Weighted model integration (WMI) is a recent formalism generalizing weighted model counting (WMC) to run probabilistic inference over hybrid domains, characterized by both discrete and continuous variables and relationships between them. Albeit powerful, the original formulation of WMI suffers from some theoretical limitations, and it is computationally very demanding as it requires to explicitly enumerate all possible models to be integrated over. In this paper we present a novel general notion of WMI, which fixes the theoretical limitations and allows for exploiting the power of SMTbased predicate abstraction techniques. A novel algorithm combines a strong reduction in the number of models to be integrated over with their efficient enumeration. Experimental results on synthetic and real-world data show drastic computational improvements over the original WMI formulation as well as existing alternatives for hybrid inference.

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Our group has recently developed gene@home, a BOINC project that permits to search for candidate genes for the expansion of a gene regulatory network using gene expression data. The gene@home project adopts intensive variablesubsetting strategies enabled by the computational power provided by the volunteers who have joined the project by means of the BOINC client, and exploits the PC algorithm for discovering putative causal relationships within each subset of variables. This paper presents our TN-Grid infrastructure that is hosting the gene@home project. Gene@home implements a novel method for Network Expansion by Subsetting and Ranking Aggregation (NESRA), producing a list of genes that are candidates for the gene network expansion task. NESRA is an algorithm that has: 1) a ranking procedure that systematically subsets the variables; the subsetting is iterated several times and a ranked list of candidates is produced by counting the number of times a relationship is found; 2) several ranking steps are executed with different values of the dimension of the subsets and with different number of iterations producing several ranked lists; 3) the ranked lists are aggregated by using a state-of-the-art ranking aggregator. In our experimental results, we show that a single ranking step is enough to outperform both PC and PC*. Evaluations and experiments are done by means of the gene@home project on a real gene regulatory network of the model plant Arabidopsis thaliana.

Weighted Model Integration (WMI) is a popular technique for probabilistic inference that extends Weighted Model Counting (WMC) -- the standard inference technique for inference in discrete domains -- to domains with both discrete and continuous variables.  However, existing WMI solvers each have different interfaces and use different formats for representing WMI problems.  Therefore, we introduce pywmi (http://pywmi.org), an open source framework and toolbox for probabilistic inference using WMI, to address these shortcomings.  Crucially, pywmi fixes a common internal format for WMI problems and introduces a common interface for WMI solvers.  To assist users in modeling WMI problems, pywmi introduces modeling languages based on SMT-LIB.v2 or MiniZinc and parsers for both.  To assist users in comparing WMI solvers, pywmi includes implementations of several state-of-the-art solvers, a fast approximate WMI solver, and a command-line interface to solve WMI problems.  Finally, to assist developers in implementing new solvers, pywmi provides Python implementations of commonly used subroutines.

Gene network expansion is a task of the foremost importance in computational biology. Gene network expansion aims at finding new genes to expand a given known gene network. To this end, we developed gene@home, a BOINC-based project that finds candidate genes that expand known local gene networks using NESRA. In this paper, we present NES 2 RA, a novel approach that extends and improves NESRA by modeling, using a probability vector, the confidence of the presence of the genes belonging to the local gene network. NES 2 RA adopts intensive variable-subsetting strategies, enabled by the computational power provided by gene@home volunteers. In particular, we use the skeleton procedure of the PC-algorithm to discover candidate causal relationships within each subset of variables. Finally, we use state-ofthe-art aggregators to combine the results into a single ranked candidate genes list. The resulting ranking guides the discovery of unknown relations between genes and a priori known local gene networks. Our experimental results show that NES 2 RA outperforms the PC-algorithm and its order-independent PC-stable version, ARACNE, and our previous approach, NESRA. In this paper we extensively discuss the computational aspects of the NES 2 RA approach and we also present and validate expansions performed on the model plant Arabidopsis thaliana and the model bacteria Escherichia coli.