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【随机矩阵与机器学习6】Nonlinear Concentration of Gaussian RVs for Lipschitz Functions
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课程主页:https://rolandspeicher.com/category/lectures/high-dimensional-analysis-random-matrices-and-machine-lernaing-2023-lectures/ The goal of this lecture series is to cover mathematical interesting aspects of neural networks, in particular, those related to random matrices. In this sixth lecture we consider concentration of Gaussian random vectors for, in general non-linear, Lipschitz functions. We first talk about properties of the class of Lipschitz functions. Then we start the proof of the concentration statement, give the main ideas and recall and prove on the way also Jensen's inequality.
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【随机矩阵与机器学习20】Asymptotic Eigenvalue Distribution in the Random Feature Model
【随机矩阵与机器学习7】Proof of Nonlinear Concentration for Gaussian Random Vectors
【随机矩阵与机器学习5】Exponential Concentration of Norm of Gaussian Random Vectors
【随机矩阵与机器学习8】General Remarks on Linear/Nonlinear Concentration Inequalities
【随机矩阵与机器学习4】Gaussian Random Vectors and Concentration of Their Norm
【随机矩阵与机器学习3】Concentration of Volumes
【随机矩阵与机器学习10】Proof of Concentration of Largest Eigenvalue
【随机矩阵与机器学习25】Gaussian Equivalence Principle for Nonlinear Random Features
【随机矩阵与机器学习9】Wishart Random Matrices and Concentration of Largest Eigenvalue
【随机矩阵与机器学习13】Proof of Marchenko-Pastur: Equation for Stieltjes Transform
【随机矩阵与机器学习29】Free Probability Theory and Linearization of Nonlinear Problems
【随机矩阵与机器学习21】Another Proof of Marchenko-Pastur: via Stein's Identity
【随机矩阵与机器学习12】Preparations for Proof of Marchenko-Pastur Law
【随机矩阵与机器学习11】The Marchenko-Pastur Law for Wishart Matrices
【随机矩阵与机器学习26】Gradient Descent for Linear Regression
【随机矩阵与机器学习17】Double Descent and Linear Regression: Over-Determined Case
【随机矩阵与机器学习14】Proof of Marchenko-Pastur: Stieltjes Inversion Formula
【随机矩阵与机器学习18】Double Descent and Linear Regression: Under-Determined Case
【随机矩阵与机器学习28】Properties of the Neural Tangent Kernel
【随机矩阵与机器学习】24. Calculation of the Random Feature Eigenvalue Distribution
【随机矩阵与机器学习23】Cumulants and Their Properties and Uses
【随机矩阵与机器学习2】Volumes in High Dimensions
【随机矩阵3】Random Matrices: Wick Formula and Gaussian Random Matrix
【高维概率论】High-Dimensional Probability
【随机矩阵与机器学习22】Resolvent Method and Cumulant Expansion
【随机矩阵与机器学习19】General Remarks on Random Feature Model
【随机矩阵与机器学习15】Spiked Signal-Plus-Noise Model
【随机矩阵与机器学习1】Introduction and Survey
【随机矩阵与机器学习16】Proof of the Signal-Plus-Noise Theorem
【随机矩阵与机器学习27】Time Evolution of Learning and Neural Tangent Kernel
【随机矩阵16】Random Matrices: Determinantal Processes and Non-Crossing Paths
【随机矩阵1】Random Matrices: Introduction
【随机矩阵11】Random Matrices: Concentration Phenomena
【随机矩阵12】Random Matrices: Gaussian Poincare Inequality
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