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Lecture
Principal Component Analysis: Theory and Applications
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Principal Components: Properties & Applications
Explores principal components, covariance, correlation, choice, and applications in data analysis.
Multivariate Statistics: Introduction and Methods
Introduces multivariate statistics, focusing on uncovering associations between components in data in vector form.
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.
Market Response Functions
Explores market response functions, flash crashes, correlation estimation, and noise filtering in finance.
Central Limit Theorem: Properties and Applications
Explores the Central Limit Theorem, covariance, correlation, joint random variables, quantiles, and the law of large numbers.
Non-Negative Definite Matrices and Covariance Matrices
Covers non-negative definite matrices, covariance matrices, and Principal Component Analysis for optimal dimension reduction.
Eigenstate Thermalization Hypothesis
Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.
Stochastic Models for Communications
Covers random vectors, joint probability density, independent random variables, functions of two random variables, and Gaussian random variables.
Principal Component Analysis: Dimension Reduction
Covers Principal Component Analysis for dimension reduction in biological data, focusing on visualization and pattern identification.
Multivariate Statistics: Normal Distribution
Introduces multivariate statistics, covering normal distribution properties and characteristic functions.