In view of the paradigm shift that makes science ever more data-driven, we consider deterministic scientific hypotheses as uncertain data. This vision comprises a probabilistic database (p-DB) design methodology for the systematic construction and management of U-relational hypothesis DBs, viz., @math -DBs. It introduces hypothesis management as a promising new class of applications for p-DBs. We illustrate the potential of @math -DB as a tool for deep predictive analytics.
Also related to the @math -DB vision is the topic of conditioning a p-DB. It has been firstly addressed by Koch and Olteanu motivated by data cleaning applications @cite_1 . They have introduced the assert operation to implement, as in AI, a kind of knowledge compilation, viz., world elimination in face of constraints (e.g., FDs). For hypothesis management, nonetheless, we need to apply by asserting observed data (not constraints). In @math , we present an example that settles the kind of conditioning problem that is relevant to @math -DB . In order to provide a concrete feel of our vision, in the next sections we present preliminary results on our methodology for constructing an @math -DB on top of MayBMS .
@cite_1
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In this paper, we study the dominance relation under a stochastic setting. Let @math be a set of @math colored stochastic points in @math , each of which is associated with an existence probability. We investigate the problem of computing the probability that a realization of @math contains inter-color dominances, which we call the (CSD) problem. We propose the first algorithm to solve the CSD problem for @math in @math time. On the other hand, we prove that, for @math , even the CSD problem with a restricted color pattern is #P-hard. In addition, even if the existence probabilities are restricted to be @math , the problem remains #P-hard for @math . A simple FPRAS is then provided to approximate the desired probability in any dimension. We also study a variant of the CSD problem in which the dominance relation is considered with respect to not only the standard basis but any orthogonal basis of @math . Specifically, this variant, which we call the free-basis colored stochastic dominance (FBCSD) problem, considers the probability that a realization of @math contains inter-color dominances with respect to any orthogonal basis of @math . We show that the CSD problem is polynomial-time reducible to the FBCSD problem in the same dimension, which proves the #P-hardness of the latter for @math . Conversely, we reduce the FBCSD problem in @math to the CSD problem in @math , by which an @math time algorithm for the former is obtained.