소장자료
LDR | 02958nam 2200505 4500 | ||
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020 | ▼a9798380313346▲ | ||
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040 | ▼aMiAaPQ▼cMiAaPQ▲ | ||
082 | 0 | ▼a004▲ | |
100 | 1 | ▼aAzevedo de Amorim, Pedro Henrique.▼0(orcid)0000-0002-8338-8973▲ | |
245 | 1 | 2 | ▼aA Unifying Semantics for Markov Kernels and Linear Operators▼h[electronic resource]▲ |
260 | ▼a[S.l.]: ▼bCornell University. ▼c2023▲ | ||
260 | 1 | ▼aAnn Arbor : ▼bProQuest Dissertations & Theses, ▼c2023▲ | |
300 | ▼a1 online resource(200 p.)▲ | ||
500 | ▼aSource: Dissertations Abstracts International, Volume: 85-03, Section: B.▲ | ||
500 | ▼aAdvisor: Kozen, Dexter.▲ | ||
502 | 1 | ▼aThesis (Ph.D.)--Cornell University, 2023.▲ | |
506 | ▼aThis item must not be sold to any third party vendors.▲ | ||
520 | ▼aThere has been much work done in developing semantic structures for interpreting probabilistic programs. In particular, there have been many models based either on Markov kernels or linear operators, each with their own set of strengths and weaknesses.Concurrently, mathematicians have been working on categorical semantics for probability theory with the goal of obtaining a more abstract understanding of the field. This has led to the definition of Markov categories, an abstraction of Markov kernels. However, a similar treatment to the linear operator approach to probability is currently eluded by existing methods.This thesis sits at the intersection of probabilistic semantics and categorical probability theory. We propose a new categorical semantics and core calculus that extends Markov categories with linear operators, we justify its viability by showing how many useful categories used in probabilistic semantics are instances of our framework and, furthermore, we define a new model inspired by a functional-analytic treatment of measure theory. We conclude by showing how this formalism can be used to reason about a generalized notion of probabilistic independence via a substructural type system.▲ | ||
590 | ▼aSchool code: 0058.▲ | ||
650 | 4 | ▼aComputer science.▲ | |
650 | 4 | ▼aMathematics.▲ | |
650 | 4 | ▼aApplied mathematics.▲ | |
653 | ▼aProbabilistic semantics▲ | ||
653 | ▼aProbabilistic programming▲ | ||
653 | ▼aProgramming languages▲ | ||
653 | ▼aProbability theory▲ | ||
653 | ▼aMeasure theory▲ | ||
690 | ▼a0984▲ | ||
690 | ▼a0405▲ | ||
690 | ▼a0364▲ | ||
710 | 2 | 0 | ▼aCornell University.▼bComputer Science.▲ |
773 | 0 | ▼tDissertations Abstracts International▼g85-03B.▲ | |
773 | ▼tDissertation Abstract International▲ | ||
790 | ▼a0058▲ | ||
791 | ▼aPh.D.▲ | ||
792 | ▼a2023▲ | ||
793 | ▼aEnglish▲ | ||
856 | 4 | 0 | ▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T16934300▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.▲ |
A Unifying Semantics for Markov Kernels and Linear Operators[electronic resource]
자료유형
국외eBook
서명/책임사항
A Unifying Semantics for Markov Kernels and Linear Operators [electronic resource]
발행사항
[S.l.] : Cornell University. 2023 Ann Arbor : ProQuest Dissertations & Theses , 2023
형태사항
1 online resource(200 p.)
일반주기
Source: Dissertations Abstracts International, Volume: 85-03, Section: B.
Advisor: Kozen, Dexter.
Advisor: Kozen, Dexter.
학위논문주기
Thesis (Ph.D.)--Cornell University, 2023.
요약주기
There has been much work done in developing semantic structures for interpreting probabilistic programs. In particular, there have been many models based either on Markov kernels or linear operators, each with their own set of strengths and weaknesses.Concurrently, mathematicians have been working on categorical semantics for probability theory with the goal of obtaining a more abstract understanding of the field. This has led to the definition of Markov categories, an abstraction of Markov kernels. However, a similar treatment to the linear operator approach to probability is currently eluded by existing methods.This thesis sits at the intersection of probabilistic semantics and categorical probability theory. We propose a new categorical semantics and core calculus that extends Markov categories with linear operators, we justify its viability by showing how many useful categories used in probabilistic semantics are instances of our framework and, furthermore, we define a new model inspired by a functional-analytic treatment of measure theory. We conclude by showing how this formalism can be used to reason about a generalized notion of probabilistic independence via a substructural type system.
주제
ISBN
9798380313346
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