Statistics 185 originated in the Fall 2019 semester when I was a college fellow in the Department of Statistics with a focus on Dimension Reduction.  

Now, Stat 185 has become a yearly offering within the department and a popular elective in the new Machine Learning track within the Statistics concentration.  We still cover foundational methods in matrix factorization and clustering with yearly updates to also focus on modern manifold learning techniques. 

A few year ago, I began working with a Cenhao Zhu (a former 185 student) to formalize the course content into a textbook. The current version has interactive visualizations to help students develop intuition for the geometric foundations behind many of these methods.  A downloadable pdf is also available at the site.

• Special thanks to Paul Bendich, Duke University, for his insight on content and course goals on original 2019 version.

This class covers computational tools for statistical inference and learning, with emphasis on the computational aspects of statistics, the statistical implications of inference algorithms, and the mathematical foundations for these ideas. Topics include: 

• Optimization: Newton-Raphson and gradient-based algorithms; the EM algorithm; 

• Monte Carlo methods: Markov chain Monte Carlo, importance sampling, data augmentation, and sequential Monte Carlo

• Variational methods: mean field, CAVI, variational autoencoders

(This course is currently bracketed, but I am always open to talk with anyone interested in spatial data analysis).

This class covered point processes, areal data, and geostatistics, balancing theory (and assumptions), techniques for exploratory analysis, and inference and prediction.  Techniques for Bayesian methods with MCMC were covered at the end of the course.

• Point processes 

  • Uses sf for visualization; spatstat for EDA and inference

• Areal data

  • Uses sp, sfdep for spatial weights and EDA; spautolm for regression

• Geostatistics

  • Uses sf for visualization, gstats for EDA and kriging

Data sources include spData and NYCOpenData.