國立虎尾科技大學 |

Relations between Information and Estimation : = A Unified View.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Relations between Information and Estimation :/
其他題名:	A Unified View.
作者:	Venkat, Kartik.
面頁冊數:	1 online resource (228 pages)
附註:	Source: Dissertations Abstracts International, Volume: 82-05, Section: B.
Contained By:	Dissertations Abstracts International82-05B.
標題:	Electrical engineering. -
電子資源:	click for full text (PQDT)
ISBN:	9798662565555

Relations between Information and Estimation : = A Unified View.
Venkat, Kartik.

Relations between Information and Estimation :A Unified View. - 1 online resource (228 pages)

Source: Dissertations Abstracts International, Volume: 82-05, Section: B.

Thesis (Ph.D.)--Stanford University, 2015.

Includes bibliographical references

Measures of information, such as entropy, mutual information, and relative entropy play important roles in various domains: underlying algorithmic procedures in machine learning, characterizing operational quantities in communication, storage and inference, and characterizing the likelihood of large deviations events in statistics and probability, among others. Such information measures also turn out to give a quantitative understanding of several estimation theoretic notions - such as the costs of causality and mismatch, and the benefit of lookahead - via relations between information and estimation. This thesis presents a new framework for understanding the rich interconnections between information and estimation for a variety of widely applicable observation models.Many of these relations can be viewed as identities between expectations of random quantities. This dissertation presents these identities and their generalizations in new light. The first part of this thesis focuses on two canonical observation models: The additive Gaussian channel and the Poisson channel. For both these models, we dispense with the expectations and explore the nature of the pointwise relations between the respective random quantities. Our results recover and generalize previously known identities involving mutual information and minimum mean loss in estimation. Classical estimation and information theoretic quantities emerge with new and surprising roles. In the second part of the thesis, we introduce a natural family of Levy channels where the distribution of the output conditioned on the input is infinitely divisible. This family includes, as special cases, both the Gaussian and Poisson channels. For Levy channels, we establish new representations relating the mutual information between the channel input and output to an optimal expected estimation loss, thereby unifying and extending previously known results. Corollaries of our results include new formulae for entropy and relative entropy. The unified framework extends to continuous-time stochastic processes as well, where we introduce and study these connections for semi-martingale channels, which include the well-known white Gaussian channel and the multivariate point process channel. In the third, and final part of this dissertation, we revisit the white Gaussian channel and study the problem of estimation with finite lookahead. We look at the properties of finite lookahead minimum mean squared error and investigate connections between this quantity and mutual information.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798662565555Subjects--Topical Terms:

596380
Electrical engineering.
Subjects--Index Terms:

Mutual informationIndex Terms--Genre/Form:

554714
Electronic books.

Relations between Information and Estimation : = A Unified View.
LDR:03881ntm a22003617 4500 001 1143955
005 20240531084152.5
006 m o d
007 cr mn ---uuuuu
008 250605s2015 xx obm 000 0 eng d
020 $a 9798662565555
035 $a (MiAaPQ)AAI28119832
035 $a (MiAaPQ)STANFORDpv323kq3283
035 $a AAI28119832
040 $a MiAaPQ $b eng $c MiAaPQ $d NTU
100 1 $a Venkat, Kartik. $3 1468785
245 1 0 $a Relations between Information and Estimation : $b A Unified View.
264 0 $c 2015
300 $a 1 online resource (228 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 82-05, Section: B.
500 $a Advisor: Weissman, Tsachy;Glynn, Peter W.;Montanari, Andrea.
502 $a Thesis (Ph.D.)--Stanford University, 2015.
504 $a Includes bibliographical references
520 $a Measures of information, such as entropy, mutual information, and relative entropy play important roles in various domains: underlying algorithmic procedures in machine learning, characterizing operational quantities in communication, storage and inference, and characterizing the likelihood of large deviations events in statistics and probability, among others. Such information measures also turn out to give a quantitative understanding of several estimation theoretic notions - such as the costs of causality and mismatch, and the benefit of lookahead - via relations between information and estimation. This thesis presents a new framework for understanding the rich interconnections between information and estimation for a variety of widely applicable observation models.Many of these relations can be viewed as identities between expectations of random quantities. This dissertation presents these identities and their generalizations in new light. The first part of this thesis focuses on two canonical observation models: The additive Gaussian channel and the Poisson channel. For both these models, we dispense with the expectations and explore the nature of the pointwise relations between the respective random quantities. Our results recover and generalize previously known identities involving mutual information and minimum mean loss in estimation. Classical estimation and information theoretic quantities emerge with new and surprising roles. In the second part of the thesis, we introduce a natural family of Levy channels where the distribution of the output conditioned on the input is infinitely divisible. This family includes, as special cases, both the Gaussian and Poisson channels. For Levy channels, we establish new representations relating the mutual information between the channel input and output to an optimal expected estimation loss, thereby unifying and extending previously known results. Corollaries of our results include new formulae for entropy and relative entropy. The unified framework extends to continuous-time stochastic processes as well, where we introduce and study these connections for semi-martingale channels, which include the well-known white Gaussian channel and the multivariate point process channel. In the third, and final part of this dissertation, we revisit the white Gaussian channel and study the problem of estimation with finite lookahead. We look at the properties of finite lookahead minimum mean squared error and investigate connections between this quantity and mutual information.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Electrical engineering. $3 596380
653 $a Mutual information
653 $a Relative entropy
653 $a Lookahead
655 7 $a Electronic books. $2 local $3 554714
690 $a 0544
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Stanford University. $3 1184533
773 0 $t Dissertations Abstracts International $g 82-05B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28119832 $z click for full text (PQDT)