# Approximation, sampling, and compression in high dimensional problems

Created: | 2019-06-18 08:28 |
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Institution: | Isaac Newton Institute for Mathematical Sciences |

Editors' group: | Members of "Isaac Newton Institute for Mathematical Sciences". |

Description: | 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. |

# Media items

This collection contains 14 media items.

### Media items

#### Beating the Curse of Dimensionality: A Theoretical Analysis of Deep Neural Networks and Parametric PDEs

15 views

Kutyniok, G

Thursday 20th June 2019 - 14:20 to 15:10

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 21 Jun 2019

#### On some theorems on the restriction of operator to coordinate subspace

3 views

Kashin, B

20th June 2019 - 11:10 to 12:00

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 21 Jun 2019

#### A sequence of well-conditioned polynomials

3 views

Ortega-Cerdà, J

Tuesday 18th June 2019 - 13:30 to 14:20

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 19 Jun 2019

#### Basis properties of the Haar system in various function spaces

2 views

Seeger, A

Wednesday 19th June 2019 - 09:00 to 09:50

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 20 Jun 2019

#### Discrete translates in function spaces

9 views

Olevskii, A

Tuesday 18th June 2019 - 09:50 to 10:40

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 19 Jun 2019

#### Dynamical sampling and frames generated from powers of exponential operators

5 views

Aldroubi, A

Monday 17th June 2019 - 09:50 to 10:40

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 18 Jun 2019

#### High Dimensional Approximation via Sparse Occupancy Trees

1 view

Binev, P

Monday 17th June 2019 - 14:20 to 15:10

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 18 Jun 2019

#### Integral norm discretization and related problems

5 views

Dai, F

Friday 21st June 2019 - 11:10 to 12:00

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 21 Jun 2019

#### Linear and one-bit compressive sensing with subsampled random convolutions

7 views

Rauhut, H

Tuesday 18th June 2019 - 14:20 to 15:10

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 19 Jun 2019

#### Markov-type inequalities and extreme zeros of orthogonal polynomials

7 views

Nikolov, G

Friday 21st June 2019 - 14:20 to 15:10

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 21 Jun 2019

#### Quasi-Monte Carlo integration in uncertainty quantification of elliptic PDEs with log-Gaussian coefficients

9 views

Herrmann, L

Tuesday 18th June 2019 - 15:40 to 16:30

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 19 Jun 2019

#### Representer theorems and convex optimization

6 views

Boyer, C

Monday 17th June 2019 - 15:40 to 16:30

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 18 Jun 2019

#### Totally positive functions in sampling theory and time-frequency analysis

1 view

Groechenig, K

Friday 21st June 2019 - 09:50 to 10:40

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 21 Jun 2019

#### Transportation cost spaces on finite metric spaces

2 views

Kutzarova, D

Monday 17th June 2019 - 11:10 to 12:00

**Collection**:
Approximation, sampling, and compression in high dimensional problems

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 18 Jun 2019