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EE-556: Mathematics of data: from theory to computation

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Lectures in this course (118)

Stochastic Gradient Descent: Theory and Applications

Covers the theory and applications of Stochastic Gradient Descent in machine learning models.

Maximum Likelihood Estimator: Expression and Gradient

Covers the maximum likelihood estimator expression and the gradient of the loss function.

Role of Computation in Optimization

Explores the role of computation in optimization, focusing on gradient descent for convex and nonconvex problems.

Optimization Basics: Norms, Convexity, Differentiability

Introduces optimization basics, covering norms, convexity, differentiability, and more, with a focus on metrics, vector norms, matrix norms, and continuity.

Gradient Descent Methods

Covers gradient descent methods for convex and nonconvex problems, including smooth unconstrained convex minimization, maximum likelihood estimation, and examples like ridge regression and image classification.

Gradient Descent Methods: Theory and Computation

Explores gradient descent methods for smooth convex and non-convex problems, covering iterative strategies, convergence rates, and challenges in optimization.

Optimization Basics: Norms, Convexity, Differentiability

Explores optimization basics such as norms, convexity, and differentiability, along with practical applications and convergence rates.

Advanced Triangulation: Gradient Maximization

Covers advanced triangulation problems related to gradient maximization.

Adversarial Training: Mock Exam Solution

Discusses the solution to a mock exam problem on adversarial training and the uniqueness of solutions.

Deep Learning Building Blocks: Linear Layers

Explains the fundamental building blocks of deep learning, focusing on linear layers and activation functions.

Optimality of Convergence Rate: Acceleration in Gradient Descent

Explores the optimality of convergence rate in gradient descent and acceleration techniques for convex and non-convex problems.

Mathematics of Data: From Theory to Computation

Covers key concepts in data mathematics, including automatic differentiation, linear layers, and attention layers.

Stochastic Gradient Descent: Optimization and Convergence

Explores stochastic gradient descent, covering convergence rates, acceleration, and practical applications in optimization problems.

Optimization Methods: Unconstrained Problems Analysis

Analyzes unconstrained optimization problems using gradient descent methods and explores convergence rates and algorithm behavior.

Interpreting Convergence Plots in Optimization

Discusses interpreting convergence plots in optimization, identifying bugs based on convergence rates, and understanding optimization algorithms.

Non-smoothness and Compressive Sensing

Explores non-smooth minimization, compressive sensing, sparse signal recovery, and simple representations using atomic sets and atoms.

Mathematics of Data: Optimization Basics

Covers optimization basics, including metrics, norms, convexity, gradients, and logistic regression, with a focus on strong convexity and convergence rates.

Structured Sparsity: Atomic Norms and Convex Optimization

Explores atomic norms, convex optimization, and structured sparsity in mathematical data analysis.

Stochastic Gradient Descent: Optimization and Convergence Analysis

Explores Stochastic Gradient Descent for non-strongly convex functions and the impact of step size on convergence.

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