Lectures related to Uncorrelatedness (probability theory)

Introduces random variables, probability measurement, expectation, moments, and relations between random variables.

Gaussian Mixture Models: Likelihood and Covariance Matrix

Explores statistical independence, Gaussian Mixture Models, and fitting data with Gaussian functions.

Biclustering & latent variables: statistical analysis of network data

Explores biclustering techniques and latent variables in network data analysis.

Explores Bayesian inference for Gaussian random variables, covering joint distribution, marginal pdfs, and the Bayes classifier.

Optimality and Asymptotics

Explores the optimality of the Least Squares Estimator and its large sample distribution.

Parameter Estimation

Discusses parameter estimation, including checks, quality, distribution, and statistical properties of estimates.

Estimating R: Moments and Cumulants

Explores the estimation of R using moments and cumulants in extreme value analysis.

Gaussian Random Vectors

Explores Gaussian random vectors and their statistical properties, emphasizing the importance of specifying statistical properties in complex valued random vectors.

Continuous-Time Stochastic Processes: Stationarity

Explores stationarity in continuous-time stochastic processes, focusing on autocorrelation and cross-correlation functions.

Statistical Estimation: Properties and Distributions

Explores statistical parameter estimation, sample accuracy, and Bernoulli variables' properties.

Hoeffding's Inequality: Binomial Distribution

Explores Hoeffding's inequality and the binomial distribution, focusing on error minimization and generalization gaps in predictor selection.

Independence and Covariance

Explores independence and covariance between random variables, discussing their implications and calculation methods.

Joint Distribution of Gaussian Random Vectors

Explores the criteria for Gaussian random vectors to have a joint PDF.

Probability Measures and Random Variables

Covers the Caratheodory extension theorem, uniqueness and existence of probability measures, Bernoulli random variables, and spaces of random variables.

Continuous-Time Stochastic Processes: Stationarity

Covers weak-sense stationarity for continuous-time stochastic processes and their properties.

Discrete Random Variables: Functions and Probabilities

Explores discrete random variables, their functions, and probabilities in various scenarios.

Long Memory and ARCH: Time Series

Explores long memory in time series and ARCH models for financial volatility.

Probability and Statistics

Delves into probability, statistics, paradoxes, and random variables, showcasing their real-world applications and properties.

Stochastic Processes: Stationarity in Continuous Time - Part 2

Discusses weak-sense stationarity in continuous-time stochastic processes and the calculation of autocorrelation and cross-correlation functions.

Canonical Correlation Analysis: Overview

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.