This will be a seminar course concentrating on the mathematical theory and technique of machine learning. The class will consist of two parts. The first part will concentrate on variational modeling and techniques in machine learning. A rigorous approach to variational mathematics will be developed, and modern applications of variational modeling will be explored. Topics include support vector machines, l1 regulatization, linear discriminate analysis, and PDE modeling. The second half of the course will cover Bayesian analysis with special emphasis on non-parametric Bayesian modeling. The connection with probablistic graphical structures, Poisson point processes, and Levy processes will be made. Topics in the area include conjugate priors, Markov-Chain Monte Carlo and Gibbs sampling methods and mean field theories. If time permits, and depending on the interest of the student, we may also cover compressed sensing, operator splitting, or Bregman iterations.
2013 Claremont Graduate University 
150 E. 10th St., Claremont, CA 91711 