Background: There is much interest in developing fast and accurate supertree methods to infer the tree of life. Supertree methods combine smaller input trees with overlapping sets of taxa to make a comprehensive phylogenetic tree that contains all of the taxa in the input trees. The intrinsically hard triplet supertree problem takes a collection of input species trees and seeks a species tree (supertree) that maximizes the number of triplet subtrees that it shares with the input trees. However, the utility of this supertree problem has been limited by a lack of efficient and effective heuristics.

BackgroundTo infer a species phylogeny from unlinked genes, phylogenetic inference methods must confront the biological processes that create incongruence between gene trees and the species phylogeny. Intra-specific gene variation in ancestral species can result in deep coalescence, also known as incomplete lineage sorting, which creates incongruence between gene trees and the species tree. One approach to account for deep coalescence in phylogenetic analyses is the deep coalescence problem, which takes a collection of gene trees and seeks the species tree that implies the fewest deep coalescence events. Although this approach is promising for phylogenetics, the consensus properties of this problem are mostly unknown and analyses of large data sets may be computationally prohibitive.ResultsWe prove that the deep coalescence consensus tree problem satisfies the highly desirable Pareto property for clusters (clades). That is, in all instances, each cluster that is present in all of the input gene trees, called a consensus cluster, will also be found in every optimal solution. Moreover, we introduce a new divide and conquer method for the deep coalescence problem based on the Pareto property. This method refines the strict consensus of the input gene trees, thereby, in practice, often greatly reducing the complexity of the tree search and guaranteeing that the estimated species tree will satisfy the Pareto property.ConclusionsAnalyses of both simulated and empirical data sets demonstrate that the divide and conquer method can greatly improve upon the speed of heuristics that do not consider the Pareto consensus property, while also guaranteeing that the proposed solution fulfills the Pareto property. The divide and conquer method extends the utility of the deep coalescence problem to data sets with enormous numbers of taxa.

Abstract. The increasing availability of large RDF datasets offers an exciting opportunity to use such data to build predictive models using machine learning algorithms. However, the massive size and distributed nature of RDF data calls for approaches to learning from RDF data in a setting where the data can be accessed only through a query interface, e.g., the SPARQL endpoint of the RDF store. In applications where the data are subject to frequent updates, there is a need for algorithms that allow the predictive model to be incrementally updated in response to changes in the data. Furthermore, in some applications, the attributes that are relevant for specific prediction tasks are not known a priori and hence need to be discovered by the algorithm. We present an approach to learning Relational Bayesian Classifiers (RBCs) from RDF data that addresses such scenarios. Specifically, we show how to build RBCs from RDF data using statistical queries through the SPARQL endpoint of the RDF store. We compare the communication complexity of our algorithm with one that requires direct centralized access to the data and hence has to retrieve the entire RDF dataset from the remote location for processing. We establish the conditions under which the RBC models can be incrementally updated in response to addition or deletion of RDF data. We show how our approach can be extended to the setting where the attributes that are relevant for prediction are not known a priori, by selectively crawling the RDF data for attributes of interest. We provide open source implementation and evaluate the proposed approach on several large RDF datasets.

Abstract-The emergence of many interlinked, physically distributed, and autonomously maintained RDF stores offers unprecedented opportunities for predictive modeling and knowledge discovery from such data. However existing machine learning approaches are limited in their applicability because it is neither desirable nor feasible to gather all of the data in a centralized location for analysis due to access, memory, bandwidth, computational restrictions, and sometimes privacy and confidentiality constraints. Against this background, we consider the problem of learning predictive models from multiple interlinked RDF stores. Specifically we: (i) introduce statistical query based formulations of several representative algorithms for learning classifiers from RDF data; (ii) introduce a distributed learning framework to learn classifiers from multiple interlinked RDF stores that form a chain; (iii) identify three special cases of RDF data fragmentation and describe effective strategies for learning predictive models in each case; (iv) consider a novel application of a matrix reconstruction technique from the field of Computerized Tomography [1] to approximate the statistics needed by the learning algorithm from projections using count queries, thus dramatically reducing the amount of information transmitted from the remote data sources to the learner; and (v) report results of experiments with a real-world social network data set (Last.fm), which demonstrate the feasibility of the proposed approach.

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