ACM 118 Stochastic Progresses and Regression

Last Update: January 6, 2020 Schedule Classes are scheduled from 1pm to 2:25pm on Mondays and Wednesdays in Annenberg 213 . Homeworks: Posted on Piazza Lecture Notes: Posted in Piazza (drop the instructor an email if you are not registered yet to be added). Prerequisite: ACM/EE 116 or CMS/ACM/EE 117 or instructor agreement. Piazza: For all class-related discussions (in particular for Q/A). https://piazza.com/caltech/winter2020/acm118/home Instructor: Houman Owhadi TAs: • Florian T. Schäfer: o Office hour: Wed 5-6pm o Location: ANB 243 o Email: florian.schaefer@caltech.edu • Ziyun Zhang o Office hour: Mon 5-6pm o Location: ANB 230 o Email: zyzhang@caltech.edu Grading: Homework (4 problem sets, one every two weeks): 100% Syllabus: • Branching (Galton-Watson) Processes. • Poisson (Point) Processes. • Gaussian vectors. • Gaussian processes, measures and fields. • Gaussian process regression. • Statistical numerical approximation. • Kernel methods and Reproducing Kernel Hilbert Spaces • Kernel PCA • Kernel LDA • Kernel mean embedding • Dirichlet processes Textbooks: The lectures will not follow closely any textbook (I will distribute my lecture notes). The following ones are (given here only as suggestions and contain only a portion of what will be covered in this class. • Probability and Random processes (G. R. Grimmett and D. R. Stirzaker). • Operator adapted wavelets, fast solvers, and numerical homogenization from a game theoretic approach to numerical approximation and algorithm design. H. Owhadi and C. Scovel. Cambridge University Press, Cambridge Monographs on Applied and Computational Mathematics, 2019 • Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar. Foundations of machine learning. MIT press, 2018 • Krikamol Muandet, Kenji Fukumizu, Bharath Sriperumbudur, Bernhard Scholkopf, et al. Kernel mean embedding of distributions: A review and beyond. Foundations and Trends in Machine Learning, 2017. • Sebastian Mika, Gunnar Ratsch, Jason Weston, Bernhard Scholkopf, and Klaus-Robert Mullers. Fisher discriminant analysis with kernels. 1999 • Bernhard Scholkopf, Alexander Smola, and Klaus-Robert Muller. Nonlinear component analysis as a kernel eigenvalue problem. Neural computation, 10(5):1299{1319, 1998. • Arthur Gretton. Reproducing kernel hilbert spaces in machine learning. Lecture notes, 2019 • Leon Gu. Dirichlet distribution, dirichlet process and dirichlet process mixture (lecture notes). • Michael I Jordan. Dirichlet processes, chinese restaurant processes and all that. NIPS tutorial, 2015.