Markov Chains: Theory and Applications

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Related lectures (30)

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Stochastic Simulation: Variance Reduction Techniques

Covers stochastic simulation and variance reduction techniques, focusing on Courra variate and auxiliary distribution generation.

Fundamental Limits of Gradient-Based Learning

Delves into the fundamental limits of gradient-based learning on neural networks, covering topics such as binomial theorem, exponential series, and moment-generating functions.

Elements of Statistics: Probability and Random Variables

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Calculations of Expectation

Covers the calculation of expectation and variance for different types of random variables, including discrete and continuous ones.

Eigenvalues and Eigenvectors of Markov Chains

Explores eigenvalues and eigenvectors of Markov chains, focusing on convergence rates and matrix properties.

Introduction to Continuous Random Variables: Probability Distributions

Introduces continuous random variables and their probability distributions, emphasizing their applications in statistics and data science.

Generating Functions: Properties and Applications

Explores generating functions, Laplace transform, and their role in probability distributions.

Invariant Measures: Properties and Applications

Covers the concept of invariant measures in Markov chains and their role in analyzing irreducible recurrent processes.

Markov Chain Monte Carlo: Rejection Sampling

Explores rejection sampling for generating sample values from a target distribution, along with Bayesian inference using MCMC.

Eigenvalues and EM Algorithm

Covers eigenvectors, principal components, likelihood variables, EM algorithm, Jensen's inequality, and maximizing lower bounds.