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

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Lectures in this course (118)

Explores implicit bias, gradient descent, stability in optimization algorithms, and generalization bounds in machine learning.

Double Descent Curves: Overparametrization

Explores double descent curves and overparametrization in machine learning models, highlighting the risks and benefits.

Deep Learning III

Delves into deep learning optimization, challenges, SGD variants, critical points, overparametrized networks, and adaptive methods.

Adaptive Gradient Methods: Theory and Applications

Explores adaptive gradient methods, their properties, convergence, and comparison with traditional optimization algorithms.

Structures in Non-Convex Optimization

Delves into structures in non-convex optimization, emphasizing scalable optimization for deep learning.

Adaptive Optimization Methods: Theory and Applications

Explores adaptive optimization methods that adapt locally and converge without knowing the smoothness constant.

Adversarial Machine Learning: Fundamentals and Techniques

Explores adversarial machine learning, covering the generation of adversarial examples, robustness challenges, and techniques like Fast Gradient Sign Method.

Adversarial Training: Theory and Applications

Covers the practical implementation and applications of adversarial training, Generative Adversarial Networks, distance between distributions, and enforcing 1-Lipschitz in GANs.

Adversarial Machine Learning: Theory and Applications

Covers the theory and applications of adversarial machine learning, focusing on minmax optimization and robustness to adversarial examples.

Primal-dual Optimization

Explores primal-dual optimization, covering minimax formulations, saddle points, and challenges in nonconvex-nonconcave settings.

Minimax Optimization: Theory and Algorithms

Explores minimax optimization theory, including weak and strong duality, saddle points, and practical algorithm performance.

Primal-dual Optimization: Fundamentals

Explores primal-dual optimization, minimax problems, and gradient descent-ascent methods for optimization algorithms.

Primal-dual Optimization: Algorithms and Convergence

Explores primal-dual optimization algorithms for convex-concave minimax problems, discussing convergence properties and applications.

Quadratic Penalty Methods: Concepts and Algorithms

Explores quadratic penalty methods for nonconvex-concave optimization problems and introduces primal-dual algorithms with penalty functions.

Primal-dual Optimization: Extra-Gradient Method

Explores the Extra-Gradient method for Primal-dual optimization, covering nonconvex-concave problems, convergence rates, and practical performance.

Primal-dual Optimization: Methods and Applications

Explores primal-dual optimization methods, algorithms, convergence, and applications in nonconvex optimization and image deconvolution.

Semidefinite Programming: Formulations and Applications

Explores Semidefinite Programming formulations, SDP relaxations, and optimization strategies with convergence guarantees.

Primal-dual Optimization III: Lagrangian Gradient Methods

Explores primal-dual optimization methods, emphasizing Lagrangian gradient techniques and their applications in data optimization.

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