K. Dziedziul

activity

20182023

collaborators

6 papers

cs.LG2023

Mercer Large-Scale Kernel Machines from Ridge Function Perspective

Karol Dziedziul, Sergey Kryzhevich, Paweł Wieczyński

To present Mercer large-scale kernel machines from a ridge function perspective, we recall the results by Lin and Pinkus from {\it Fundamentality of ridge functions}. We consider t…

math.FA2020

Parseval wavelet frames on Riemannian manifold

Marcin Bownik, Karol Dziedziul, Anna Kamont

We construct Parseval wavelet frames in $L^{2} (M)$ for a general Riemannian manifold $M$ and we show the existence of wavelet unconditional frames in $L^{p} (M)$ for $1 < p < \infty$ . Th…

math.ST2018

Note on universal algorithms for learning theory

Karol Dziedziul, Barbara Wolnik

We propose the general way of study the universal estimator for the regression problem in learning theory considered in "Universal algorithms for learning theory Part I: piecewise…

math.ST2018

Multiresolution analysis and adaptive estimation on a sphere using stereographic wavelets

Bogdan Ćmiel, Karol Dziedziul, Natalia Jarzębkowska

We construct an adaptive estimator of a density function on $d$ dimensional unit sphere $S^{d}$ ( $d \geq 2$ ), using a new type of spherical frames. The frames, or as we call them, s…

math.ST2018

The smoothness test for a density function

Bogdan Ćmiel, Karol Dziedziul, Barbara Wolnik

The problem of testing hypothesis that a density function has no more than $μ$ derivatives versus it has more than $μ$ derivatives is considered. For a solution, the $L^{2}$ norms of…

math.CA2018

Smooth orthogonal projections on Riemannian manifold

Marcin Bownik, Karol Dziedziul, Anna Kamont

We construct a decomposition of the identity operator on a Riemannian manifold $M$ as a sum of smooth orthogonal projections subordinate to an open cover of $M$ . This extends a dec…