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

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Lectures in this course (118)

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.

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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Stochastic Gradient Descent Convergence Proof

Explores the convergence proof of Stochastic Gradient Descent with strongly-convex functions and the impact of step-size on convergence properties.

Complexity Analysis of FGD Algorithm

Analyzes the complexity of the FGD algorithm in terms of computational and memory requirements.

Mirror Prox: Optimization and Norms

Explores Mirror Prox optimization, argmin function, norms, and their practical applications in optimization problems.

Algorithms for Composite Optimization

Explores algorithms for composite optimization, including proximal operators and gradient methods, with examples and theoretical bounds.

Constraint Formulation and Lagrangian Dual Optimum

Explains constraint formulation using Lagrangian and augmented Lagrangian functions.

Proximal Operators and Constrained Optimization

Introduces proximal operators, gradient methods, and constrained optimization, exploring their convergence and practical applications.

Constrained Convex Optimization: Min-Max Formulation and Fenchel Conjugation

Explores constrained convex optimization with min-max formulation and Fenchel conjugation.

Time-Data Tradeoffs and Sparse Representations

Explores time-data trade-offs, sparse representations, and convexity in mathematical data analysis.

Trade-offs in Data and Time

Explores trade-offs between data and time in computational problems, emphasizing diminishing returns and continuous trade-offs.

Optimization Trade-offs: Variance Reduction and Statistical Dimension

Explores optimization trade-offs, variance reduction, statistical dimension, and convergence analysis in optimization algorithms.

Deep Learning: Theory and Applications

Explores the mathematics of deep learning, neural networks, and their applications in computer vision tasks, addressing challenges and the need for robustness.

Challenges in DL/ML Applications

Explores challenges in deep learning and machine learning applications, covering surveillance, privacy, manipulation, fairness, interpretability, energy efficiency, cost, and generalization.

Deep Learning: Theory and Practice

By Prof. Volkan Cevher delves into the mathematics of deep learning, exploring model complexity, risk trade-offs, and the generalization mystery.

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