We investigate the detectability of modules in large networks when the number of modules is not known in advance. We employ the minimum description length (MDL) principle which seeks to minimize the total amount of information required to describe the network, and avoid overfitting. According to this criterion, we obtain general bounds on the detectability of any prescribed block structure, given the number of nodes and edges in the sampled network. We also obtain that the maximum number of detectable blocks scales as $\sqrt{N}$, where $N$ is the number of nodes in the network, for a fixed average degree $$. We also show that the simplicity of the MDL approach yields an efficient multilevel Monte Carlo inference algorithm with a complexity of $O(\tau N\log N)$, if the number of blocks is unknown, and $O(\tau N)$ if it is known, where $\tau$ is the mixing time of the Markov chain. We illustrate the application of the method on a large network of actors and films with over $10^6$ edges, and a dissortative, bipartite block structure.

CLUSTERCLUSTER: PARALLEL MARKOV CHAIN MONTE CARLO FOR DIRICHLET PROCESS MIXTURES By Dan Lovell, Jonathan Malmaud, Ryan P. Adams and Vikash K. Mansinghka Massachusetts Institute of Technology and Harvard University The Dirichlet process (DP) is a fundamental mathematical tool for Bayesian nonparametric modeling, and is widely used in tasks such as density estimation, natural language processing, and time series modeling. Although MCMC inference methods for the DP often provide a gold standard in terms asymptotic accuracy, they can be computationally expensive and are not obviously parallelizable. We propose a reparameterization of the Dirichlet process that induces conditional independencies between the atoms that form the random measure. This conditional independence enables many of the Markov chain transition operators for DP inference to be simulated in parallel across multiple cores. Applied to mixture modeling, our approach enables the Dirichlet process to simultaneously learn clusters that describe the data and superclusters that define the granularity of parallelization. Unlike previous approaches, our technique does not require alteration of the model and leaves the true posterior distribution invariant. It also naturally lends itself to a distributed software implementation in terms of Map-Reduce, which we test in cluster configurations of over 50 machines and 100 cores.

Approaches for testing sets of variants, such as a set of rare or common variants within a gene or pathway, for association with complex traits are important. In particular, set tests allow for aggregation of weak signal within a set, can capture interplay among variants, and reduce the burden of multiple hypothesis testing. Until now, these approaches did not address confounding by family relatedness and population structure, a problem that is becoming more important as larger data sets are used to increase power. Results: We introduce a new approach for set tests that handles confounders. Our model is based on the linear mixed model and uses two random effects-one to capture the set association signal and one to capture confounders. We also introduce a computational speedup for two-random-effects models that makes this approach feasible even for extremely large cohorts. Using this model with both the likelihood ratio test and score test, we find that the former yields more power while controlling type I error. Application of our approach to richly structured GAW14 data demonstrates that our method successfully corrects for population structure and family relatedness, while application of our method to a 15,000 individual Crohn's disease case-control cohort demonstrates that it additionally recovers genes not recoverable by univariate analysis. Availability: A Python-based library implementing our approach is available at http://mscompbio.codeplex.com

Rewriting-based approaches for answering queries over an OWL 2 DL ontology have so far been developed mainly for Horn fragments of OWL 2 DL. In this paper, we study the possibilities of answering queries over non-Horn ontologies using datalog rewritings. We prove that this is impossible in general even for very simple ontology languages, and even if PTIME = NP. Furthermore, we present a resolution-based procedure for $\SHI$ ontologies that, in case it terminates, produces a datalog rewriting of the ontology. Our procedure necessarily terminates on DL-Lite_{bool}^H ontologies---an extension of OWL 2 QL with transitive roles and Boolean connectives.

Automatically classifying the tissues types of Region of Interest (ROI) in medical imaging has been an important application in Computer-Aided Diagnosis (CAD), such as classification of breast parenchymal tissue in the mammogram, classify lung disease patterns in High-Resolution Computed Tomography (HRCT) etc. Recently, bag-of-features method has shown its power in this field, treating each ROI as a set of local features. In this paper, we investigate using the bag-of-features strategy to classify the tissue types in medical imaging applications. Two important issues are considered here: the visual vocabulary learning and weighting. Although there are already plenty of algorithms to deal with them, all of them treat them independently, namely, the vocabulary learned first and then the histogram weighted. Inspired by Auto-Context who learns the features and classifier jointly, we try to develop a novel algorithm that learns the vocabulary and weights jointly. The new algorithm, called Joint-ViVo, works in an iterative way. In each iteration, we first learn the weights for each visual word by maximizing the margin of ROI triplets, and then select the most discriminate visual words based on the learned weights for the next iteration. We test our algorithm on three tissue classification tasks: identifying brain tissue type in magnetic resonance imaging (MRI), classifying lung tissue in HRCT images, and classifying breast tissue density in mammograms. The results show that Joint-ViVo can perform effectively for classifying tissues.

Probability answer set programming is a declarative programming that has been shown effective for representing and reasoning about a variety of probability reasoning tasks. However, the lack of probability aggregates, e.g. {\em expected values}, in the language of disjunctive hybrid probability logic programs (DHPP) disallows the natural and concise representation of many interesting problems. In this paper, we extend DHPP to allow arbitrary probability aggregates. We introduce two types of probability aggregates; a type that computes the expected value of a classical aggregate, e.g., the expected value of the minimum, and a type that computes the probability of a classical aggregate, e.g, the probability of sum of values. In addition, we define a probability answer set semantics for DHPP with arbitrary probability aggregates including monotone, antimonotone, and nonmonotone probability aggregates. We show that the proposed probability answer set semantics of DHPP subsumes both the original probability answer set semantics of DHPP and the classical answer set semantics of classical disjunctive logic programs with classical aggregates, and consequently subsumes the classical answer set semantics of the original disjunctive logic programs. We show that the proposed probability answer sets of DHPP with probability aggregates are minimal probability models and hence incomparable, which is an important property for nonmonotonic probability reasoning.

Pattern-Based Constraint Satisfaction and Logic Puzzles develops a pure logic, pattern-based perspective of solving the finite Constraint Satisfaction Problem (CSP), with emphasis on finding the "simplest" solution. Different ways of reasoning with the constraints are formalised by various families of "resolution rules", each of them carrying its own notion of simplicity. A large part of the book illustrates the power of the approach by applying it to various popular logic puzzles. It provides a unified view of how to model and solve them, even though they involve very different types of constraints: obvious symmetric ones in Sudoku, non-symmetric but transitive ones (inequalities) in Futoshiki, topological and geometric ones in Map colouring, Numbrix and Hidato, and even much more complex non-binary arithmetic ones in Kakuro (or Cross Sums). It also shows that the most familiar techniques for these puzzles can indeed be understood as mere application-specific presentations of the general rules. Sudoku is used as the main example throughout the book, making it also an advanced level sequel to "The Hidden Logic of Sudoku" (another book by the same author), with: many examples of relationships among different rules and of exceptional situations; comparisons of the resolution potential of various families of rules; detailed statistics of puzzles hardness; analysis of extreme instances.

We present a unified logical framework for representing and reasoning about both probability quantitative and qualitative preferences in probability answer set programming [Saad and Pontelli, 2006; Saad, 2006; Saad, 2007a], called probability answer set optimization programs. The proposed framework is vital to allow defining probability quantitative preferences over the possible outcomes of qualitative preferences. We show the application of probability answer set optimization programs to a variant of the well-known nurse restoring problem [Bard and Purnomo, 2005], called the nurse restoring with probability preferences problem. To the best of our knowledge, this development is the first to consider a logical framework for reasoning about probability quantitative preferences, in general, and reasoning about both probability quantitative and qualitative preferences in particular.

We allow representing and reasoning in the presence of nested multiple aggregates over multiple variables and nested multiple aggregates over functions involving multiple variables in answer sets, precisely, in answer set optimization programming and in answer set programming. We show the applicability of the answer set optimization programming with nested multiple aggregates and the answer set programming with nested multiple aggregates to the Probabilistic Traveling Salesman Problem, a fundamental a priori optimization problem in Operation Research.

We present a unified logical framework for representing and reasoning about both quantitative and qualitative preferences in fuzzy answer set programming [Saad, 2010; Saad, 2009; Subrahmanian, 1994], called fuzzy answer set optimization programs. The proposed framework is vital to allow defining quantitative preferences over the possible outcomes of qualitative preferences. We show the application of fuzzy answer set optimization programs to the course scheduling with fuzzy preferences problem described in [Saad, 2010]. To the best of our knowledge, this development is the first to consider a logical framework for reasoning about quantitative preferences, in general, and reasoning about both quantitative and qualitative preferences in particular.