相关论文: Random sampling in chirp space

In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary…

In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…

In this paper, we extend several approximation theorems, originally formulated in the context of the standard $L^p$ norm, to the more general framework of variable exponent spaces. Our study is motivated by applications in neural networks,…

This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a…

We prove convergence rates of linear sampling recovery of functions in abstract Bochner spaces satisfying weighted summability of their generalized polynomial chaos expansion coefficients. The underlying algorithm is a function-valued…

Maximum-likelihood methods are applied to the problem of absorption tomography. The reconstruction is done with the help of an iterative algorithm. We show how the statistics of the illuminating beam can be incorporated into the…

A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…

We describe the minimax reconstruction rates in linear ill-posed equations in Hilbert space when smoothness is given in terms of general source sets. The underlying fundamental result, the minimax rate on ellipsoids, is proved similarly to…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…

Random forests are a powerful method for non-parametric regression, but are limited in their ability to fit smooth signals, and can show poor predictive performance in the presence of strong, smooth effects. Taking the perspective of random…

We present necessary and sufficient conditions to hold true a Kramer type sampling theorem over semi-inner product reproducing kernel Banach spaces. Under some sampling-type hypotheses over a sequence of functions on these Banach spaces it…

We study the space of functions computed by random-layered machines, including deep neural networks and Boolean circuits. Investigating the distribution of Boolean functions computed on the recurrent and layer-dependent architectures, we…

Random features is one of the most popular techniques to speed up kernel methods in large-scale problems. Related works have been recognized by the NeurIPS Test-of-Time award in 2017 and the ICML Best Paper Finalist in 2019. The body of…

We study a class of countably-infinite-dimensional linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined spaces of measures. The optimal value, optimal points, and minimal points of these CILPs can be…

We proved direct and inverse theorems on B-spline quasi-interpolation sampling representation with a Littlewood-Paley-type norm equivalence in Sobolev spaces $W^r_p$ of mixed smoothness $r$, established estimates of the approximation error…

For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…

We study the problem of sampling a random signal with sparse support in frequency domain. Shannon famously considered a scheme that instantaneously samples the signal at equispaced times. He proved that the signal can be reconstructed as…

Ratios of random variables often appear in probability and statistical applications. We aim to approximate the moments of such ratios under several dependence assumptions. Extending the ideas in Collomb [C. R. Acad. Sci. Paris 285 (1977)…

In this paper we analyze a greedy procedure to approximate a linear functional defined in a Reproducing Kernel Hilbert Space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals, including…

A general approach to selective inference is considered for hypothesis testing of the null hypothesis represented as an arbitrary shaped region in the parameter space of multivariate normal model. This approach is useful for hierarchical…