Lecture

Markov Chains: Applications and Sampling Methods

Related lectures (32)

Markov Chains: Applications and Analysis

Explores Markov chains, focusing on the coloring problem and algorithm analysis.

Covers the theory and applications of graph coloring, focusing on disassortative stochastic block models and planted coloring.

Markov Chains and Algorithm Applications

Covers the fundamentals of Markov chains and their applications in algorithms, focusing on proper coloring and the Metropolis algorithm.

Probability & Stochastic Processes

Covers applied probability, stochastic processes, Markov chains, rejection sampling, and Bayesian inference methods.

Markov Chains and Algorithm Applications

Covers Markov chains and their applications in algorithms, focusing on Markov Chain Monte Carlo sampling and the Metropolis-Hastings algorithm.

Theory of MCMC

Covers the theory of Markov Chain Monte Carlo (MCMC) sampling and discusses convergence conditions, transition matrix choice, and target distribution evolution.

Belief Propagation

Explores Belief Propagation in graphical models, factor graphs, spin glass examples, Boltzmann distributions, and graph coloring properties.

Markov Chain Monte Carlo: Sampling and Convergence

Explores Markov Chain Monte Carlo for sampling high-dimensional distributions and optimizing functions using the Metropolis-Hastings algorithm.

Belief Propagation for Graph Coloring

Explores Belief Propagation for graph coloring and its convergence properties.

Monte Carlo Markov Chains

Covers the theory of Markov chains and Monte Carlo methods.

Information Theory: Basics

Covers the basics of information theory, entropy, and fixed points in graph colorings and the Ising model.

Graph Coloring: Random vs Symmetrical

Compares random and symmetrical graph coloring in terms of cluster colorability and equilibrium.

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Monte Carlo Techniques: Sampling and Simulation

Explores Monte Carlo techniques for sampling and simulation, covering integration, importance sampling, ergodicity, equilibration, and Metropolis acceptance.

Markov Chains and Algorithm Applications

Covers the application of Markov chains and algorithms for function optimization and graph colorings.

Graph Coloring and Directed Cycles

Explores graph coloring, directed cycles, LLL algorithm applications, and element dependencies in graphs.

MCMC Examples and Error Estimation

Covers Markov Chain Monte Carlo examples and error estimation methods.

MCMC with Metropolis

Covers the implementation of Markov Chain Monte Carlo (MCMC) with the Metropolis algorithm for sampling from posterior distributions.

Graphical Models: Probability Distributions and Factor Graphs

Covers graphical models for probability distributions and factor graphs representation.

Graph Theory Basics

Introduces graph theory basics, Ramsey theory, and graph coloring concepts.