Abstract
dc:description.abstractIn this thesis, we present an MCMC-based method to extract near-uniform samples from a level set of a provided function 𝑓 : Rᵈ → Rᵏ . We propose a sequence of unnormalized distributions over Rᵈ with asymptotic convergence to the Hausdorff measure of the level set, therefore resulting in uniform samples. Beyond our formulation’s 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.
Degree
thesis:*- Name thesis:degree_name
- Master
- Department dc:contributor.department
- Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
- Grantor dc:publisher
- Massachusetts Institute of Technology
- Year dc:date.issued
- 2022
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Chiu, Erica
- Advisor dc:contributor.advisor
-
- Solomon, Justin
Rights
dc:rights- Statement dc:rights
-
- In Copyright - Educational Use Permitted
- Copyright MIT
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Handle dc:identifier.uri
- https://hdl.handle.net/1721.1/144987
- OAI identifier oai:identifier
- oai:dspace.mit.edu:1721.1/144987