DeepAI AI Chat
Log In Sign Up

On the Error of Random Sampling: Uniformly Distributed Random Points on Parametric Curves

03/05/2022
βˆ™
by   Apostolos Chalkis, et al.
βˆ™
Inria
βˆ™
University of Athens
βˆ™
0
βˆ™

Given a parametric polynomial curve Ξ³:[a,b]→ℝ^n, how can we sample a random point π”΅βˆˆim(Ξ³) in such a way that it is distributed uniformly with respect to the arc-length? Unfortunately, we cannot sample exactly such a point-even assuming we can perform exact arithmetic operations. So we end up with the following question: how does the method we choose affect the quality of the approximate sample we obtain? In practice, there are many answers. However, in theory, there are still gaps in our understanding. In this paper, we address this question from the point of view of complexity theory, providing bounds in terms of the size of the desired error.

READ FULL TEXT

page 1

page 2

page 3

page 4

βˆ™ 11/27/2019

Expected dispersion of uniformly distributed points

The dispersion of a point set in [0,1]^d is the volume of the largest ax...
βˆ™ 06/03/2019

A library to compute the density of the distance between a point and a random variable uniformly distributed in some sets

In [3], algorithms to compute the density of the distance to a random va...
βˆ™ 03/29/2021

A Sharp Discrepancy Bound for Jittered Sampling

For m, d βˆˆβ„•, a jittered sampling point set P having N = m^d points in [0...
βˆ™ 12/10/2019

Almost Uniform Sampling From Neural Networks

Given a length n sample from R^d and a neural network with a fixed archi...
βˆ™ 09/23/2020

Sampling an Edge Uniformly in Sublinear Time

The area of sublinear algorithms have recently received a lot of attenti...
βˆ™ 11/09/2012

Efficient learning of simplices

We show an efficient algorithm for the following problem: Given uniforml...
βˆ™ 11/22/2019

Parametric Models Analysed with Linear Maps

Parametric entities appear in many contexts, be it in optimisation, cont...