Introduction to Statistical Learning [syllabus]
This course is designed to introduce students to the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This class will present a number of important modeling and prediction techniques that are staples in the fields of machine learning, artificial intelligence, and data science (more broadly). Unlike a standalone machine learning class, special attention will be given to the statistical underpinnings of common methods. This class will consist of 4 parts:
- A review of probability theory and an introduction to maximum likelihood estimation: probability theory review, Bayes' rule, maximum likelihood estimation, model fitting, model comparison, predictive accuracy, overfitting
- Regression as a predictive task and general model fitting: review of linear regression, cross validation and leave-one-out cross validation, bootstrapping, alternative prediction methods for continuous outcomes, sparse regression (Ridge, LASSO, and Elastic Net), non-linear methods, tree-based methods
- Classification methods: K-nearest neighbors, naïve Bayes classifiers, linear discriminants, logistic regression, support vector machines, deep learning
- Unsupervised methods: Principal components analysis, clustering (generative and geometric), hierarchical clustering, factor analyzers, semi-supervised methods
Introduction to Bayesian Statistics [syllabus]
This course is designed to introduce students to Bayesian methods for data analysis. While this course is largely an applied course, it is intended to provide modeling and computational tools to its students so that they will be able to implement the methods presented and develop new models for analyzing original data. The course will consist of three parts:
- A review of probability theory and an introduction to the basic tools needed for Bayesian statistics including Bayes' theorem, maximum likelihood, prior elicitation, conjugacy, decision theory, model comparison, and other topics that form the basis of the recipe for Bayesian data analysis.
- An overview of modern computational approaches used to perform statistical inference for Bayesian models including Markov Chain Monte Carlo methods, Hamiltonian Monte Carlo, variational approximations, and other computational tools that are used for Bayesian inference.
- An introduction to modern problems in Bayesian statistics and the usage of Bayesian methods in machine learning. Topics discussed will include regression, regularization, latent variable estimation, and other important statistical domains where Bayesian methods provide solutions to long-standing problems.
Introduction to Research Design [syllabus]
An undergraduate course. Introduces methods of scientific inquiry targeted to quantative social science majors. Introduces concepts of correlation and regression leading to causal inference through the potential outcomes framework and the predictive foundations of machine learning. Topics covered include: Experiments, Regression and Matching, Difference in Differences, Regression Discontinuity, Predictive Modeling and Machine Learning, Bayesian Inference.
Computational Methods for the Social Sciences [lectures] [syllabus]
A second course in computational methods for exploration and analysis of social science data. Introduction of a number of advanced computational techniques in R including parallelization, SQL-like syntax for large data sets, statistical sampling via Monte Carlo, and a light introduction to text analysis.
Math Camp [notes1] [notes2] [syllabus]
An introductory course for incoming political science PhD students. Introduces basic notions of probability and statistics such as probability measures, applied probability, conditional probability, expectations, density functions, and concepts of linear algebra.
A Quick Introduction to Bayesian Statistics [lecture]
A two-week lecture series introducing some basic concepts of Bayesian statistics given as a part of University of Michigan's statistical learning workshop. A brief overview of key concepts in Bayesian statistics and an introduction to conjugacy and kernel matching methods.