Anytime Inference in Valuation Algebras

Abstract: Anytime inference is inference performed incrementally, with the accuracy of the inference being controlled by a tunable parameter, usually time. Such anytime inference algorithms are also usually interruptible, gradually converging to the exact inference value until terminated. While anytime inference algorithms for specific domains like probability potentials exist in the literature, our objective in this article is to obtain an anytime inference algorithm which is sufficiently generic to cover a wide range of domains. For this we utilise the theory of generic inference as a basis for constructing an anytime inference algorithm, and in particular, extending work done on ordered valuation algebras. The novel contribution of this work is the construction of anytime algorithms in a generic framework, which automatically gives us instantiations in various useful domains. We also show how to apply this generic framework for anytime inference in semiring induced valuation algebras, an important subclass of valuation algebras, which includes instances like probability potentials, disjunctive normal forms and distributive lattices. Keywords: Approximation; Anytime algorithms; Resource-bounded computation; Generic inference; Valuation algebras; Local computation; Binary join trees.