Open-Universe Probabilistic Models
A long-standing goal in AI has been to mimic the natural ability of human beings to infer things about sensory inputs and unforeseen data, usually involving a combination of logical and probabilistic reasoning. The last 10 years of research in statistical relational models have demonstrated how one can successfully borrow syntactic devices from first-order logic to define large graphical models over complex interacting random variables, classes, hierarchies, dependencies and constraints. Statistical relational models continue to be widely used for learning in large-scale knowledge bases, probabilistic configurations, natural language processing, question answering, probabilistic programming and automated planning.
While this progress has been significant, there are some fundamental limitations in the expressivity of these models. Statistical relational models make the finite domain assumption: given a clause such as “friends of smokers are smokers themselves”, the set of friends and those who smoke is assumed to be finite and known. It then makes it difficult to talk about unknown atoms and values (e.g., “All of John’s friends are worth more than a million”), categorical assumptions (e.g., “every animal eats”) and identity uncertainty (“James’ partner wore a red shawl”). Currently, approaches often simply ignore this issue, or deal with it in ad hoc ways.
In this work, we attempt to study this systematically. We begin with first-order probabilistic relational models. But now, we allow quantifiers to range over infinite sets, and although that makes matters undecidable in general, we show when limited to certain classes of statements, probabilistic reasoning becomes computable with attractive properties (e.g., satisfies the additive and equivalence axioms of probability in a first-order setting).
Parts of this work appeared at AAAI-17.
Vaishak Belle is a Chancellor’s Fellow at the School of Informatics, University of Edinburgh, UK. Vaishak’s research is in artificial intelligence, specifically on the theme of unifying logic and probability in different guises. Previously, he was at KU Leuven, the University of Toronto, and the Aachen University of Technology. He has co-authored several articles in AI-related venues, and won the Microsoft best paper award at UAI, the Machine learning journal best student paper award at ECML-PKDD, and the Kurt Goedel silver medal.
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12 May 2017 - Vaishak Belle: Seminar
Informatics Forum 4.31/4.33