Constriction for sets of probabilities

Michele Caprio; Teddy Seidenfeld

Constriction for sets of probabilities

Michele Caprio, Teddy Seidenfeld

Machine Learning and Robotics

Carnegie Mellon University

Research output: Chapter in Book/Conference proceeding › Conference contribution › peer-review

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Abstract

Given a set of probability measures P representing an agent’s knowledge on the elements of a sigma-algebra F , we can compute upper and lower bounds for the probability of any event A∈F of interest. A procedure generating a new assessment of beliefs is said to constrict A if the bounds on the probability of A after the procedure are contained in those before the procedure. It is well documented that (generalized) Bayes’ updating does not allow for constriction, for all A∈F . In this work, we show that constriction can take place with and without evidence being observed, and we characterize these possibilities.

Original language	English
Title of host publication	Proceedings of Machine Learning Research, ISIPTA 2023
Pages	84-95
Number of pages	12
Publication status	Published - 28 Jul 2023

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Constriction_ISIPTA

https://proceedings.mlr.press/v215/caprio23b.html#:~:text=A%20procedure%20generating%20a%20new,in%20those%20before%20the%20procedure.

MCAIF: Centre for AI Fundamentals
Kaski, S. (PI), Alvarez, M. (Researcher), Pan, W. (Researcher), Mu, T. (Researcher), Rivasplata, O. (PI), Sun, M. (PI), Mukherjee, A. (PI), Caprio, M. (PI), Sonee, A. (Researcher), Leroy, A. (Researcher), Wang, J. (Researcher), Lee, J. (Researcher), Parakkal Unni, M. (Researcher), Sloman, S. (Researcher), Menary, S. (Researcher), Quilter, T. (Researcher), Hosseinzadeh, A. (PGR student), Mousa, A. (PGR student), Glover, E. (PGR student), Das, A. (PGR student), DURSUN, F. (PGR student), Zhu, H. (PGR student), Abdi, H. (PGR student), Dandago, K. (PGR student), Piriyajitakonkij, M. (PGR student), Rachman, R. (PGR student), Shi, X. (PGR student), Keany, T. (PGR student), Liu, X. (PGR student), Jiang, Y. (PGR student), Wan, Z. (PGR student), Harrison, M. (Support team), Hartford, J. (PI), Kangin, D. (Researcher), Harikumar, H. (PI), Dubey, M. (PI), Parakkal Unni, M. (PI), Dash, S. P. (PGR student), Mi, X. (PGR student), Barlas, Y. (PGR student), Osho, T. (Support team) & Tariq, M. (Support team)
1/10/21 → 30/09/26
Project: Research

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@inproceedings{03e11cae64ba483d81944ee88c310374,

title = "Constriction for sets of probabilities",

abstract = "Given a set of probability measures P representing an agent{\textquoteright}s knowledge on the elements of a sigma-algebra F , we can compute upper and lower bounds for the probability of any event A∈F of interest. A procedure generating a new assessment of beliefs is said to constrict A if the bounds on the probability of A after the procedure are contained in those before the procedure. It is well documented that (generalized) Bayes{\textquoteright} updating does not allow for constriction, for all A∈F . In this work, we show that constriction can take place with and without evidence being observed, and we characterize these possibilities.",

author = "Michele Caprio and Teddy Seidenfeld",

year = "2023",

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language = "English",

pages = "84--95",

booktitle = "Proceedings of Machine Learning Research, ISIPTA 2023",

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AU - Seidenfeld, Teddy

PY - 2023/7/28

Y1 - 2023/7/28

N2 - Given a set of probability measures P representing an agent’s knowledge on the elements of a sigma-algebra F , we can compute upper and lower bounds for the probability of any event A∈F of interest. A procedure generating a new assessment of beliefs is said to constrict A if the bounds on the probability of A after the procedure are contained in those before the procedure. It is well documented that (generalized) Bayes’ updating does not allow for constriction, for all A∈F . In this work, we show that constriction can take place with and without evidence being observed, and we characterize these possibilities.

AB - Given a set of probability measures P representing an agent’s knowledge on the elements of a sigma-algebra F , we can compute upper and lower bounds for the probability of any event A∈F of interest. A procedure generating a new assessment of beliefs is said to constrict A if the bounds on the probability of A after the procedure are contained in those before the procedure. It is well documented that (generalized) Bayes’ updating does not allow for constriction, for all A∈F . In this work, we show that constriction can take place with and without evidence being observed, and we characterize these possibilities.

M3 - Conference contribution

SP - 84

EP - 95

BT - Proceedings of Machine Learning Research, ISIPTA 2023

ER -

Constriction for sets of probabilities

Abstract

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MCAIF: Centre for AI Fundamentals

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