Lectures related to Generalization Error

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Covers the concept of graph sketching with a focus on connected components.

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Multivariate Statistics: Normal Distribution

Covers the multivariate normal distribution, properties, and sampling methods.

Exponential Family: Maximum Entropy Distributions

Covers exponential families and maximum entropy distributions under moment constraints.

Information Measures

Covers variational representation and information measures such as entropy and mutual information.

Linear Similarities and Similitudes

Explores linear similarities and similitudes, demonstrating their properties and applications in geometry.

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.

Sparsest Cut: Leighton-Rao Algorithm

Covers the Leighton-Rao algorithm for finding the sparsest cut in a graph, focusing on its steps and theoretical foundations.

Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Landscape and Generalisation in Deep Learning

Explores the challenges and insights of deep learning, focusing on loss landscape, generalization, and feature learning.

Untitled

Information Measures: Entropy and Information Theory

Explains how entropy measures uncertainty in a system based on possible outcomes.

Stable Laws and Limit Theorems

Explores stable laws, limit theorems, and random variable properties.

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Generalization Error

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.