Approximation, sampling and compression in data science
| Created: | 2019-02-12 11:00 |
|---|---|
| Institution: | Isaac Newton Institute for Mathematical Sciences |
| Editors' group: | Members of "Isaac Newton Institute for Mathematical Sciences". |
| Description: | 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. |
Media items
This collection contains 31 media items.
Media items
Hardy-type inequalities for fractional powers of the Dunkl--Hermite operator
25 views
Roncal, L
Monday 8th April 2019 - 15:00 to 16:00
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 17 Apr 2019
Lecture 1: Some old and new results on Information-Based Complexity
47 views
Novak, E
Monday 11th February 2019 - 15:00 to 16:30
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Tue 12 Feb 2019
Reconstruction of a 3D object from a finite number of its 1D parallel cross-sections
30 views
Dyn, N
Thursday 9th May 2019 - 14:00 to 15:00
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 10 May 2019
Approximation of Ridge Functions and Sparse Additive Models
22 views
Vybiral, J
Monday 18th February 2019 - 13:40 to 14:15
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Tue 19 Feb 2019
Ball Average Characterizations of Function Spaces
20 views
Yang, D
Tuesday 19th February 2019 - 09:40 to 10:15
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 20 Feb 2019
Best m-term approximation of the "step-function" and related problems
23 views
Ryutin, K
Thursday 21st February 2019 - 09:40 to 10:15
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Thu 21 Feb 2019
Directional Framelets with Low Redundancy and Directional Quasi-tight Framelets
22 views
Han, B
Tuesday 19th February 2019 - 11:40 to 12:15
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 20 Feb 2019
Discrete Spherical Averages
40 views
Lacey, M
Monday 25th February 2019 - 15:00 to 16:00
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Mon 25 Feb 2019
Embedding and continuity envelopes of Besov-type spaces
20 views
Yuan, W
Tuesday 19th February 2019 - 11:00 to 11:35
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 20 Feb 2019
Explicit error bounds for randomized Smolyak algorithms and an application to infinite-dimensional integration
12 views
Gnewuch, M
Thursday 21st February 2019 - 11:00 to 11:35
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Thu 21 Feb 2019
Exponential tractability of weighted tensor product problems
17 views
Wozniakowski, H
Monday 18th February 2019 - 09:40 to 10:15
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Tue 19 Feb 2019
Kirk Distinguished Visiting Fellow Lecture: The hidden landscape of localization
27 views
Mayboroda, S
Wednesday 12th June 2019 - 16:00 to 17:00
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Thu 13 Jun 2019
Least squares regression on sparse grids
23 views
Bohn, B
Friday 22nd February 2019 - 09:40 to 10:15
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 22 Feb 2019
Lecture 2: Complexity results for integration.
30 views
Novak, E
Wednesday 13th February 2019 - 15:00 to 16:30
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 15 Feb 2019
Local restriction theorem and maximal Bochner-Riesz operator for the Dunkl transforms
20 views
Ye, W
Tuesday 19th February 2019 - 15:30 to 16:05
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 20 Feb 2019
Metric Approximation of Set-Valued Functions
39 views
Berdysheva, E
Tuesday 12th March 2019 - 15:00 to 16:30
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 13 Mar 2019
Monte Carlo methods for Lq approximation on periodic Sobolev spaces with mixed smoothness
27 views
Wang, H
Thursday 21st February 2019 - 11:40 to 12:15
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Thu 21 Feb 2019
Morrey sequence spaces
35 views
Haroske, D
Monday 25th March 2019 - 11:00 to 12:00
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 27 Mar 2019
On some lower bounds for Kolmogorov widths
16 views
Malykhin, Y
Monday 18th February 2019 - 11:40 to 12:15
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Tue 19 Feb 2019
Optimal Confidence for Monte Carlo Integration of Smooth Functions
23 views
Kunsch, R
Thursday 21st February 2019 - 13:40 to 14:15
Collection: Approximation, sampling and compression in data science
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Thu 21 Feb 2019