A Theory of Uncertainty Variables for State Estimation and Inference
Name
1909.10673.pdf
Description
Accepted version
Size
595.5 KB
Format
Adobe PDF
Checksum (MD5)
5a40c33f9eeb9c1a5a51a199360b4bba
Author(s)
Talak, Rajat
Karaman, Sertac
Modiano, Eytan
Date Issued
September 2019
Journal
2019 57th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2019
Publisher
IEEE
Citation
Talak, Rajat, Karaman, Sertac and Modiano, Eytan. 2019. "A Theory of Uncertainty Variables for State Estimation and Inference." 2019 57th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2019.
Version
Author's final manuscript
Abstract
© 2019 IEEE. Probability theory forms an overarching framework for modeling uncertainty, and by extension, also in designing state estimation and inference algorithms. While it provides a good foundation to system modeling, analysis, and an understanding of the real world, its application to algorithm design suffers from computational intractability. In this work, we develop a new framework of uncertainty variables to model uncertainty. A simple uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set map, from a given realization of a variable to a set of possible realizations of another variable. We prove Bayes' law and the law of total probability equivalents for uncertainty variables. We define a notion of independence, conditional independence, and pairwise independence for a collection of uncertainty variables, and show that this new notion of independence preserves the properties of independence defined over random variables. We then develop a graphical model, namely Bayesian uncertainty network, a Bayesian network equivalent defined over a collection of uncertainty variables, and show that all the natural conditional independence properties, expected out of a Bayesian network, hold for the Bayesian uncertainty network. We also define the notion of point estimate, and show its relation with the maximum a posteriori estimate.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/allerton.2019.8919919
