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pro vyhledávání: '"Mhaskar, H. N."'
Motivated by a number of applications in signal processing, we study the following question. Given samples of a multidimensional signal of the form \begin{align*} f(\bs\ell)=\sum_{k=1}^K a_k\exp(-i\langle \bs\ell, \w_k\rangle), \\ \w_1,\cdots,\w_k\in
Externí odkaz:
http://arxiv.org/abs/2404.11004
Autor:
Mhaskar, H. N., O'Dowd, Ryan
Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional Euclidean space.
Externí odkaz:
http://arxiv.org/abs/2402.12687
Autor:
Gia, Q. T. Le, Mhaskar, H. N.
In this work, we construct numerical solutions to an inverse problem of a nonlinear Helmholtz equation defined in a spherical shell between two concentric spheres centered at the origin.Assuming that the values of the forward problem are known at suf
Externí odkaz:
http://arxiv.org/abs/2302.01475
Autor:
Mhaskar, H. N., O'Dowd, Ryan
A fundamental problem in manifold learning is to approximate a functional relationship in a data chosen randomly from a probability distribution supported on a low dimensional sub-manifold of a high dimensional ambient Euclidean space. The manifold i
Externí odkaz:
http://arxiv.org/abs/2302.00160
The problem of real time prediction of blood glucose (BG) levels based on the readings from a continuous glucose monitoring (CGM) device is a problem of great importance in diabetes care, and therefore, has attracted a lot of research in recent years
Externí odkaz:
http://arxiv.org/abs/2105.05893
Autor:
Cloninger, A., Mhaskar, H. N.
Many applications such as election forecasting, environmental monitoring, health policy, and graph based machine learning require taking expectation of functions defined on the vertices of a graph. We describe a construction of a sampling scheme anal
Externí odkaz:
http://arxiv.org/abs/2010.04227
Autor:
Mhaskar, H. N.
The problem of super-resolution in general terms is to recuperate a finitely supported measure $\mu$ given finitely many of its coefficients $\hat{\mu}(k)$ with respect to some orthonormal system. The interesting case concerns situations, where the n
Externí odkaz:
http://arxiv.org/abs/1907.04895
Autor:
Mhaskar, H. N., Poggio, T.
We show that deep networks are better than shallow networks at approximating functions that can be expressed as a composition of functions described by a directed acyclic graph, because the deep networks can be designed to have the same compositional
Externí odkaz:
http://arxiv.org/abs/1905.12882
In machine learning, we are given a dataset of the form $\{(\mathbf{x}_j,y_j)\}_{j=1}^M$, drawn as i.i.d. samples from an unknown probability distribution $\mu$; the marginal distribution for the $\mathbf{x}_j$'s being $\mu^*$. We propose that rather
Externí odkaz:
http://arxiv.org/abs/1901.02975
We study the problem of reconstructing a function on a manifold satisfying some mild conditions, given data on the values and some derivatives of the function at arbitrary points on the manifold. While the problem of finding a polynomial of two varia
Externí odkaz:
http://arxiv.org/abs/1710.01419