Related papers: Restoring a smooth function from its noisy integra…
We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a…
Learning the Green's function using deep learning models enables to solve different classes of partial differential equations. A practical limitation of using deep learning for the Green's function is the repeated computationally expensive…
Detector response to a high-energy physics process is often estimated by Monte Carlo simulation. For purposes of data analysis, the results of this simulation are typically stored in large multi-dimensional histograms, which can quickly…
Given a way to evaluate an unknown polynomial with integer coefficients, we present new algorithms to recover its nonzero coefficients and corresponding exponents. As an application, we adapt this interpolation algorithm to the problem of…
We consider the problem of numerically integrating functions with hyperplane discontinuities over the entire Euclidean space in many dimensions. We describe a simple process through which the Euclidean space is partitioned into simplices on…
We constructed linear algorithms of sampling recovery and cubature formulas on Smolyak grids parametrized by $m \in \mathbb{N}$ of periodic $d$-variate functions having Lipschitz-H\"older mixed smoothness $\alpha > 0$ based on B-spline…
In this paper, in a multivariate setting we derive near optimal rates of convergence in the minimax sense for estimating partial derivatives of the mean function for functional data observed under a fixed synchronous design over H\"older…
We present an algorithm for the rapid numerical integration of smooth, time-periodic differential equations with small nonlinearity, particularly suited to problems with small dissipation. The emphasis is on speed without compromising…
The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely-differentiable…
3D Lidar imaging can be a challenging modality when using multiple wavelengths, or when imaging in high noise environments (e.g., imaging through obscurants). This paper presents a hierarchical Bayesian algorithm for the robust…
Binary neural networks leverage $\mathrm{Sign}$ function to binarize weights and activations, which require gradient estimators to overcome its non-differentiability and will inevitably bring gradient errors during backpropagation. Although…
This work deals with the numerical solution of systems of oscillatory second-order differential equations which often arise from the semi-discretization in space of partial differential equations. Since these differential equations exhibit…
Population Monte Carlo simulations in the form commonly referred to as population annealing can serve as a useful meta-algorithm for simulating systems with complex free-energy landscapes. In the present paper we provide an easily…
We consider the problem of minimizing a smooth, Lipschitz, convex function over a compact, convex set using sub-zeroth-order oracles: an oracle that outputs the sign of the directional derivative for a given point and a given direction, an…
Traditional Monte Carlo integration using uniform random sampling exhibits degraded efficiency in low-regularity or high-dimensional problems. We propose a novel deep learning framework based on deterministic number-theoretic sampling…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames.…
Although numerous algorithms have been proposed to solve the categorical data clustering problem, how to access the statistical significance of a set of categorical clusters remains unaddressed. To fulfill this void, we employ the…
Estimating properties of unknown unitary operations is a fundamental task in quantum information science. While full unitary tomography requires a number of samples to the unknown unitary scaling linearly with the dimension (implying…
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…