Universal discretization and sparse sampling recovery

01/14/2023
by   F. Dai, et al.
0

Recently, it was discovered that for a given function class 𝐅 the error of best linear recovery in the square norm can be bounded above by the Kolmogorov width of 𝐅 in the uniform norm. That analysis is based on deep results in discretization of the square norm of functions from finite dimensional subspaces. In this paper we show how very recent results on universal discretization of the square norm of functions from a collection of finite dimensional subspaces lead to an inequality between optimal sparse recovery in the square norm and best sparse approximations in the uniform norm with respect to appropriate dictionaries.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/08/2023

On universal sampling recovery in the uniform norm

It is known that results on universal sampling discretization of the squ...
research
09/24/2020

L_2-norm sampling discretization and recovery of functions from RKHS with finite trace

We provide a spectral norm concentration inequality for infinite random ...
research
10/07/2020

On optimal recovery in L_2

We prove that the optimal error of recovery in the L_2 norm of functions...
research
07/09/2023

Lebesgue-type inequalities in sparse sampling recovery

Recently, it has been discovered that results on universal sampling disc...
research
03/14/2022

Sampling discretization error of integral norms for function classes with small smoothness

We consider infinitely dimensional classes of functions and instead of t...
research
08/03/2022

On cardinality of the lower sets and universal discretization

A set Q in ℤ_+^d is a lower set if (k_1,…,k_d)∈ Q implies (l_1,…,l_d)∈ Q...
research
02/04/2022

On Universal Portfolios with Continuous Side Information

A new portfolio selection strategy that adapts to a continuous side-info...

Please sign up or login with your details

Forgot password? Click here to reset