Uniform Sampling over Level Sets
In 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 samp...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2022
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| Online Access: | https://hdl.handle.net/1721.1/144987 |
| _version_ | 1826203420065792000 |
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| author | Chiu, Erica |
| author2 | Solomon, Justin |
| author_facet | Solomon, Justin Chiu, Erica |
| author_sort | Chiu, Erica |
| collection | MIT |
| description | In 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. |
| first_indexed | 2024-09-23T12:36:42Z |
| format | Thesis |
| id | mit-1721.1/144987 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T12:36:42Z |
| publishDate | 2022 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1449872022-08-30T03:34:31Z Uniform Sampling over Level Sets Chiu, Erica Solomon, Justin Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science In 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. M.Eng. 2022-08-29T16:25:31Z 2022-08-29T16:25:31Z 2022-05 2022-05-27T16:19:24.539Z Thesis https://hdl.handle.net/1721.1/144987 In Copyright - Educational Use Permitted Copyright MIT http://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Chiu, Erica Uniform Sampling over Level Sets |
| title | Uniform Sampling over Level Sets |
| title_full | Uniform Sampling over Level Sets |
| title_fullStr | Uniform Sampling over Level Sets |
| title_full_unstemmed | Uniform Sampling over Level Sets |
| title_short | Uniform Sampling over Level Sets |
| title_sort | uniform sampling over level sets |
| url | https://hdl.handle.net/1721.1/144987 |
| work_keys_str_mv | AT chiuerica uniformsamplingoverlevelsets |