Lectures related to Cross-covariance matrix

Principal Components: Properties & Applications

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

Gaussian Mixture Models: Likelihood and Covariance Matrix

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

PCA: Derivation and Optimization

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

Multivariate Statistics: Normal Distribution

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

Principal Component Analysis: Understanding Data Structure

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

Max-Stable Models: Smith and Schlather

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

Fluctuation-dissipation relations for reversible diffusions

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

Extreme Value Models: Technical Derivation

Explores the technical derivation and properties of Multivariate Extreme Value models.

Estimating the Term Structure: Principal Component Analysis

Covers Principal Component Analysis for yield curve shape estimation and dimension reduction in interest rate models.

Principal Component Analysis: Covariance Matrix and Eigenvalues

Explores Principal Component Analysis focusing on maximizing variance and finding eigenvalues.

Linear Dimensionality Reduction: PCA and LDA

Explores PCA and LDA for linear dimensionality reduction in data, emphasizing clustering and class separation techniques.

Stable Laws: Lindeberg-Rafeller Theorem

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

Fitting data with one Gauss function

Explains Gaussian functions, modeling data, likelihood function, and maximum likelihood optimization.

Covariance Cleaning and Estimators

Explores covariance matrix cleaning, optimal estimators, and rotationally invariant methods for portfolio optimization.

Oja's Rule

Covers Oja's rule in Neurorobotics, focusing on learning eigenvectors and eigenvalues for capturing maximal variance.

Gaussian Discriminant Analysis

Covers Gaussian discriminant analysis, log-likelihood, supervised learning, and logistic regression.

Multivariate Normal Distribution

Covers the multivariate normal distribution, moment-generating function, and combinatorics.

Estimating R: Moments and Covariance

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

Gaussian Random Vectors

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