Active learning aims to obtain a classifier of high accuracy by using fewer label requests in comparison to passive learning by selecting effective queries. Many active learning methods have been developed in the past two decades, which sample queries based on informativeness or representativeness of unlabeled data points. In this work, we explore a novel querying criterion based on statistical leverage scores. The statistical leverage scores of a row in a matrix are the squared row-norms of the matrix containing its (top) left singular vectors and is a measure of influence of the row on the matrix. Leverage scores have been used for detecting high influential points in regression diagnostics and have been recently shown to be useful for data analysis and randomized low-rank matrix approximation algorithms. We explore how sampling data instances with high statistical leverage scores perform in active learning. Our empirical comparison on several binary classification datasets indicate that querying high leverage points is an effective strategy.

We study the problem of structured output learning from a regression perspective. We first provide a general formulation of the kernel dependency estimation (KDE) problem using operator-valued kernels. We show that some of the existing formulations of this problem are special cases of our framework. We then propose a covariance-based operator-valued kernel that allows us to take into account the structure of the kernel feature space. This kernel operates on the output space and encodes the interactions between the outputs without any reference to the input space. To address this issue, we introduce a variant of our KDE method based on the conditional covariance operator that in addition to the correlation between the outputs takes into account the effects of the input variables. Finally, we evaluate the performance of our KDE approach using both covariance and conditional covariance kernels on two structured output problems, and compare it to the state-of-the-art kernel-based structured output regression methods.

Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF factorization. Empirically, the running time of pMMF scales linearly in the dimension for sparse matrices. We argue that this makes pMMF a valuable new computational primitive in its own right, and present experiments on using pMMF for two distinct purposes: compressing matrices and preconditioning large sparse linear systems.

The rapidly growing of Location-based Social Networks (LBSNs) provides a vast amount of check-in data, which enables many services, e.g., point-of-interest (POI) recommendation. In this paper, we study the next new POI recommendation problem in which new POIs with respect to users' current location are to be recommended. The challenge lies in the difficulty in precisely learning users' sequential information and personalizing the recommendation model. To this end, we resort to the Metric Embedding method for the recommendation, which avoids drawbacks of the Matrix Factorization technique. We propose a personalized ranking metric embedding method (PRME) to model personalized check-in sequences. We further develop a PRME-G model, which integrates sequential information, individual preference, and geographical influence, to improve the recommendation performance. Experiments on two real-world LBSN datasets demonstrate that our new algorithm outperforms the state-of-the-art next POI recommendation methods.

Nicod's criterion states that observing a black raven is evidence for the hypothesis H that all ravens are black. We show that Solomonoff induction does not satisfy Nicod's criterion: there are time steps in which observing black ravens decreases the belief in H. Moreover, while observing any computable infinite string compatible with H, the belief in H decreases infinitely often when using the unnormalized Solomonoff prior, but only finitely often when using the normalized Solomonoff prior. We argue that the fault is not with Solomonoff induction; instead we should reject Nicod's criterion.

Gaussian processes (GP) are powerful tools for probabilistic modeling purposes. They can be used to define prior distributions over latent functions in hierarchical Bayesian models. The prior over functions is defined implicitly by the mean and covariance function, which determine the smoothness and variability of the function. The inference can then be conducted directly in the function space by evaluating or approximating the posterior process. Despite their attractive theoretical properties GPs provide practical challenges in their implementation. GPstuff is a versatile collection of computational tools for GP models compatible with Linux and Windows MATLAB and Octave. It includes, among others, various inference methods, sparse approximations and tools for model assessment. In this work, we review these tools and demonstrate the use of GPstuff in several models.

We propose a new type of algorithm for computing first-order (FO) rewritings of concept queries under ELHdr-TBoxes. The algorithm is tailored towards efficient implementation, yet complete. It outputs a succinct non-recursive datalog rewriting if the input is FO-rewritable and otherwise reports non-FO-rewritability. We carry out experiments with real-world ontologies which demonstrate excellent performance in practice and show that TBoxes originating from applications admit FO-rewritings of reasonable size in almost all cases, even when in theory such rewritings are not guaranteed to exist.

The classical probabilistic entailment problem is to We apply the family of minimal violation measures from determine upper and lower bounds on the probability [Potyka, 2014] since they allow us to extend the classical notion of formulas, given a consistent set of probabilistic of models of a probabilistic knowledge base to inconsistent assertions. We generalize this problem ones. Intuitively, the generalized models are those probability by omitting the consistency assumption and, thus, functions that minimally violate the knowledge base provide a general framework for probabilistic reasoning [Potyka and Thimm, 2014]. We incorporate integrity constraints under inconsistency. To do so, we utilize and study a family of generalized entailment problems inconsistency measures to determine probability for probabilistic knowledge bases. More specifically, functions that are closest to satisfying the knowledge the contributions of this work are as follows: base. We illustrate our approach on several 1. We introduce the computational problem of generalized examples and show that it has both nice formal and entailment with integrity constraints in probabilistic logics computational properties.

We address an ensemble clustering problem, where reliable clusters are locally embedded in given multiple partitions. We propose a new nonnegative matrix factorization (NMF)-based method, in which locally reliable clusters are explicitly considered by using instance-wise weights over clusters. Our method factorizes the input cluster assignment matrix into two matrices H and W, which are optimized by iteratively 1) updating H and W while keeping the weight matrix constant and 2) updating the weight matrix while keeping H and W constant, alternatively. The weights in the second step were updated by solving a convex problem, which makes our algorithm significantly faster than existing NMF-based ensemble clustering methods. We empirically proved that our method outperformed a lot of cutting-edge ensemble clustering methods by using a variety of datasets.

We study the computational complexity of finding maximum a posteriori configurations in Bayesian networks whose probabilities are specified by logical formulas. This approach leads to a fine grained study in which local information such as context-sensitive independence and determinism can be considered. It also allows us to characterize more precisely the jump from tractability to NP-hardness and beyond, and to consider the complexity introduced by evidence alone.