Related papers: Differential and falsified sampling expansions

Generalized Fiducial Inference (GFI) is motivated by R.A. Fisher's approach of obtaining posterior-like distributions when there is no prior information available for the unknown parameter. Without the use of Bayes' theorem GFI proposes a…

We study the random sampling of the short-time Fourier transform of functions that are localized in a compact region in the time-frequency plane. We follow the approach introduced by Bass and Gr\"ochenig for band-limited functions, and show…

We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we…

In reinforcement learning and imitation learning, an object of central importance is the state distribution induced by the policy. It plays a crucial role in the policy gradient theorem, and references to it--along with the related…

In the first part of the paper we study absolute error of sampling discretization of the integral $L_p$-norm for function classes of continuous functions. We use basic approaches from chaining technique to provide general upper bounds for…

This paper introduces an upper bound on the absolute difference between: (a) the cumulative distribution function (CDF) of the sum of a finite number of independent and identically distributed random variables with finite absolute third…

This paper introduces a weighted generalized inverse framework for Fourier extensions, designed to suppress spurious oscillations in the extended region while maintaining high approximation accuracy on the original interval. By formulating…

A new analytical approximation function is proposed to accurately fit the solution of a fractional differential equation of order one-half, whose nonhomogeneous term is defined by a modified Bessel function of the first kind. The exact…

We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for controlled paths which is interesting in its own right.

This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…

Let $f(n)$ denote a multiplicative function with range $\{-1,0,1\}$, and let $F(x) = \sum_{n\leq x} f(n)$. Then $F(x)/\sqrt{x} = a\sqrt{x} + b + E(x)$, where $a$ and $b$ are constants and $E(x)$ is an error term that either tends to $0$ in…

This work introduces a new approximate proximal sampler that operates solely with zeroth-order information of the potential function. Prior theoretical analyses have revealed that proximal sampling corresponds to alternating forward and…

The most popular algorithm for the nonuniform fast Fourier transform (NUFFT) uses the dilation of a kernel $\phi$ to spread (or interpolate) between given nonuniform points and a uniform upsampled grid, combined with an FFT and diagonal…

This paper addresses a problem of estimating an additive functional given $n$ i.i.d. samples drawn from a discrete distribution $P=(p_1,...,p_k)$ with alphabet size $k$. The additive functional is defined as…

We give algorithms for estimating the expectation of a given real-valued function $\phi:X\to {\bf R}$ on a sample drawn randomly from some unknown distribution $D$ over domain $X$, namely ${\bf E}_{{\bf x}\sim D}[\phi({\bf x})]$. Our…

We derandomize G. Valiant's [J. ACM 62 (2015) Art. 13] subquadratic-time algorithm for finding outlier correlations in binary data. Our derandomized algorithm gives deterministic subquadratic scaling essentially for the same parameter range…

We study convergence properties of sparse averages of partial sums of Fourier series of continuous functions. By sparse averages, we are considering an increasing sequences of integers $n_0 < n_1 < n_2 < ...$ and looking at…

In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…

In this paper we recall some results and some criteria on the convergence of matrix continued fractions. The aim of this paper is to give some properties and results of continued fractions with matrix arguments. Then we give continued…

Fix integers $m\ge 2$, $n\ge 1$. We prove the existence of a bounded linear extension operator for $C^{m-1,1}(\R^n)$ with operator norm at most $\exp(\gamma D^k)$, where $D := \binom{m+n-1}{n}$ is the number of multiindices of length $n$…