Operator sum representation for Markov transition models of human inference processes

Ji Woong Lee; Shashi Phoha

doi:10.1109/ACC.2016.7525143

Operator sum representation for Markov transition models of human inference processes

Ji Woong Lee
, Shashi Phoha

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

The standard Bayesian framework does not account for the decision maker's errors, such as the conjunction and disjunction fallacies, in updating the belief state upon measuring the uncertain quantities. Moreover, the classical probability theory does not distinguish a mixed state (e.g., being of two minds) from a superposed state (e.g., being of neutral mind). The operator sum representation of completely positive linear maps can address these limitations in a unified manner, and allows for numerical determination of a general belief-state update rule. In particular, examples show that the operator sum approach yields an improvement over the existing quantum model of human inference, and that it can be used to explain the mixing and superposition effects of gossip interactions.

Original language	English (US)
Title of host publication	2016 American Control Conference, ACC 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1590-1595
Number of pages	6
ISBN (Electronic)	9781467386821
DOIs	https://doi.org/10.1109/ACC.2016.7525143
State	Published - Jul 28 2016
Event	2016 American Control Conference, ACC 2016 - Boston, United States Duration: Jul 6 2016 → Jul 8 2016

Publication series

Name	Proceedings of the American Control Conference
Volume	2016-July
ISSN (Print)	0743-1619

Other

Other	2016 American Control Conference, ACC 2016
Country/Territory	United States
City	Boston
Period	7/6/16 → 7/8/16

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

Access to Document

10.1109/ACC.2016.7525143

Cite this

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title = "Operator sum representation for Markov transition models of human inference processes",

abstract = "The standard Bayesian framework does not account for the decision maker's errors, such as the conjunction and disjunction fallacies, in updating the belief state upon measuring the uncertain quantities. Moreover, the classical probability theory does not distinguish a mixed state (e.g., being of two minds) from a superposed state (e.g., being of neutral mind). The operator sum representation of completely positive linear maps can address these limitations in a unified manner, and allows for numerical determination of a general belief-state update rule. In particular, examples show that the operator sum approach yields an improvement over the existing quantum model of human inference, and that it can be used to explain the mixing and superposition effects of gossip interactions.",

author = "Lee, \{Ji Woong\} and Shashi Phoha",

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doi = "10.1109/ACC.2016.7525143",

language = "English (US)",

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Lee, JW & Phoha, S 2016, Operator sum representation for Markov transition models of human inference processes. in 2016 American Control Conference, ACC 2016., 7525143, Proceedings of the American Control Conference, vol. 2016-July, Institute of Electrical and Electronics Engineers Inc., pp. 1590-1595, 2016 American Control Conference, ACC 2016, Boston, United States, 7/6/16. https://doi.org/10.1109/ACC.2016.7525143

Operator sum representation for Markov transition models of human inference processes. / Lee, Ji Woong; Phoha, Shashi.
2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 1590-1595 7525143 (Proceedings of the American Control Conference; Vol. 2016-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

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AU - Phoha, Shashi

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N2 - The standard Bayesian framework does not account for the decision maker's errors, such as the conjunction and disjunction fallacies, in updating the belief state upon measuring the uncertain quantities. Moreover, the classical probability theory does not distinguish a mixed state (e.g., being of two minds) from a superposed state (e.g., being of neutral mind). The operator sum representation of completely positive linear maps can address these limitations in a unified manner, and allows for numerical determination of a general belief-state update rule. In particular, examples show that the operator sum approach yields an improvement over the existing quantum model of human inference, and that it can be used to explain the mixing and superposition effects of gossip interactions.

AB - The standard Bayesian framework does not account for the decision maker's errors, such as the conjunction and disjunction fallacies, in updating the belief state upon measuring the uncertain quantities. Moreover, the classical probability theory does not distinguish a mixed state (e.g., being of two minds) from a superposed state (e.g., being of neutral mind). The operator sum representation of completely positive linear maps can address these limitations in a unified manner, and allows for numerical determination of a general belief-state update rule. In particular, examples show that the operator sum approach yields an improvement over the existing quantum model of human inference, and that it can be used to explain the mixing and superposition effects of gossip interactions.

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PB - Institute of Electrical and Electronics Engineers Inc.

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Y2 - 6 July 2016 through 8 July 2016

ER -

Operator sum representation for Markov transition models of human inference processes

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