Probabilistic Methods
Bayesian methods, graphical models, and probabilistic inference.
Bayesian Inference
Updating beliefs with evidence via Bayes’ theorem – treating parameters as distributions rather than fixed values.
Expectation-Maximization
Iteratively inferring latent variables (E-step) and optimizing parameters (M-step) – the workhorse for incomplete data.
Gaussian Processes
Nonparametric Bayesian regression defining distributions over functions – elegant uncertainty quantification with O(n^3) cost.
Graphical Models
Bayesian networks and Markov random fields representing conditional dependencies as graphs – structured probabilistic reasoning.
Markov Chain Monte Carlo
Sampling from complex posterior distributions by constructing Markov chains – when exact inference is intractable.
Variational Inference
Approximating intractable posteriors by optimization rather than sampling – trading exactness for scalability.