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The Sum-Product Theorem and Its Applications.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	The Sum-Product Theorem and Its Applications./
作者:	Friesen, Abram L.
面頁冊數:	1 online resource (159 pages)
附註:	Source: Dissertation Abstracts International, Volume: 79-05(E), Section: B.
Contained By:	Dissertation Abstracts International79-05B(E).
標題:	Computer science. -
電子資源:	click for full text (PQDT)
ISBN:	9780355597127

The Sum-Product Theorem and Its Applications.
Friesen, Abram L.

The Sum-Product Theorem and Its Applications. - 1 online resource (159 pages)

Source: Dissertation Abstracts International, Volume: 79-05(E), Section: B.

Thesis (Ph.D.)--University of Washington, 2017.

Includes bibliographical references

Models in artificial intelligence (AI) and machine learning (ML) must be expressive enough to accurately capture the state of the world, but tractable enough that reasoning and inference within them is feasible. However, many standard models are incapable of capturing sufficiently complex phenomena when constrained to be tractable. In this dissertation, I study the cause of this inexpressiveness and its relationship to inference complexity. I use the resulting insights to develop more efficient and expressive models and algorithms for many problems in AI and ML, including nonconvex optimization, computer vision, and deep learning.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355597127Subjects--Topical Terms:

573171
Computer science.
Index Terms--Genre/Form:

554714
Electronic books.

The Sum-Product Theorem and Its Applications.
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500 $a Source: Dissertation Abstracts International, Volume: 79-05(E), Section: B.
500 $a Adviser: Pedro Domingos.
502 $a Thesis (Ph.D.)--University of Washington, 2017.
504 $a Includes bibliographical references
520 $a Models in artificial intelligence (AI) and machine learning (ML) must be expressive enough to accurately capture the state of the world, but tractable enough that reasoning and inference within them is feasible. However, many standard models are incapable of capturing sufficiently complex phenomena when constrained to be tractable. In this dissertation, I study the cause of this inexpressiveness and its relationship to inference complexity. I use the resulting insights to develop more efficient and expressive models and algorithms for many problems in AI and ML, including nonconvex optimization, computer vision, and deep learning.
520 $a I first identify and prove the sum-product theorem, which states that in any semiring for inference to be tractable it suffices that the factors of every product have disjoint scopes; i.e., that they are decomposable . I show that this simple condition unifies and extends many results in the literature and enables the definition of highly-expressive model classes that are tractable and learnable for many of the most important problems in AI and ML. Second, I develop RDIS, a novel nonconvex optimization algorithm based on the sum-product theorem. I show both analytically and empirically that RDIS can be exponentially faster than standard approaches because it finds and exploits local decomposability. Third, I combine decomposability with submodularity to define submodular field grammars (SFGs), a novel class of probabilistic models that extends both sum-product networks and submodular Markov random fields. SFGs define a novel stochastic image grammar in which each object in the grammar can have arbitrary region shape but in which approximate MAP inference remains tractable, the first image grammar formulation in which this is possible. Finally, I demonstrate the applicability of decomposability to deep learning. I present feasible target propagation, a novel algorithm for learning deep neural networks with hard-threshold activations---which cannot be trained with standard backpropagation-based methods---that learns more accurate models than competing methods.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Computer science. $3 573171
650 4 $a Artificial intelligence. $3 559380
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710 2 $a University of Washington. $b Computer Science and Engineering. $3 1182238
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