Explores linear dimensionality reduction through PCA, variance maximization, and real-world applications like medical data analysis.
Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.
Explores market response functions, flash crashes, correlation estimation, and noise filtering in finance.
Covers Oja's rule in Neurorobotics, focusing on learning eigenvectors and eigenvalues for capturing maximal variance.
Explores dependence in random vectors, covering joint density, conditional independence, covariance, and moment generating functions.
Covers the key concepts of PCA, including reducing data dimensionality and extracting features, with practical exercises.
