# Approximation, sampling and compression in data science

Created: | 2019-02-12 11:00 |
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Institution: | 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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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