Math & Optimization · advanced · concept 73 of 311 · Updated Nov 4, 2026

📐Probabilistic Graphical Models & HMMs

Networks of random variables whose edges encode dependence: Bayesian networks for causal structure, hidden Markov models for sequences with hidden state. Pre-deep-learning speech recognition and gene finding ran on HMMs and Viterbi decoding, and the toolkit (EM, Kalman filters) still runs tracking, robotics, and diagnosis systems today.