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

03/05/2022
āˆ™
by   Apostolos Chalkis, et al.
āˆ™
0
āˆ™

Given a parametric polynomial curve Ī³:[a,b]ā†’ā„^n, how can we sample a random point š”µāˆˆim(Ī³) 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

research
āˆ™ 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...
research
āˆ™ 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...
research
āˆ™ 06/23/2023

Breakdown points of Fermat-Weber problems under gauge distances

We compute the robustness of Fermatā€“Weber points with respect to any fin...
research
āˆ™ 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...
research
āˆ™ 09/23/2020

Sampling an Edge Uniformly in Sublinear Time

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

Efficient learning of simplices

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

Parametric Models Analysed with Linear Maps

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

Please sign up or login with your details

Forgot password? Click here to reset