Applied Statistics III · Statistics
Traditional nonparametric methods such as k-NN (classification and regression), kernel density estimation. Free lunch theorem and how smoothness of the function space can give rise to generalization bounds and convergence rates. Kernel machines, Hilbert spaces, RKHS, infinite dimensional function spaces.
Broad coverage of a variety of topics in modern computational biology. Great selection of papers and lots of insightful and deep discussions.
Climate modeling, machine learning techniques, hybrids which combine physics motivated models and ML techniques. Broad discussion on many topics, channeled through a specific application. Lots of interesting "meta" discussions on research, grant writing, and research proposals.
I learned a lot from one of the best professors in the department. Besides the theory you get a better understanding of how to think and tackle problems in real world which I find extremely interesting. We speak about the things and prepare for every class, which I really like.
Non-parametric methods, no free lunch theorem, classification is easier than regression, assumptions under which minimax rates improve, abstract treatment of linear operators, Hilbert spaces, techniques to complete a space, RKHS.
I gained some exposure to contemporary research in the areas of statistical modeling and computational biology, as well as practice performing literature review and presenting on/exploring some of these ideas.
The first half of the course focus on traditional nonparametrics, with an emphasis on proving upper bounds and minimax lower bounds on excess risk. The second half of the course focus on kernel machines, with an emphasis on RKHS and operators.
Being encouraged to read and discuss the class topics was very helpful and I think very important in helping me develop my literature review skills.
I'd say anyone who wants to do research in this area should definitely take the course. For someone who does more applied work but uses the methods covered in class, it's a "probably recommend". Make sure you have a good project for the class, since you'll be spending some time on it.
I would strongly recommend this course to any PhD. student who is interested in machine learning and wants to learn about the theory of nonparametric machine learning.