Lectures related to Covariance

Principal Components: Properties & Applications

Explores principal components, covariance, correlation, choice, and applications in data analysis.

Covers the estimation of R, focusing on moments and covariance.

Explores dependence in random vectors, covering joint density, conditional independence, covariance, and moment generating functions.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Quantifying Statistical Dependence: Covariance and Correlation

Explores covariance, correlation, and mutual information in quantifying statistical dependence between random variables.

Multivariate Statistics: Normal Distribution

Covers the multivariate normal distribution, properties, and sampling methods.

Dynamical Frames in Gravity: Observables, Locality, and Covariance

Explores dynamical frames in gravity, focusing on observables, locality, and covariance.

Central Limit Theorem: Properties and Applications

Explores the Central Limit Theorem, covariance, correlation, joint random variables, quantiles, and the law of large numbers.

Conditional Gaussian Generation

Explores the generation of multivariate Gaussian distributions and the challenges of factorizing covariance matrices.

Covariance of Differenced Measurements

Explores the concept of covariance in differenced measurements and correlation between observations.

Dependence and Correlation

Explores dependence, correlation, and conditional expectations in probability and statistics, highlighting their significance and limitations.

Variance and Covariance: Properties and Examples

Explores variance, covariance, and practical applications in statistics and probability.

PCA: Derivation and Optimization

Covers the derivation of PCA projection, error minimization, and eigenvector optimization.

Principal Component Analysis: Understanding Data Structure

Explores Principal Component Analysis, dimensionality reduction, data quality assessment, and error rate control.

Stochastic Models for Communications

Covers random vectors, stochastic models, functions, matrices, and expectations in communication systems.

Propagation of Uncertainty: Estimation and Distribution

Discusses estimation and propagation of uncertainty in random variables and the importance of managing uncertainty in statistical analysis.

Fluctuation-dissipation relations for reversible diffusions

Covers linear response, steady states, Girsanov transforms, and covariance limits in reversible diffusions.

Max-Stable Models: Smith and Schlather

Covers the Smith and Schlather max-stable models, exploring their validity and interpretation.

Stable Laws: Lindeberg-Rafeller Theorem

Covers the Lindeberg-Rafeller theorem, discussing characteristic functions, moment problems, and the Central Limit Theorem.

Unsupervised Learning: PCA & K-means

Covers unsupervised learning with PCA and K-means for dimensionality reduction and data clustering.