probabilistic_models

Probabilistic Models

Implementation of probabilistic graphical models, inference algorithms, and learning techniques for Bayesian networks.

Contents

Inference by Enumeration

Notebook	Description
inference_by_enumeration.ipynb	Exact inference through variable elimination and enumeration

Approximate Inference

Notebook	Description
BayesNet Introduction.ipynb	Introduction to Bayesian network structure and semantics
rejection_sampling.ipynb	Monte Carlo sampling with rejection for probabilistic queries
likelihood_weighting.ipynb	Importance sampling for efficient approximate inference

Hidden Markov Models

Notebook	Description
hmm_algorithms.ipynb	Forward-backward algorithm, Viterbi decoding, and Baum-Welch learning

Parameter Learning

Notebook	Description
BayesNet Introduction.ipynb	Bayesian network fundamentals and conditional probability tables
Problem 1.ipynb	Maximum Likelihood Estimation for CPT parameters
Problem 2.ipynb	Bayesian parameter estimation with prior distributions

Structure Learning

Notebook	Description
structural_learning.ipynb	Learning network topology from data using scoring functions

Key Concepts

• Bayesian Networks: Directed acyclic graphs representing conditional dependencies
• Exact Inference: Computing posterior probabilities through enumeration
• Approximate Inference: Sampling-based methods for intractable distributions
• HMM: Temporal models for sequential observations with hidden states
• Parameter Learning: Estimating CPT entries from observed data
• Structure Learning: Discovering graph topology from data

Supporting Modules

• bayesian_network.py - Core Bayesian network class implementation
• utils.py - Helper functions for inference and learning algorithms