Sampling, integration and computing volumes:
Abstract: "Sampling is a fundamental method for approximating answers that cannot be directly computed. Samples often need to be taken from a non-uniform distribution. In this thesis, I present an algorithm to generate samples from log-concave and nearly log-concave distributions. This sampling...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Pittsburgh, Pa.
School of Computer Science, Carnegie Mellon Univ.
1991
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| Schriftenreihe: | School of Computer Science <Pittsburgh, Pa.>: CMU-CS
1991,207 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "Sampling is a fundamental method for approximating answers that cannot be directly computed. Samples often need to be taken from a non-uniform distribution. In this thesis, I present an algorithm to generate samples from log-concave and nearly log-concave distributions. This sampling algorithm is based on a biased random walk, and the proof of correctness also provides bounds on the mixing time of the Gibbs sampler with the random sweep strategy. To demonstrate the usefulness of sampling from log-concave distributions, I use this algorithm to integrate log- concave functions and to compute the volume of convex sets This resulting volume algorithm improves on the existing volume algorithms due to Dyer, Frieze, and Kannan, and Lovasz and Simonovits. Samples generated by the sampling algorithm can also be used to estimate marginal densities and as a tool for Bayesian inference. |
| Beschreibung: | Zugl.: Pittsburgh, Pa., Univ., Diss., 1991 |
| Beschreibung: | IV, 71 S. graph. Darst. |
Internformat
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| 490 | 1 | |a School of Computer Science <Pittsburgh, Pa.>: CMU-CS |v 1991,207 | |
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| 520 | 3 | |a Abstract: "Sampling is a fundamental method for approximating answers that cannot be directly computed. Samples often need to be taken from a non-uniform distribution. In this thesis, I present an algorithm to generate samples from log-concave and nearly log-concave distributions. This sampling algorithm is based on a biased random walk, and the proof of correctness also provides bounds on the mixing time of the Gibbs sampler with the random sweep strategy. To demonstrate the usefulness of sampling from log-concave distributions, I use this algorithm to integrate log- concave functions and to compute the volume of convex sets | |
| 520 | 3 | |a This resulting volume algorithm improves on the existing volume algorithms due to Dyer, Frieze, and Kannan, and Lovasz and Simonovits. Samples generated by the sampling algorithm can also be used to estimate marginal densities and as a tool for Bayesian inference. | |
| 650 | 4 | |a Markov processes | |
| 650 | 4 | |a Sampling (Statistics) | |
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| 650 | 0 | 7 | |a Integration |g Mathematik |0 (DE-588)4072852-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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| author | Applegate, David L. |
| author_GND | (DE-588)1089639260 |
| author_facet | Applegate, David L. |
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| author_sort | Applegate, David L. |
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| dewey-full | 510.7808 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.7808 |
| dewey-search | 510.7808 |
| dewey-sort | 3510.7808 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV009667634 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:38:54Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006393399 |
| oclc_num | 26241874 |
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| owner | DE-91 DE-BY-TUM |
| owner_facet | DE-91 DE-BY-TUM |
| physical | IV, 71 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | School of Computer Science, Carnegie Mellon Univ. |
| record_format | marc |
| series | School of Computer Science <Pittsburgh, Pa.>: CMU-CS |
| series2 | School of Computer Science <Pittsburgh, Pa.>: CMU-CS |
| spelling | Applegate, David L. Verfasser (DE-588)1089639260 aut Sampling, integration and computing volumes David Applegate CMU CS 91 207 Pittsburgh, Pa. School of Computer Science, Carnegie Mellon Univ. 1991 IV, 71 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier School of Computer Science <Pittsburgh, Pa.>: CMU-CS 1991,207 Zugl.: Pittsburgh, Pa., Univ., Diss., 1991 Abstract: "Sampling is a fundamental method for approximating answers that cannot be directly computed. Samples often need to be taken from a non-uniform distribution. In this thesis, I present an algorithm to generate samples from log-concave and nearly log-concave distributions. This sampling algorithm is based on a biased random walk, and the proof of correctness also provides bounds on the mixing time of the Gibbs sampler with the random sweep strategy. To demonstrate the usefulness of sampling from log-concave distributions, I use this algorithm to integrate log- concave functions and to compute the volume of convex sets This resulting volume algorithm improves on the existing volume algorithms due to Dyer, Frieze, and Kannan, and Lovasz and Simonovits. Samples generated by the sampling algorithm can also be used to estimate marginal densities and as a tool for Bayesian inference. Markov processes Sampling (Statistics) Stichprobe (DE-588)4057502-0 gnd rswk-swf Integration Mathematik (DE-588)4072852-3 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s Integration Mathematik (DE-588)4072852-3 s Stichprobe (DE-588)4057502-0 s Algorithmus (DE-588)4001183-5 s DE-604 School of Computer Science <Pittsburgh, Pa.>: CMU-CS 1991,207 (DE-604)BV006187264 1991,207 |
| spellingShingle | Applegate, David L. Sampling, integration and computing volumes School of Computer Science <Pittsburgh, Pa.>: CMU-CS Markov processes Sampling (Statistics) Stichprobe (DE-588)4057502-0 gnd Integration Mathematik (DE-588)4072852-3 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4057502-0 (DE-588)4072852-3 (DE-588)4121894-2 (DE-588)4001183-5 (DE-588)4113937-9 |
| title | Sampling, integration and computing volumes |
| title_alt | CMU CS 91 207 |
| title_auth | Sampling, integration and computing volumes |
| title_exact_search | Sampling, integration and computing volumes |
| title_full | Sampling, integration and computing volumes David Applegate |
| title_fullStr | Sampling, integration and computing volumes David Applegate |
| title_full_unstemmed | Sampling, integration and computing volumes David Applegate |
| title_short | Sampling, integration and computing volumes |
| title_sort | sampling integration and computing volumes |
| topic | Markov processes Sampling (Statistics) Stichprobe (DE-588)4057502-0 gnd Integration Mathematik (DE-588)4072852-3 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Markov processes Sampling (Statistics) Stichprobe Integration Mathematik Wahrscheinlichkeitsverteilung Algorithmus Hochschulschrift |
| volume_link | (DE-604)BV006187264 |
| work_keys_str_mv | AT applegatedavidl samplingintegrationandcomputingvolumes AT applegatedavidl cmucs91207 |