Approximation, sampling, and compression in high dimensional problems

Workshop theme

In a number of problems, both in theory and applications, one faces a situation when the ambient dimension is extremely high. Such problems often include approximating, sampling, or compressing functions on high-dimensional domains. Classical methods fail to be effective in this case due to the effect known as `curse of dimensionality'; hence new tools and algorithms need to be devised. Compressed sensing, which has gained great popularity in this century, is one example of a circle of ideas which make high-dimensional problems feasible. Methods which allow one to overcome the curse of dimensionality come from a mixture of mathematical fields: approximation, probability, functional and harmonic analysis, linear algebra, combinatorics, geometry, etc. In addition to pure mathematical interest, this field has great importance in numerous applications, in particular in data science and signal processing. Despite decades of research, many important questions in this area are still open. This workshop will bring together researchers in pure and applied mathematics, who attack high-dimensional problems.

Applications for this workshop are now closed

The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:

The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Approximation, sampling, and compression in high dimensional problems, where work on this paper was undertaken. This work was supported by EPSRC grant EP/R014604/1.

Timetable

Monday 17th June 2019
09:20 to 09:40	Registration	No Room Required
09:40 to 09:50	Welcome from David Abrahams (Isaac Newton Institute)	No Room Required
09:50 to 10:40	Akram Aldroubi Vanderbilt University Dynamical sampling and frames generated from powers of exponential operators	Room 1
10:40 to 11:10	Morning Coffee	No Room Required
11:10 to 12:00	Denka Kutzarova University of Illinois at Urbana-Champaign; Bulgarian Academy of Sciences Transportation cost spaces on finite metric spaces	Room 1
12:00 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:20	Albert Cohen Université Pierre et Marie Curie Paris Optimal sampling for approximation on general domains	Room 1
14:20 to 15:10	Peter Binev University of South Carolina High Dimensional Approximation via Sparse Occupancy Trees	Room 1
15:10 to 15:40	Afternoon Tea	No Room Required
15:40 to 16:30	Claire Boyer Sorbonne Université; ENS - Paris Representer theorems and convex optimization	Room 1
16:30 to 17:30	Welcome Wine Reception at INI	No Room Required

Tuesday 18th June 2019
09:00 to 09:50	Simon Foucart Texas A&M University Functions of Few Coordinate Variables: Sampling Schemes and Recovery Algorithms	Room 1
09:50 to 10:40	Alexander Olevskii Tel Aviv University Discrete translates in function spaces	Room 1
10:40 to 11:10	Morning Coffee	No Room Required
11:10 to 12:00	Olga Mula Université Paris-Dauphine Optimal algorithms for state estimation using reduced models	Room 1
12:00 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:20	Joaquim Ortega-Cerdà Universitat de Barcelona A sequence of well-conditioned polynomials	Room 1
14:20 to 15:10	Holger Rauhut RWTH Aachen University Linear and one-bit compressive sensing with subsampled random convolutions	Room 1
15:10 to 15:40	Afternoon Tea	No Room Required
15:40 to 16:30	Lukas Herrmann ETH Zürich Quasi-Monte Carlo integration in uncertainty quantification of elliptic PDEs with log-Gaussian coefficients	Room 1

Wednesday 19th June 2019
09:00 to 09:50	Andreas Seeger University of Wisconsin-Madison Basis properties of the Haar system in various function spaces	Room 1
09:50 to 10:40	Christoph Thiele University of Bonn On singular Brascamp Lieb integrals	Room 1
10:40 to 11:10	Morning Coffee	No Room Required
11:10 to 12:00	Hans Feichtinger University of Vienna Approximation of continuous problems in Fourier Analysis by finite dimensional ones: The setting of the Banach Gelfand Triple	Room 1
12:00 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 18:00	Free afternoon	No Room Required
19:30 to 22:00	Formal Dinner at Christ's College	No Room Required

Thursday 20th June 2019
09:00 to 09:50	Sinan Güntürk Courant Institute of Mathematical Sciences; New York University Extracting bits from analog samples: in pursuit of optimality	Room 1
09:50 to 10:40	Peter Richtarik University of Edinburgh; King Abdullah University of Science and Technology (KAUST) Stochastic Quasi-Gradient Methods: Variance Reduction via Jacobian Sketching	Room 1
10:40 to 11:10	Morning Coffee	No Room Required
11:10 to 12:00	Boris Kashin Steklov Mathematical Institute, Russian Academy of Sciences; Russian Academy of Sciences On some theorems on the restriction of operator to coordinate subspace	Room 1
12:00 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:20	Yuan Xu University of Oregon Orthogonal structure in and on quadratic surfaces	Room 1
14:20 to 15:10	Gitta Kutyniok Technische Universität Berlin Beating the Curse of Dimensionality: A Theoretical Analysis of Deep Neural Networks and Parametric PDEs	Room 1
15:10 to 16:10	Afternoon tea and poster session	No Room Required

Friday 21st June 2019
09:00 to 09:50	Aicke Hinrichs Johannes Kepler Universität How good is random information compared to optimal information?	Room 1
09:50 to 10:40	Karlheinz Groechenig University of Vienna Totally positive functions in sampling theory and time-frequency analysis	Room 1
10:40 to 11:10	Morning Coffee	No Room Required
11:10 to 12:00	Feng Dai University of Alberta Integral norm discretization and related problems	Room 1
12:00 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:20	Milana Gataric University of Cambridge Imaging through optical fibres	Room 1
14:20 to 15:10	Geno Nikolov Sofia University St. Kliment Ohridski Markov-type inequalities and extreme zeros of orthogonal polynomials	Room 1

Approximation, sampling and compression in data science

Approximation, sampling, and compression in high dimensional problems

Organisers

Dmitriy Bilyk University of Minnesota
Eugenio Hernandez Universidad Autonoma de Madrid
Alexei Shadrin University of Cambridge
Sergey Tikhonov ICREA and Universitat Autonoma de Barcelona; Centre de Recerca Matematica (CRM)

Speakers

Akram Aldroubi Vanderbilt University
Peter Binev University of South Carolina
Claire Boyer Sorbonne Université; ENS - Paris
Albert Cohen Université Pierre et Marie Curie Paris
Feng Dai University of Alberta
Hans Feichtinger University of Vienna
Simon Foucart Texas A&M University
Milana Gataric University of Cambridge
Karlheinz Groechenig University of Vienna
Sinan Güntürk Courant Institute of Mathematical Sciences; New York University
Lukas Herrmann ETH Zürich
Aicke Hinrichs Johannes Kepler Universität
Boris Kashin Steklov Mathematical Institute, Russian Academy of Sciences; Russian Academy of Sciences
Gitta Kutyniok Technische Universität Berlin
Denka Kutzarova University of Illinois at Urbana-Champaign; Bulgarian Academy of Sciences
Olga Mula Université Paris-Dauphine
Geno Nikolov Sofia University St. Kliment Ohridski
Alexander Olevskii Tel Aviv University
Joaquim Ortega-Cerdà Universitat de Barcelona
Holger Rauhut RWTH Aachen University
Peter Richtarik University of Edinburgh; King Abdullah University of Science and Technology (KAUST)
Andreas Seeger University of Wisconsin-Madison
Christoph Thiele University of Bonn
Yuan Xu University of Oregon

Show All

Participants

Akram Aldroubi Vanderbilt University
Laura Angeloni Università degli Studi di Perugia
Simon Arridge University College London
Bubacarr Bah African Institute for Mathematical Sciences (AIMS); Stellenbosch University
Davide Barbieri Universidad Autonoma de Madrid
Daurenbek Bazarkhanov Institute of Mathematics and Mathematical Modeling
Pablo Manuel Berna Universidad Autonoma de Madrid
Dmitriy Bilyk University of Minnesota
Peter Binev University of South Carolina
Thomas Blumensath University of Southampton
Claire Boyer Sorbonne Université; ENS - Paris
Martin Buhmann Justus-Liebig-Universität Gießen
Glenn Byrenheid Friedrich-Schiller-Universität Jena
Priscilla Canizares Universiteit van Amsterdam
Albert Cohen Université Pierre et Marie Curie Paris
Feng Dai University of Alberta
Marta de León Contreras Universidad Autonoma de Madrid
Alberto Debernardi Pinos Bar-Ilan University
Ronald DeVore Texas A&M University
Stephen Dilworth University of South Carolina
Dũng Dinh Vietnam National University
Oscar Dominguez Universidad Complutense de Madrid
Ujué Etayo Graz University of Technology
Hans Feichtinger University of Vienna
Damir Ferizovic Graz University of Technology
Simon Foucart Texas A&M University
Gustavo Garrigos Universidad de Murcia
Milana Gataric University of Cambridge
Michael Gnewuch Universität Osnabrück
Karlheinz Groechenig University of Vienna
Anupam Gumber Indian Institute of Science
Sinan Güntürk Courant Institute of Mathematical Sciences; New York University
Anders Hansen University of Cambridge
Dorothee Haroske Friedrich-Schiller-Universität Jena
Eugenio Hernandez Universidad Autonoma de Madrid
Lukas Herrmann ETH Zürich
Aicke Hinrichs Johannes Kepler Universität
Arieh Iserles University of Cambridge
Boris Kashin Steklov Mathematical Institute, Russian Academy of Sciences; Russian Academy of Sciences
Yurii Kolomoitsev Universität zu Lübeck
Frances Kuo University of New South Wales
Gitta Kutyniok Technische Universität Berlin
Denka Kutzarova University of Illinois at Urbana-Champaign; Bulgarian Academy of Sciences
Martin Lotz University of Warwick
Ryan Matzke University of Minnesota
Svitlana Mayboroda University of Minnesota
Jason McEwen University College London
Hrushikesh Mhaskar Claremont Graduate University
Olga Mula Université Paris-Dauphine
James Nichols Sorbonne Université
Geno Nikolov Sofia University St. Kliment Ohridski
Kristina Oganesyan Lomonosov Moscow State University
Alexander Olevskii Tel Aviv University
Joaquim Ortega-Cerdà Universitat de Barcelona
Josiah Park Georgia Institute of Technology
Guergana Petrova Texas A&M University
Holger Rauhut RWTH Aachen University
Peter Richtarik University of Edinburgh; King Abdullah University of Science and Technology (KAUST)
Dmitry Savostyanov None / Other
Andreas Seeger University of Wisconsin-Madison
Alexei Shadrin University of Cambridge
Teresa Signes Universidad de Murcia
Ian Sloan University of New South Wales
Tetiana Stepaniuk Austrian Academy of Sciences
Alex Stokolos Georgia Southern University
Jared Tanner University of Oxford
Vladimir Temlyakov University of South Carolina; Steklov Mathematical Institute, Russian Academy of Sciences
Laura Thesing University of Cambridge
Christoph Thiele University of Bonn
Sergey Tikhonov ICREA and Universitat Autonoma de Barcelona; Centre de Recerca Matematica (CRM)
Mikhail Tyaglov Shanghai Jiao Tong University
Tino Ullrich Chemnitz University of Technology
Gianluca Vinti Università degli Studi di Perugia
Oleksandr Vlasiuk Florida State University
Ferenc Weisz Eötvös Loránd University
Yuan Xu University of Oregon