Lectures related to The Spike-Wigner model

Spiked Matrix Estimation

Covers the AMP algorithm for spiked matrix estimation and its application to low-rank matrix factorization and GLM models.

Hypothesis Testing with Gaussian Noise

Covers hypothesis testing with Gaussian noise and the standard Gaussian distribution.

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.

Canonical Correlation Analysis: Overview

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

Singular Value Decomposition

Explores Singular Value Decomposition, low-rank approximation, fundamental subspaces, and matrix norms.

Spectral Estimation: Gaussian vs Binary Signals

Explores spectral estimation for Gaussian and binary signals in the spiked matrix estimation problem, analyzing the impact of signal-to-noise ratio.

Gaussian Noise: Decision Making

Covers Gaussian noise and decision-making in communication systems, emphasizing the importance of understanding Gaussian noise in signal processing.

Diagonalization Techniques: Jacobi Method

Covers the Jacobi method, Givens rotation, QR decomposition, and diagonalization techniques in computational physics.

Linear Regression: Absence or Presence of Covariates

Explores linear regression with and without covariates, covering models captured by independent distributions and tools like subspaces and orthogonal projections.

Multivariate Statistics: Normal Distribution

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

Diffusion Models

Explores diffusion models, focusing on generating samples from a distribution and the importance of denoising in the process.

Eigenstate Thermalization Hypothesis Log in to Mediaspace to watch this video

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Finite Element Modeling: Dynamics Log in to Mediaspace to watch this video

Introduces the basics of finite element modeling for dynamics and discusses the Newmark method for time integration.

Wireless Receivers: Gaussian Noise and Error Probability Estimation Log in to Mediaspace to watch this video

Covers wireless receivers in the presence of Gaussian noise and error probability estimation.

Sparse Regression Log in to Mediaspace to watch this video

Covers the concept of sparse regression and the use of Gaussian additive noise in the context of MAP estimator and regularization.

Singular Value Decomposition Log in to Mediaspace to watch this video

Covers the Singular Value Decomposition theorem and its application in decomposing matrices.

Parametric Signal Models: Matlab Practice Log in to Mediaspace to watch this video

Covers parametric signal models and practical Matlab applications for Markov chains and AutoRegressive processes.

Poisson Shot Noise: Signal-to-Noise Ratio of a Photodetector Log in to Mediaspace to watch this video

Explores Poisson processes in communication systems, focusing on photodetectors and signal-to-noise ratio calculations.

Convex Optimization: Linear Algebra Review Log in to Mediaspace to watch this video

Provides a review of linear algebra concepts crucial for convex optimization, covering topics such as vector norms, eigenvalues, and positive semidefinite matrices.

Finite Element Method Log in to Mediaspace to watch this video

Covers the Finite Element Method, discussing the derivation of the equation of motion and exploring mass and stiffness matrices.