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Approximation, sampling and compression in data science

Participation in INI programmes is by invitation only. Anyone wishing to apply to participate in the associated workshop(s) should use the relevant workshop application form.

Programme
3rd January 2019 to 26th June 2019
Organisers: 
Alexei Shadrin University of Cambridge
Anders Hansen University of Cambridge
Vladimir Temlyakov University of South Carolina, Steklov Mathematical Institute, Russian Academy of Sciences
Sergey Tikhonov ICREA and Universitat Autonoma de Barcelona, Centre de Recerca Matematica (CRM)
Scientific Advisors: 
Robert Calderbank Duke University
Emmanuel Candes Stanford University
Ronald DeVore Texas A&M University
Ingrid Daubechies Duke University
Arieh Iserles University of Cambridge, Mathematics, University of Cambridge

 

Programme Theme

 

Approximation theory is the study of simulating potentially extremely complicated functions, called target functions, with simpler, more easily computable functions called approximants.  The purpose of the simulation could be to approximate values of the target function with respect to a given norm, to estimate the integral of the target function, or to compute its minimum value. Approximation theory's relationship with computer science and engineering encourages solutions that are efficient with regards to computation time and space.  In addition, approximation theory problems may also deal with real-life restrictions on data, which can be incomplete, expensive, or noisy.  As a result, approximation theory often overlaps with sampling and compression problems.

The main aim of this programme is to understand and solve challenging problems in the high-dimensional context, but this aim is dual.  On one hand, we would like to use the high-dimensional context to understand classical approximation problems.  For example, recent developments have revealed promising new directions towards a break-through in a set of classical unsolved problems related to sampling in hyperbolic cross approximations. On the other hand, we want to understand why classical multivariate approximation methods fail in the modern high-dimensional context and to find methods that will be better and more efficient for modern approximation in very high dimensions.  This direction will focus on two conceptual steps: First, replacement of classical smoothness assumptions by structural assumptions, such as those of sparsity used by compressed sensing.  Second, the use of a nonlinear method, for instance a greedy algorithm, to find an appropriate sparse approximant. 

In order to achieve the goal the programme will bring together researchers from different fields to work in groups on modern problems of high-dimensional approximation and related topics. It will foster exchange between different groups of researchers and practitioners.

The programme includes the following three workshops:

Workshop 1: Challenges in optimal recovery and hyperbolic cross approximation, February 18-22, 2019

Workshop 2: Mathematics of data: structured representations for sensing, approximation and learning, May 27-31, 2019

Workshop 3: Approximation, sampling, and compression in high dimensional problems, June 17-21, 2019

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons