learning techniques.

Industry Standard

Widely used in industry for natural language processing, computer vision, bioinformatics, and recommendation systems where structured probabilistic reasoning is crucial.

Start Learning