Uniform Sampling over Level Sets
Name
Chiu-ejchiu-meng-eecs-2022-thesis.pdf
Description
Thesis PDF
Size
7.86 MB
Format
Adobe PDF
Checksum (MD5)
a2b8903671331470a178e6b1051bbf23
Author(s)
Chiu, Erica
Advisor(s)
Solomon, Justin
Date Issued
May 2022
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, we present an MCMC-based method to extract near-uniform samples from a level set of a provided function š : Rįµ ā Rįµ . We propose a sequence of unnormalized distributions over Rįµ with asymptotic convergence to the Hausdorff measure of the level set, therefore resulting in uniform samples. Beyond our formulationās asymptotic convergence, we demonstrate its practicality by using MCMC to sample a distribution in the sequence for some analytical functions. Finally, we test our sampling method on representative applications related to machine learning, including extracting geometry from neural implicit representations and multi-objective optimization.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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