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Register a new userReasoning about Independence in Probabilistic Models of Relational Data
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Marc Maier
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data inaccurately infers conditional independence. We introduce relational d-separation, a theory for deriving conditional independence facts from relational models. We provide a new representation, the abstract ground graph, that enables a sound, complete, and computationally efficient method for answering d-separation queries about relational models, and we present empirical results that demonstrate effectiveness.
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The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for deriving conditional independence in relational models. We provide a sound, complete, and computationally efficient method for relational d-separation, and we present empirical results that demonstrate effectiveness.
Functional dependencies restrict the potential interactions among variables connected in a probabilistic network. This restriction can be exploited in qualitative probabilistic reasoning by introducing deterministic variables and modifying the inference rules to produce stronger conclusions in the presence of functional relations. I describe how to accomplish these modifications in qualitative probabilistic networks by exhibiting the update procedures for graphical transformations involving probabilistic and deterministic variables and combinations. A simple example demonstrates that the augmented scheme can reduce qualitative ambiguity that would arise without the special treatment of functional dependency. Analysis of qualitative synergy reveals that new higher-order relations are required to reason effectively about synergistic interactions among deterministic variables.
As a contribution to the challenge of building game-playing AI systems, we develop and analyse a formal language for representing and reasoning about strategies. Our logical language builds on the existing general Game Description Language (GDL) and extends it by a standard modality for linear time along with two dual connectives to express preferences when combining strategies. The semantics of the language is provided by a standard state-transition model. As such, problems that require reasoning about games can be solved by the standard methods for reasoning about actions and change. We also endow the language with a specific semantics by which strategy formulas are understood as move recommendations for a player. To illustrate how our formalism supports automated reasoning about strategies, we demonstrate two example methods of implementation/: first, we formalise the semantic interpretation of our language in conjunction with game rules and strategy rules in the Situation Calculus; second, we show how the reasoning problem can be solved with Answer Set Programming.
We propose a new deep learning model for goal-driven tasks that require intuitive physical reasoning and intervention in the scene to achieve a desired end goal. Its modular structure is motivated by hypothesizing a sequence of intuitive steps that humans apply when trying to solve such a task. The model first predicts the path the target object would follow without intervention and the path the target object should follow in order to solve the task. Next, it predicts the desired path of the action object and generates the placement of the action object. All components of the model are trained jointly in a supervised way; each component receives its own learning signal but learning signals are also backpropagated through the entire architecture. To evaluate the model we use PHYRE - a benchmark test for goal-driven physical reasoning in 2D mechanics puzzles.
In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) v D, whose intuitive meaning is that normally/typically Cs are also Ds. This extension is based on a minimal model semantics corresponding to a notion of rational closure, built upon preferential models. We recall the basic concepts underlying preferential Description Logics. We also present two extensions of the preferential semantics: on the one hand, we consider probabilistic extensions, based on a distributed semantics that is suitable for tackling the problem of commonsense concept combination, on the other hand, we consider other strengthening of the rational closure semantics and construction to avoid the so-called blocking of property inheritance problem.
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