# Probabilistic Graphical Models and Inference

Canonical: https://manyspace.aporia.systems/subjects/ai/probabilistic-graphical-models-and-inference-94
Updated: 2026-10-13

Probabilistic Graphical Models and Inference: about 12 hours. Each topic lists what you need first and what it unlocks.

## Representation

- [Bayesian Networks](https://manyspace.aporia.systems/topics/bayesian-networks-aiml-pgm-001)
- [Conditional Independence and d-Separation](https://manyspace.aporia.systems/topics/conditional-independence-and-d-separation-aiml-pgm-002)
- [Markov Random Fields](https://manyspace.aporia.systems/topics/markov-random-fields-aiml-pgm-003)

## Inference

- [Exact Inference: Variable Elimination and Belief Propagation](https://manyspace.aporia.systems/topics/exact-inference-variable-elimination-and-belief-propagation-aiml-pgm-004)
- [Monte Carlo Estimation and Importance Sampling](https://manyspace.aporia.systems/topics/monte-carlo-estimation-and-importance-sampling-aiml-pgm-008)
- [Markov Chain Monte Carlo](https://manyspace.aporia.systems/topics/markov-chain-monte-carlo-aiml-pgm-009)
- [Variational Inference and the ELBO](https://manyspace.aporia.systems/topics/variational-inference-and-the-elbo-aiml-pgm-010)
- [Probabilistic Programming](https://manyspace.aporia.systems/topics/probabilistic-programming-aiml-pgm-012)

## Learning

- [Expectation-Maximization](https://manyspace.aporia.systems/topics/expectation-maximization-aiml-pgm-005)

## Temporal

- [Hidden Markov Models](https://manyspace.aporia.systems/topics/hidden-markov-models-aiml-pgm-006)
- [Kalman Filters and Linear-Gaussian State Space Models](https://manyspace.aporia.systems/topics/kalman-filters-and-linear-gaussian-state-space-models-aiml-pgm-007)
- [Conditional Random Fields](https://manyspace.aporia.systems/topics/conditional-random-fields-aiml-pgm-011)