The Department is delighted to welcome Professor Dejan Slepcev (Carnegie Mellon University) who will be giving the following lectures on Variational problems on random structures: analysis and applications to data science.
These lectures will focus on variational problems that arise in data analysis and machine learning. Modern data-acquisition techniques produce a wealth of data about the world we live in. Extracting the information from the data leads to machine learning/statistics tasks such as clustering, classification, low-dimensional embedding, and others. Many of these tasks seek to minimize a functional, defined on the available random sample, which specifies the desired properties of the object sought.
The lectures will discuss a mathematical framework suitable for studies of asymptotic properties of such, variational, problems posed on random samples and related random geometries (e.g. proximity graphs). In particular we will discuss the passage from discrete variational problems on random samples to continuum limits.
The lectures will introduce the basic elements of the background material on calculus of variations and optimal transportation. They will also explain the motivation for the studies of the given functionals and their significance to machine learning. Finally the asymptotic consistency of several important machine learning algorithms will be shown.
Lecture 1, Tuesday 31st May 2016, 16:00-18:00
- Variational problems on graphs and machine learning
- Brief introduction to calculus of variations in BV spaces
- Convergence and nonlocal functionals
Lecture 2, Thursday 2nd June 2016, 16:00-18:00
- Optimal transportation and random approximation of measures
- Asymptotic properties of graph-cut based objective functionals on random samples
- Asymptotic consistency of spectral clustering and extensions
Further information about Professor Dejan Slepcev can be found on his webpage here. A copy of the lecture slides can be found here.