Expectation Value and Convex Functions

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Related lectures (30)

Introduction to Convexity

Introduces the key concepts of convexity and its applications in different fields.

Subgradients and Convex Functions

Explores subgradients in convex functions, emphasizing non-differentiable yet convex scenarios and properties of subdifferentials.

Convex Sets and Functions

Introduces convex sets and functions, discussing minimizers, optimality conditions, and characterizations, along with examples and key inequalities.

Basic Properties of Conditional Expectation

Covers basic properties of conditional expectation and Jensen's inequality in probability theory.

Optimization Techniques: Convexity in Machine Learning

Covers optimization techniques in machine learning, focusing on convexity and its implications for efficient problem-solving.

Mathematics of Data: Optimization Basics

Covers basics on optimization, including norms, Lipschitz continuity, and convexity concepts.

Proximal and Subgradient Descent: Optimization Techniques

Discusses proximal and subgradient descent methods for optimization in machine learning.

K-means and Gaussian Mixture Model

Introduces K-means clustering, the Gaussian mixture model, Jensen's inequality, and the EM algorithm.

Optimization Basics

Introduces optimization basics, covering logistic regression, derivatives, convex functions, gradient descent, and second-order methods.

Optimal Transport: Rockafellar Theorem Log in to Mediaspace to watch this video

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Convexity: Functions and Global Minima Log in to Mediaspace to watch this video

Explores convex functions, global minima, and their relationship with differentiability.

Convex Optimization: Convex Functions Log in to Mediaspace to watch this video

Covers the concept of convex functions and their applications in optimization problems.

Geodesic Convexity: Theory and Applications Log in to Mediaspace to watch this video

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Convex Optimization: Elementary Results Log in to Mediaspace to watch this video

Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.

Convex Optimization: Sets and Functions Log in to Mediaspace to watch this video

Introduces convex optimization through sets and functions, covering intersections, examples, operations, gradient, Hessian, and real-world applications.

Convex Functions Log in to Mediaspace to watch this video

Covers the properties and operations of convex functions.

Optimization Problems: Path Finding and Portfolio Allocation Log in to Mediaspace to watch this video

Covers optimization problems in path finding and portfolio allocation.

Optimization Techniques: Convexity and Algorithms in Machine Learning Log in to Mediaspace to watch this video

Covers optimization techniques in machine learning, focusing on convexity, algorithms, and their applications in ensuring efficient convergence to global minima.

Convex Optimization Log in to Mediaspace to watch this video

Introduces convex optimization, focusing on the importance of convexity in algorithms and optimization problems.

Conjugate Duality: Understanding Convex Optimization Log in to Mediaspace to watch this video

Explores conjugate duality in convex optimization, covering weak and supporting hyperplanes, subgradients, duality gap, and strong duality conditions.

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