CCIMI Short course - Graph-based Approaches to Learning: Mathematical Theory and Perspectives

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This short course is organised by the CCIMI and open to all. Lectures run 11:00-12:30, Monday 3rd, Wednesday 5th, Friday 7th, Monday 10th and Wednesday 12th June in MR14 .

Instructor: Nicolas Garcia Trillos, University of Wisconsin-Madison

In this mini course we will explore graph-based approaches to supervised, semi-supervised, and unsupervised learning. We will use graphs as a way to summarize the measure of similarity between observed data points (endowing the data set with a geometric structure in this way), and in particular we will use them to define “priors” or “regularizers” on unknown quantities of interest (be it a classification rule, a clustering of a data set, etc), in direct analogy with PDE or variational models found in the applied analysis literature (like for example in image analysis or geosciences).

The proposed outline for the mini-course is as follows: Lecture 1: Introduction. How can geometry help us learn from data? Optimization and Bayesian approaches. Lecture 2: Consistency results. Spectral methods, Calculus of Variations methods, PDE methods. Part 1. Lecture 3: Consistency results. Spectral methods, Calculus of Variations methods, PDE methods. Part 2. Lecture 4: Stability of algorithms in Bayesian computing. Lecture 5: How can we learn geometry from data?