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Recent work on weighted model counting has been very successfully applie...
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Oblivious Bounds on the Probability of Boolean Functions
This paper develops upper and lower bounds for the probability of Boolea...
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The Tractability of SHAPscores over Deterministic and Decomposable Boolean Circuits
Scores based on Shapley values are currently widely used for providing e...
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Sufficiency, Separability and Temporal Probabilistic Models
Suppose we are given the conditional probability of one variable given s...
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Dynamic programming in in uence diagrams with decision circuits
Decision circuits perform efficient evaluation of influence diagrams, bu...
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Generalizing Fuzzy Logic Probabilistic Inferences
Linear representations for a subclass of boolean symmetric functions sel...
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CaseFactor Diagrams for Structured Probabilistic Modeling
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Tractable Inference in Credal Sentential Decision Diagrams
Probabilistic sentential decision diagrams are logic circuits where the inputs of disjunctive gates are annotated by probability values. They allow for a compact representation of joint probability mass functions defined over sets of Boolean variables, that are also consistent with the logical constraints defined by the circuit. The probabilities in such a model are usually learned from a set of observations. This leads to overconfident and priordependent inferences when data are scarce, unreliable or conflicting. In this work, we develop the credal sentential decision diagrams, a generalisation of their probabilistic counterpart that allows for replacing the local probabilities with (socalled credal) sets of mass functions. These models induce a joint credal set over the set of Boolean variables, that sharply assigns probability zero to states inconsistent with the logical constraints. Three inference algorithms are derived for these models, these allow to compute: (i) the lower and upper probabilities of an observation for an arbitrary number of variables; (ii) the lower and upper conditional probabilities for the state of a single variable given an observation; (iii) whether or not all the probabilistic sentential decision diagrams compatible with the credal specification have the same most probable explanation of a given set of variables given an observation of the other variables. These inferences are tractable, as all the three algorithms, based on bottomup traversal with local linear programming tasks on the disjunctive gates, can be solved in polynomial time with respect to the circuit size. For a first empirical validation, we consider a simple application based on noisy sevensegment display images. The credal models are observed to properly distinguish between easy and hardtodetect instances and outperform other generative models not able to cope with logical constraints.
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