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Course

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

Lectures in this course (118)

Parametric Models: Mathematics of Data

Explores parametric models in data analysis, covering regression estimators, optimization problems, and statistical models.

Mathematics of Data: Overview and Examples

Covers empirical risk minimization, statistical learning, and examples of cancer prediction, house pricing, and image generation.

Optimization Basics: Linear Algebra, Analysis, Convexity

Introduces optimization basics, covering linear algebra, analysis, and convexity principles.

Convexity and Jacobians

Explores convexity, Jacobians, subdifferentials, and convergence rates in optimization and function analysis.

Deep Learning Building Blocks

Covers tensors, loss functions, autograd, and convolutional layers in deep learning.

Concise Signal Models and Compressive Sensing

Explores concise signal models, compressive sensing, sparsity, atomic norms, and non-smooth minimization using subgradient descent.

Iterative Descent Methods: Optimization Principles

Explores iterative descent methods in optimization, gradient descent, local minima, and convergence principles.

Optimization Methods: Convexity and Gradient Descent

Explores optimization methods, including convexity, gradient descent, and non-convex minimization, with examples like maximum likelihood estimation and ridge regression.

Proximal Operators: Optimization Methods

Explores proximal operators, subgradient methods, and composite minimization in optimization.

Optimality of Convergence Rates: Accelerated Gradient Descent

Explores the optimality of convergence rates in convex minimization problems using accelerated gradient descent methods.

Adaptive Gradient Methods

Explores adaptive gradient methods like AdaGrad, AcceleGrad, and UniXGrad, focusing on their local adaptation and convergence rates.

Optimization Methods: Convergence and Trade-offs

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Statistical Estimation: Gaussian Linear Model

Delves into statistical estimation, highlighting the Gaussian linear model and the limitations of ML estimators.

Stochastic Gradient Descent: Optimization Techniques

Explores stochastic gradient descent and non-smooth optimization techniques for sparsity and compressive sensing.

Stochastic Gradient Descent: Optimization Techniques

Explores Stochastic Gradient Descent with Averaging, comparing it with Gradient Descent, and discusses challenges in non-convex optimization and sparse recovery techniques.

Mathematics of Data: Deep Learning Introduction

Covers a mathematical introduction to deep learning, including challenges, power of linear classifiers, model scaling, and theoretical aspects.

Sparse Regression and Convex Optimization

Explores sparse regression, convex optimization, and efficient solution algorithms in data analysis.

Composite Convex Minimization

Covers solution methods for composite convex minimization and explores examples like ₁-regularized least squares and phase retrieval.

Variance Reduction in Deep Learning

Explores variance reduction techniques in deep learning, covering gradient descent, stochastic gradient descent, SVRG method, and performance comparison of algorithms.

Deep Learning Paradigm

Explores the deep learning paradigm, including challenges, neural networks, robustness, fairness, interpretability, and energy efficiency.