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Lecture
PCA: Derivation and Optimization
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Optimization Techniques: Stochastic Gradient Descent and Beyond
Discusses optimization techniques in machine learning, focusing on stochastic gradient descent and its applications in constrained and non-convex problems.
Gradient Descent
Covers the concept of gradient descent, a universal algorithm used to find the minimum of a function.
Monte Carlo Chain: Motivation and Algorithm
Explores the motivation and algorithm behind the Monte Carlo Chain method.
Dependence in Random Vectors
Explores dependence in random vectors, covering joint density, conditional independence, covariance, and moment generating functions.
Coin Rendering: Part 1
Covers coin rendering and the limitations of the greedy algorithm in finding optimal solutions.
Calcul de valeurs propres
Covers the calculation of eigenvalues and eigenvectors, emphasizing their significance and applications.
Covariance Cleaning and Estimators
Explores covariance matrix cleaning, optimal estimators, and rotationally invariant methods for portfolio optimization.
Principal Component Analysis: Properties and Applications
Explores Principal Component Analysis theory, properties, applications, and hypothesis testing in multivariate statistics.
Linear Dimensionality Reduction: PCA and LDA
Explores PCA and LDA for linear dimensionality reduction in data, emphasizing clustering and class separation techniques.
Multivariate Statistics: Introduction and Methods
Introduces multivariate statistics, focusing on uncovering associations between components in data in vector form.