2026-09-19T08:07:06Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1449872022-08-30T03:34:31Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Solomon, Justin
Chiu, Erica
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2022-08-29T16:25:31Z
2022-08-29T16:25:31Z
2022-05
2022-05-27T16:19:24.539Z
https://hdl.handle.net/1721.1/144987
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.
M.Eng.
Massachusetts Institute of Technology
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http://rightsstatements.org/page/InC-EDU/1.0/
Uniform Sampling over Level Sets
Thesis
application/pdf
Master
Master of Engineering in Electrical Engineering and Computer Science
Publication
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unknown
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<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.</Abstract>
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