Mathematics of Data: Data, Models, and Optimization

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Page 3 of 4

Statistical Learning Models: Risk and Empirical Risk Minimization

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

Spin Glasses and Bayesian Estimation

Covers the concepts of spin glasses and Bayesian estimation, focusing on observing and inferring information from a system closely.

Basic Principles of Point Estimation

Explores the Method of Moments, Bias-Variance tradeoff, Consistency, Plug-In Principle, and Likelihood Principle in point estimation.

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.

Learning Chemical Reaction Networks

Explores sparse learning of chemical reaction networks from trajectory data using data-based methods and learning approaches.

Discrete Choice Analysis

Introduces Discrete Choice Analysis, covering scale, depth, data collection, and statistical inference.

Maximum Likelihood Inference

Explores maximum likelihood inference, comparing models based on likelihood ratios and demonstrating with a coin example.

Statistical Theory: Inference and Optimality

Explores constructing confidence regions, inverting hypothesis tests, and the pivotal method, emphasizing the importance of likelihood methods in statistical inference.

The Stein Phenomenon and Superefficiency

Explores the Stein Phenomenon, showcasing the benefits of bias in high-dimensional statistics and the superiority of the James-Stein Estimator over the Maximum Likelihood Estimator.

Statistical Significance: Maximum Likelihood Estimation and Confidence Intervals

Explores type I and type II errors, critical values, and confidence intervals in statistical significance.