Point cloud data sets are frequently used in machines to sense the real world because sensors such as LIDAR readily available be many applications including autonomous cars and drones. PointNet PointNet++ widely point-wise embedding methods for interpreting clouds. However, even recent models based on PointNet, real-time inference is still challenging. The solution a faster sampling, where, sam...

A simple method to select a spatially balanced sample using equal or unequal inclusion probabilities is presented. For populations with spatial trends in the variables of interest, the estimation can be much improved by selecting samples that are well spread over the population. The method can be used for any number of dimensions and can hence also select spatially balanced samples in a space s...

We give the first algorithm for kernel Nyström approximation that runs in linear time in the number of training points and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions. The algorithm projects the kernel onto a set of s landmark points sampled by their ridge leverage scores, requiring just O(ns) kernel evaluations and O(ns) additional r...

A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large number of δ functions, treated as a statistical-mechanics problem, it avoids distortions caused by (as demonstrated here) configurational entropy in previous samp...

In this work, we are concerned with the di↵usive optical tomography (DOT) problem in the case when only one or two pairs of Cauchy data is available. We propose a simple and e cient direct sampling method (DSM) to locate inhomogeneities inside a homogeneous background and solve the DOT problem in both full and limited aperture cases. This new method is easy to implement and less expensive compu...

The Nyström method is an efficient technique to generate low-rank matrix approximations and is used in several large-scale learning applications. A key aspect of this method is the distribution according to which columns are sampled from the original matrix. In this work, we present an analysis of different sampling techniques for the Nyström method. Our analysis includes both empirical and the...

We consider the inverse scattering problem of determining the support of an anisotropic inhomogeneous medium from a knowledge of the incident and scattered time harmonic acoustic wave at 1xed frequency. To this end, we extend the linear sampling method from the isotropic case to the case of anisotropic medium. In the case when the coe6cients are real we also show that the set of transmission ei...