A generalized iterative scaling algorithm for maximum entropy reasoning in relational probabilistic conditional logic under aggregation semantics
Recently, different semantics for relational probabilistic con- ditionals and corresponding maximum entropy (ME) inference operators have been proposed. In this paper, we study the so-called aggregation semantics that covers both notions of a statistical and subjective view. The computation of its inference operator requires the calculation of the ME-distribution satisfying all probabilistic conditionals. Since each conditional induces a linear constraint on the probability distribution, the optimization problem to solve is the calculation of the probability distribution with maximum entropy under linear constraints. We demon- strate how the well-known Generalized Iterative Scaling (GIS) algorithm technique can be applied to this optimization problem to calculate the maximum entropy distribution in an iterative way. We show how the linear constrains are transformed into normalized feature functions to meet the requirements of GIS and present a practical algorithm which is tailor-made for the computation of the ME-inference operator based on aggregation semantics. We also present a practical implementation of the developed algorithm.
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