Open world Dempster-Shafer using complementary sets

Erik Skau, Cassandra Armstrong, Duc P. Truong, David Gerts, Kari Sentz
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:438-449, 2023.

Abstract

Dempster-Shafer Theory (DST) is a mathematical framework to handle imprecision and uncertainty in reasoning and decision making. One assumption of DST is that of a closed-world, or the assumption that all propositions are known a priori. In this work, we explore an alternative formulation of Dempster-Shafer that allows for the dynamic inclusion of new propositions. Specifically, we expand the framework to include the complement of every set of propositions. This adjustment enables an open-world interpretation that can support unspecified and dynamic propositions as we learn about the problem space. Including complementary sets distinguishes this from previous work in DST where the open world is attributed to the empty set. We demonstrate our open world Dempster-Shafer Theory on a variety of synthetic and real datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-skau23a, title = {Open world {D}empster-{S}hafer using complementary sets}, author = {Skau, Erik and Armstrong, Cassandra and Truong, Duc P. and Gerts, David and Sentz, Kari}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {438--449}, year = {2023}, editor = {Miranda, Enrique and Montes, Ignacio and Quaeghebeur, Erik and Vantaggi, Barbara}, volume = {215}, series = {Proceedings of Machine Learning Research}, month = {11--14 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v215/skau23a/skau23a.pdf}, url = {https://proceedings.mlr.press/v215/skau23a.html}, abstract = {Dempster-Shafer Theory (DST) is a mathematical framework to handle imprecision and uncertainty in reasoning and decision making. One assumption of DST is that of a closed-world, or the assumption that all propositions are known a priori. In this work, we explore an alternative formulation of Dempster-Shafer that allows for the dynamic inclusion of new propositions. Specifically, we expand the framework to include the complement of every set of propositions. This adjustment enables an open-world interpretation that can support unspecified and dynamic propositions as we learn about the problem space. Including complementary sets distinguishes this from previous work in DST where the open world is attributed to the empty set. We demonstrate our open world Dempster-Shafer Theory on a variety of synthetic and real datasets.} }
Endnote
%0 Conference Paper %T Open world Dempster-Shafer using complementary sets %A Erik Skau %A Cassandra Armstrong %A Duc P. Truong %A David Gerts %A Kari Sentz %B Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2023 %E Enrique Miranda %E Ignacio Montes %E Erik Quaeghebeur %E Barbara Vantaggi %F pmlr-v215-skau23a %I PMLR %P 438--449 %U https://proceedings.mlr.press/v215/skau23a.html %V 215 %X Dempster-Shafer Theory (DST) is a mathematical framework to handle imprecision and uncertainty in reasoning and decision making. One assumption of DST is that of a closed-world, or the assumption that all propositions are known a priori. In this work, we explore an alternative formulation of Dempster-Shafer that allows for the dynamic inclusion of new propositions. Specifically, we expand the framework to include the complement of every set of propositions. This adjustment enables an open-world interpretation that can support unspecified and dynamic propositions as we learn about the problem space. Including complementary sets distinguishes this from previous work in DST where the open world is attributed to the empty set. We demonstrate our open world Dempster-Shafer Theory on a variety of synthetic and real datasets.
APA
Skau, E., Armstrong, C., Truong, D.P., Gerts, D. & Sentz, K.. (2023). Open world Dempster-Shafer using complementary sets. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:438-449 Available from https://proceedings.mlr.press/v215/skau23a.html.

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