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

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Lectures in this course (118)

Generalization in Deep Learning

Delves into the trade-off between model complexity and risk, generalization bounds, and the dangers of overfitting complex function classes.

Understanding Generalization: Implicit Bias & Optimization

Explores the trade-off between complexity and risk in machine learning models, the benefits of overparametrization, and the implicit bias of optimization algorithms.

Structures in Non-Convex Optimization

Explores non-convex optimization in deep learning, covering critical points, SGD convergence, saddle points, and adaptive gradient methods.

Mathematics of Data: Models and Learning

Explores models, learning paradigms, and applications in Mathematics of Data.

Optimizing Adaptive Gradient Methods

Explores advanced optimization techniques for machine learning models, focusing on adaptive gradient methods and their applications in non-convex optimization problems.

Adversarial Machine Learning

Delves into adversarial machine learning, exploring optimization formulations and robustness examples.

Adversarial Training: Optimization and Applications

Explores adversarial training optimization, practical implementation, interpretability, fairness, Wasserstein distance, and Wasserstein GANs.

Robustness and Diffusion Models

Explores robustness in GAN training, Gaussian algorithms, saddle points, and mixed Nash equilibrium.

Score-Based Generative Models

Delves into score-based generative models, exploring learning natural distributions and the impact of neural network architecture on robustness.

Fenchel Conjugation: Basics and Applications

Introduces Fenchel conjugation, exploring its properties, examples, and applications in nonsmooth optimization problems and minimax formulations.

Optimization Duality: Theory and Algorithms

Explores optimization duality, weak and strong duality, practical optimization algorithms, and challenges in nonconvex-concave problems.

Primal-dual Optimization: Extra-Gradient Method

Explores the Extra-Gradient Method for primal-dual optimization in min-max problems and its convergence properties.

Primal-dual Methods for Composite Minimization

Covers primal-dual methods for composite minimization, stochastic algorithms, nonconvex problems, and quadratic penalty techniques.

Primal-dual Optimization: Lagrangian Methods

Explores primal-dual optimization with a focus on Lagrangian methods and their convergence, drawbacks, and enhancements.

Statistical Learning Models: Risk and Empirical Risk Minimization

Covers statistical learning models, risk minimization, and empirical risk minimization with examples of maximum-likelihood estimators.

Nonconvex Optimization: Challenges and Strategies

Explores nonconvex optimization challenges and strategies, including blind image deconvolution and SDP relaxations.

Parametric Models: Regression Estimators and Optimization

Covers parametric models, regression estimators, and optimization in statistical modeling.

Mathematics of Data: Data, Models, and Optimization

Covers the role of models and data in statistical learning and optimization formulations, with examples of classification, regression, and density estimation problems.

Statistical Estimation: Models and Learning Machines

Covers statistical estimation models, ML estimators, learning machines, practical issues, and challenges in estimation.

Logistic Regression: Maximum Likelihood Estimation

Covers logistic regression and maximum likelihood estimation in depth.

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