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.

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.

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.

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.

Exploiting information induced from (query-specific) clustering of top-retrieved documents has long been proposed as a means for improving precision at the very top ranks of the returned results. We present a novel language model approach to ranking query-specific clusters by the presumed percentage of relevant documents that they contain. While most previous cluster ranking approaches focus on the cluster as a whole, our model utilizes also information induced from documents associated with the cluster. Our model substantially outperforms previous approaches for identifying clusters containing a high relevant-document percentage. Furthermore, using the model to produce document ranking yields precision-at-top-ranks performance that is consistently better than that of the initial ranking upon which clustering is performed. The performance also favorably compares with that of a state-of-the-art pseudo-feedback-based retrieval method.

ROC curves and cost curves are two popular ways of visualising classifier performance, finding appropriate thresholds according to the operating condition, and deriving useful aggregated measures such as the area under the ROC curve (AUC) or the area under the optimal cost curve. In this note we present some new findings and connections between ROC space and cost space, by using the expected loss over a range of operating conditions. In particular, we show that ROC curves can be transferred to cost space by means of a very natural way of understanding how thresholds should be chosen, by selecting the threshold such that the proportion of positive predictions equals the operating condition (either in the form of cost proportion or skew). We call these new curves {ROC Cost Curves}, and we demonstrate that the expected loss as measured by the area under these curves is linearly related to AUC. This opens up a series of new possibilities and clarifies the notion of cost curve and its relation to ROC analysis. In addition, we show that for a classifier that assigns the scores in an evenly-spaced way, these curves are equal to the Brier Curves. As a result, this establishes the first clear connection between AUC and the Brier score.

Perfectly rational decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions. Here we propose an axiomatic framework for bounded rational decision-making based on a thermodynamic interpretation of resource costs as information costs. We show that this axiomatic framework enforces a unique conversion law between utility and information, which can be characterized by a variational "free utility" principle akin to thermodynamical free energy. This variational principle constitutes a normative criterion that trades off utility and information costs, the latter measured by the Kullback-Leibler deviation between a distribution representing a desired policy and a reference distribution representing an initial default policy. We show that bounded optimal control solutions can be derived from this variational principle, which leads in general to stochastic policies. Furthermore, we show that risk-sensitive and robust (minimax) control schemes fall out naturally from this framework if the environment is considered as an adversarial opponent. When resource costs are ignored, the maximum expected utility principle is recovered.

We theoretically investigate the convergence rate and support consistency (i.e., correctly identifying the subset of non-zero coefficients in the large sample limit) of multiple kernel learning (MKL). We focus on MKL with block-l1 regularization (inducing sparse kernel combination), block-l2 regularization (inducing uniform kernel combination), and elastic-net regularization (including both block-l1 and block-l2 regularization). For the case where the true kernel combination is sparse, we show a sharper convergence rate of the block-l1 and elastic-net MKL methods than the existing rate for block-l1 MKL. We further show that elastic-net MKL requires a milder condition for being consistent than block-l1 MKL. For the case where the optimal kernel combination is not exactly sparse, we prove that elastic-net MKL can achieve a faster convergence rate than the block-l1 and block-l2 MKL methods by carefully controlling the balance between the block-l1and block-l2 regularizers. Thus, our theoretical results overall suggest the use of elastic-net regularization in MKL.

Preference handling and optimization are indispensable means for addressing non-trivial applications in Answer Set Programming (ASP). However, their implementation becomes difficult whenever they bring about a significant increase in computational complexity. As a consequence, existing ASP systems do not offer complex optimization capacities, supporting, for instance, inclusion-based minimization or Pareto efficiency. Rather, such complex criteria are typically addressed by resorting to dedicated modeling techniques, like saturation. Unlike the ease of common ASP modeling, however, these techniques are rather involved and hardly usable by ASP laymen. We address this problem by developing a general implementation technique by means of meta-programming, thus reusing existing ASP systems to capture various forms of qualitative preferences among answer sets. In this way, complex preferences and optimization capacities become readily available for ASP applications.