2013-14: LDHD: SAMSI-CRM Workshop on Geometric Aspects of High-dimensional Inference: March 31-April 2, 2014


The workshop was held at SAMSI in Research Triangle Park, NC, and was a joint venture between SAMSI and Centre de Recerca Matemàtica (CRM) in Barcelona, Spain.


logoCRM_PThe development of methods of statistical inference for high-dimensional data has become a focal point of research in statistics and machine learning in the recent years. One of the crucial problems is to understand how to estimate efficiently a very high-dimensional object under certain “low complexity” constraints that make the estimation possible. In specific settings, “low complexity” could mean, for instance, sparsity of a vector in a high-dimensional space or low-rank properties of a large matrix. The goal is to develop methods that would be adaptive to the underlying “low complexity” structure. Such problems are extremely important both in statistics — for instance, in high-dimensional regression or in covariance matrix estimation — and in a variety of applications, including compressed sensing, collaborative filtering, and quantum state tomography.

Theoretical analysis of methods of high-dimensional inference often relies on deep understanding of the underlying geometry of high-dimensional spaces that leads to highly nontrivial problems of geometric nature. Similar problems have occurred and have been studied in such areas of mathematics as high-dimensional probability, random matrix theory, asymptotic geometric analysis, convex geometry, and additive combinatorics. Some of the tools developed in these areas proved to be extremely useful in high-dimensional statistics; these tools include empirical processes methods, concentration inequalities, and various techniques from the theory of random matrices. There is also great potential for applications of other tools developed in recent years, such as generic chaining bounds for stochastic processes or an emerging theory of log-concave distributions in high-dimensional spaces.

The goal of this workshop was to bring together researchers actively working on the development of high-dimensional inference in statistics, machine learning, compressed sensing, and other related areas with mathematicians who made major contributions to high-dimensional probability and asymptotic geometric analysis in recent years. This provided a great opportunity for fruitful discussions of cutting edge problems in high-dimensional statistics and major advances in our understanding of geometry of high-dimensional spaces.

Topics covered by the workshop may included:

  • low rank matrix estimation;
  • sparse recovery and compressed sensing;
  • covariance estimation for high-dimensional data;
  • model selection and oracle inequalities in high-dimensional statistics;
  • statistical inference for log-concave distributions in high dimensions;
  • non-asymptotic theory of random matrices;
  • concentration inequalities, generic chaining, and empirical processes methods in high-dimensional statistics;
  • hypotheses testing for high-dimensional objects.

Questions: email ldhd@samsi.info

Schedule and Supporting Media

Participant List
Speaker Titles and Abstracts
Poster Titles

Monday, March 31, 2014
at SAMSI, Room 150

Time Description Speaker Slides Videos
8:30-8:55 Registration
8:55-9:00 Welcome
9:00-10:30 High-Dimensional Estimation: Geometric and Probabilistic Insights Roman Vershynin, University of Michigan pdf
10:30-11:00 Break
11:00-11:45 Least Squares under Convex Constraint Sourav Chatterjee, Stanford University pdf
11:45-1:00 Lunch (at SAMSI)
1:00-1:45 Bernoulli Theorem and Empirical Processes Witold Bednorz, University of Warsaw pdf
1:45-2:00 Break
2:00-2:45 On the Limiting Law of the Length of the Longest Common and Increasing Subsequence Christian Houdre, Georgia Institute of Technology
2:45-3:00 Break
3:00-3:45 Compressed Sensing Under Weak Moment Conditions Guillaume Lecue, University Marne-le-Vallee pdf
3:45-4:00 Break
4:00-5:00 Geometric Median: Applications to Robust and Scalable Statistical Estimation Stas Minsker, Duke University pdf
5:00-6:30 Poster Session and Reception

Tuesday, April 1, 2014
at SAMSI, Room 150

Time Description Speaker Slides Videos
9:00-10:30 Detection of Correlations and High-Dimensional Random Geometric Graphs Gabor Lugosi, Pompeu Fabra University pdf
10:30-11:00 Break
11:00-11:45 Large Average Submatrices of a Gaussian Random Matrix: Landscapes and Local Optima Andrew Nobel, University of North Carolina pdf
11:45-1:00 Lunch (at SAMSI)
1:00-1:45 Estimating High-dimensional Matrices: Convex Geometry and Computational Barriers Zongming Ma, University of Pennsylvania pdf
1:45-2:00 Break
2:00-2:45 GEMINI: Graph Estimation with Matrix Variate Normal Instances Shuheng Zhou, University of Michigan pdf
2:45-3:00 Break
3:00-3:45 Sparse Canonical Correlation Analysis Harrison Zhou, Yale University pdf
3:45-4:00 Break
4:00-4:45 Uniform Martingale LLN, Sequential Complexities, and Applications to Online Learning Alexander Rakhlin, University of Pennsylvania

Wednesday, April 2, 2014
at SAMSI, Room 150

Time Description Speaker Slides Videos
9:00-9:45 Compressed Subspace Matching on the Continuum Justin Romberg, Georgia Institute of Technology pdf
9:45-10:00 Break
10:00-10:45 Logistic Regression with Structured Sparsity Rob Nowak, University of Wisconsin pdf
10:45-11:00 Break
11:00-11:45 Don’t Fall for Tuning Parameters Johannes Lederer, Cornell University
11:45-1:00 Lunch (at SAMSI)