A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number of factors in factor analysis. In this tutorial we describe Bayesian nonparametric methods, a class of methods that side-steps this issue by allowing the data to determine the complexity of the model. This tutorial is a high-level introduction to Bayesian nonparametric methods and contains several examples of their application.

In order to address complex systems, apply pattern recongnition on their evolution could play an key role to understand their dynamics. Global patterns are required to detect emergent concepts and trends, some of them with qualitative nature. Formal Concept Analysis (FCA) is a theory whose goal is to discover and to extract Knowledge from qualitative data. It provides tools for reasoning with implication basis (and association rules). Implications and association rules are usefull to reasoning on previously selected attributes, providing a formal foundation for logical reasoning. In this paper we analyse how to apply FCA reasoning to increase confidence in sports betting, by means of detecting temporal regularities from data. It is applied to build a Knowledge-Based system for confidence reasoning.

In this paper, a methodology for the automated detection and classification of Tuberculosis(TB) is presented. Tuberculosis is a disease caused by mycobacterium which spreads through the air and attacks low immune bodies easily. Our methodology is based on clustering and classification that classifies TB into two categories, Pulmonary Tuberculosis(PTB) and retroviral PTB(RPTB) that is those with Human Immunodeficiency Virus (HIV) infection. Initially K-means clustering is used to group the TB data into two clusters and assigns classes to clusters. Subsequently multiple different classification algorithms are trained on the result set to build the final classifier model based on K-fold cross validation method. This methodology is evaluated using 700 raw TB data obtained from a city hospital. The best obtained accuracy was 98.7% from support vector machine (SVM) compared to other classifiers. The proposed approach helps doctors in their diagnosis decisions and also in their treatment planning procedures for different categories.

We consider the general problem of finding the minimum weight $\bm$-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP) algorithm converges to the correct solution. We also show that when the LP relaxation has a fractional solution then the BP algorithm can be used to solve the LP relaxation. Our proof is based on the notion of graph covers and extends the analysis of (Bayati-Shah-Sharma 2005 and Huang-Jebara 2007}. These results are notable in the following regards: (1) It is one of a very small number of proofs showing correctness of BP without any constraint on the graph structure. (2) Variants of the proof work for both synchronous and asynchronous BP; it is the first proof of convergence and correctness of an asynchronous BP algorithm for a combinatorial optimization problem.

Minwise hashing is the standard technique in the context of search and databases for efficiently estimating set (e.g., high-dimensional 0/1 vector) similarities. Recently, b-bit minwise hashing was proposed which significantly improves upon the original minwise hashing in practice by storing only the lowest b bits of each hashed value, as opposed to using 64 bits. b-bit hashing is particularly effective in applications which mainly concern sets of high similarities (e.g., the resemblance >0.5). However, there are other important applications in which not just pairs of high similarities matter. For example, many learning algorithms require all pairwise similarities and it is expected that only a small fraction of the pairs are similar. Furthermore, many applications care more about containment (e.g., how much one object is contained by another object) than the resemblance. In this paper, we show that the estimators for minwise hashing and b-bit minwise hashing used in the current practice can be systematically improved and the improvements are most significant for set pairs of low resemblance and high containment.

We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation crucially depends on a set of points, called knots, at which the original process is retained, while the rest is approximated via a deterministic extrapolation. Knots should be few in number to keep the computational complexity low, but provide a good coverage of the process domain to limit approximation error. We present theoretical calculations to show that coverage must be judged by the canonical metric of the Gaussian process. This necessitates having in place a knots selection algorithm that automatically adapts to the changes in the canonical metric affected by changes in the parameter values controlling the Gaussian process covariance function. We present an algorithm toward this by employing an incomplete Cholesky factorization with pivoting and dynamic stopping. Although these concepts already exist in the literature, our contribution lies in unifying them into a fast algorithm and in using computable error bounds to finesse implementation of the predictive process approximation. The resulting adaptive predictive process offers a substantial automatization of Guassian process model fitting, especially for Bayesian applications where thousands of values of the covariance parameters are to be explored.

In many data mining applications collection of sufficiently large datasets is the most time consuming and expensive. On the other hand, industrial methods of data collection create huge databases, and make difficult direct applications of the advanced machine learning algorithms. To address the above problems, we consider active learning (AL), which may be very efficient either for the experimental design or for the data filtering. In this paper we demonstrate using the online evaluation opportunity provided by the AL Challenge that quite competitive results may be produced using a small percentage of the available data. Also, we present several alternative criteria, which may be useful for the evaluation of the active learning processes. The author of this paper attended special presentation in Barcelona, where results of the WCCI 2010 AL Challenge were discussed.

OWL 2 has been standardized by the World Wide Web Consortium (W3C) as a family of ontology languages for the Semantic Web. The most expressive of these languages is OWL 2 Full, but to date no reasoner has been implemented for this language. Consistency and entailment checking are known to be undecidable for OWL 2 Full. We have translated a large fragment of the OWL 2 Full semantics into first-order logic, and used automated theorem proving systems to do reasoning based on this theory. The results are promising, and indicate that this approach can be applied in practice for effective OWL reasoning, beyond the capabilities of current Semantic Web reasoners. This is an extended version of a paper with the same title that has been published at CADE 2011, LNAI 6803, pp. 446-460. The extended version provides appendices with additional resources that were used in the reported evaluation.

Local search algorithms applied to optimization problems often suffer from getting trapped in a local optimum. The common solution for this deficiency is to restart the algorithm when no progress is observed. Alternatively, one can start multiple instances of a local search algorithm, and allocate computational resources (in particular, processing time) to the instances depending on their behavior. Hence, a multi-start strategy has to decide (dynamically) when to allocate additional resources to a particular instance and when to start new instances. In this paper we propose multi-start strategies motivated by works on multi-armed bandit problems and Lipschitz optimization with an unknown constant. The strategies continuously estimate the potential performance of each algorithm instance by supposing a convergence rate of the local search algorithm up to an unknown constant, and in every phase allocate resources to those instances that could converge to the optimum for a particular range of the constant. Asymptotic bounds are given on the performance of the strategies. In particular, we prove that at most a quadratic increase in the number of times the target function is evaluated is needed to achieve the performance of a local search algorithm started from the attraction region of the optimum. Experiments are provided using SPSA (Simultaneous Perturbation Stochastic Approximation) and k-means as local search algorithms, and the results indicate that the proposed strategies work well in practice, and, in all cases studied, need only logarithmically more evaluations of the target function as opposed to the theoretically suggested quadratic increase.

We extend the potential-based shaping method from Markov decision processes to multi-player general-sum stochastic games. We prove that the Nash equilibria in a stochastic game remains unchanged after potential-based shaping is applied to the environment. The property of policy invariance provides a possible way of speeding convergence when learning to play a stochastic game.