
Center of the Garching Campus. Image: Andreas Heddergott.
Joint ISAM – TopMath – DGD ^{} Summer School 2016
Mathematical Methods for HighDimensional Data Analysis
July 18 – 22, 2016, TU München, Garching
Scope and Goals Organizers Program Registration Venue Accommodation Contact
Scope and Goals
This summer school is hosted by the mathematics department at TUM and generously supported by the International School of Applied Mathematics, the graduate program TopMath, and the Collaborative Research Center "Discretization in Geometry and Dynamics" ^{}.
The goal of the summer school is to bridge developments in machine learning, randomized methods, and topological approaches.
Main topics of the summer school are:
 Probabilistic methods for dimension reduction,
 Geometric and topological methods for data analysis,
 Optimal stochastic regularization for large scale machine learning,
 Algebraic foundations of persistent homology.
This summer school is mostly aimed at young researchers (PhD students and postdocs) whose interests are related to the topics presented in the summer school.
Organizers
Program
 Date: Monday, July 18, 9 am to Friday, July 22, 2016, 12:30 pm.
The schedule of the summer school can be found here.
As a preparation for the practical part of the lectures and tutorials of Jose Perea and Steve Oudet, please follow the these instructions ^{}. We recommend to install the indicated VirtualBox image before the first sessions on Monday. This ^{} is a mirror of the image file of Step 2.
Speakers

Tutorial by Jarosław Błasiok (Harvard University) A "sketch" of data with respect to some family of queries is a compression of that data that still allows those queries to be answered. The study of streaming algorithms is concerned with maintaining sketches, often consuming exponentially less memory than the data itself, subject to continuous updates to the data. Streaming and sketching can be used to:
(1) Reduce storage requirements; (2) Minimize communication, by allowing holders of different datasets in a network to compare data while only transmitting short sketches; (3) Speed up algorithms, by reducing the memory footprint of the algorithm to the point that it fits in fast cache
This lecture series will introduces some of the core techniques in the design and analysis of sketching and streaming algorithms.
[Lecture notes by Jelani Nelson ^{}] [Problems ^{}] [Solutions ^{}] 
Tutorial by Mathieu Carrière ^{} (INRIA Saclay) The aim of this course is to demonstrate how topology can help in the design of new features for geometric data, with distinctive properties such as: invariance under data reparametrization, stability with respect to data perturbation, complementarity to other descriptors in terms of information content. These features are derived from classical topological constructions such as filtered nerves or flag complexes. Their structural properties can be analyzed through the lens of algebraic topology — in particular homology and persistence theories.
The course will cover all aspects of the feature design pipeline, albeit not in full extent: topological constructions, associated homological algebra, resulting invariants (a.k.a. features), metrics and kernels for such invariants. Examples will be provided along the way to illustrate the potential and versatility of the obtained features.
[Slides, notes and practical session ^{}] 


Jose Perea ^{}: Topological Time Series Analysis  Theory and Practice
Tutorial by Chris Tralie ^{} (Michigan State University) Time series are ubiquitous in today's data rich world, so naturally their analysis is a fundamental object of study. In recent years, tools from the growing field of topological data analysis have been adapted to the analysis of time series data. In short, time series can be transformed into highdimensional point clouds (via delayembeddings) and their shape can be probed (via persistent homology) to quantify characteristics such as periodicity, quasiperiodicity, existence of motifs, presence of dynamic chaos, etc. In this minicourse we will cover some of the theory behind topological time series analysis, and will explore applications ranging from biology to music analysis.
Slides of Jose Perea: [Lecture 1] [Lecture 2] Code and multimedia files of Chris Tralie: [GitHub ^{}] Lecture about audio applications: [Slides] Lecture about video applications: [Slides] [Some videos ^{}] [Writeup ^{}] 
Lorenzo Rosasco ^{} : Optimal Stochastic Regularization for Large Scale Machine Learning
Tutorial by Alessandro Rudi ^{} (Università di Genova, Massachusetts Institute of Technology) The basic problem of machine learning is recovering a function from scattered noisy data. This problem is illposed and regularization techniques are key to obtain stable solutions that can predict well new data.
After reviewing the main concepts of statistical learning theory, we give a fresh view on classical penalized (Tikhonov) regularization methods, emphasizing statistical as well as computational aspects. The discussion covers both parametric and nonparametric techniques. Then, we describe randomized regularization techniques proposed to scale methods to large scale scenarios and discuss the connection with deep learning methods. Slides: [Lecture 1] [Lecture 2] [Lecture 3] For slides and videos of a lecture series covering similar topics: Summer School RegML 2016 ^{}
MATLABfiles for the tutorial by Alessandro Rudi on Friday: [Lab.zip ^{}]. 

Registration
Registration is mandatory and restricted to at most 80 participants. The registration is closed now.
Financial support
Limited funding is available to provide hotel accommodation in a shared twin room for the week of the summer school. If you wish to apply, please include a letter of motivation with your application.
Venue
The venue of the summer school is the lecture hall H.E.009 of the LeibnizRechenzentrum ^{} (LRZ, 'Leibniz Supercomputing Centre') located on the Garching campus of TU München (Boltzmannstr. 1, 85747 Garching ^{}). A campus map with the relevant locations can be found here.
The Garching campus can easily be reached by subway (UBahn Linie U6, station GarchingForschungszentrum) from Munich city center. There are many parking lots free of charge in LudwigPrandtlStraße at the back of the building. Further details can be found here.
Accommodation
We recommend the following hotels.
Contact
Scope and Goals Organizers Program Registration Venue Accommodation Contact
