Lectures related to Multivariate Gaussian Distribution

Multivariate Normal Distribution

Covers the multivariate normal distribution, moment-generating function, and combinatorics.

Multivariate Statistics: Normal Distribution

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

Linear Combinations: Moment-Generating Functions

Explores moment-generating functions, linear combinations, and normality of random variables.

Linear Models: Least Squares

Explores linear models, least squares, Gaussian vectors, and model selection methods.

Canonical Correlation Analysis: Overview

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

Moment Generating Function and Multivariate Normal Distribution

Explores moment generating functions and multivariate normal distributions in probability and statistics.

Multivariate Statistics: Normal Distribution

Introduces multivariate statistics, covering normal distribution properties and characteristic functions.

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.

Fundamental Limits of Gradient-Based Learning

Delves into the fundamental limits of gradient-based learning on neural networks, covering topics such as binomial theorem, exponential series, and moment-generating functions.

Linear Applications: Vector Spaces and Subspaces

Explores linear applications in vector spaces, emphasizing subspaces and properties of linear maps.

Common Distributions: Moment Generating Functions

Explores common probability distributions, special distributions, and entropy concepts.

Probability Distributions: Independence and Linear Combinations

Explores independence, linear combinations of variables, and probability laws.

Gaussian Vectors: Properties and Distributions

Explains multivariate Gaussian distribution properties and moment generating functions for random vectors.

Gaussian Random Vectors

Explores Gaussian vectors, moment generating functions, independence, density functions, affine transformations, and quadratic forms.

Linear Algebra Review

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Linear Algebra Basics: Vector Spaces, Transformations, Eigenvalues

Covers fundamental linear algebra concepts like vector spaces and eigenvalues.

Diagonalisation of Symmetric Matrix by Orthogonal Matrix

Covers the method of diagonalizing a symmetric matrix using an orthogonal matrix.

Vector Subspaces in R4

Explores vector subspaces in R4, symmetric matrices, basis vectors, and canonical forms.

Random Vectors and Stochastic Models for Communications

Covers random vectors, joint probability, and conditional probability in communication stochastic models.

Probability Distributions: Central Limit Theorem and Applications

Discusses probability distributions and the Central Limit Theorem, emphasizing their importance in data science and statistical analysis.