Principal Component Analysis: Covariance Matrix and Eigenvalues

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PCA: Derivation and Optimization

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

Principal Component Analysis: Properties and Applications

Explores Principal Component Analysis theory, properties, applications, and hypothesis testing in multivariate statistics.

Oja's Rule

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

Dimensionality Reduction

Explores Singular Value Decomposition and Principal Component Analysis for dimensionality reduction, with applications in visualization and efficiency.

Dependence in Random Vectors

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

Estimating R: Moments and Covariance

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

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.

Covariance Cleaning and Estimators

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

Non-Negative Definite Matrices and Covariance Matrices

Covers non-negative definite matrices, covariance matrices, and Principal Component Analysis for optimal dimension reduction.