Abstracting Probabilistic Models: A Logical Perspective.

Research output: Contribution to conferencePaperpeer-review

Abstract

Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic systems, the case for abstracting probabilistic models is not yet fully understood.

In this paper, we provide a semantical framework for analyzing such abstractions from first principles. We develop the framework in a general way, allowing for expressive languages, including logic-based ones that admit relational and hierarchical constructs with stochastic primitives. We motivate a definition of consistency between a high-level model and its low-level counterpart, but also treat the case when the high-level model is missing critical information present in the low-level model. We go on to prove prove properties of abstractions, both at the level of the parameter as well as the structure of the models. We conclude with some observations about how abstractions can be derived automatically.
Original languageEnglish
Number of pages24
Publication statusPublished - 7 Feb 2020
EventNinth International Workshop on Statistical Relational AI - New York, United States
Duration: 7 Feb 20207 Feb 2020
Conference number: 9
http://www.starai.org/2020/

Workshop

WorkshopNinth International Workshop on Statistical Relational AI
Abbreviated titleStarAI 2020
CountryUnited States
CityNew York
Period7/02/207/02/20
Internet address

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