Community detection is the task of detecting hidden communities from observed interactions. Guaranteed community detection has so far been mostly limited to models with non-overlapping communities such as the stochastic block model. In this paper, we remove this restriction, and provide guaranteed community detection for a family of probabilistic network models with overlapping communities, termed as the mixed membership Dirichlet model, first introduced by Airoldi et al. This model allows for nodes to have fractional memberships in multiple communities and assumes that the community memberships are drawn from a Dirichlet distribution. Moreover, it contains the stochastic block model as a special case. We propose a unified approach to learning these models via a tensor spectral decomposition method. Our estimator is based on low-order moment tensor of the observed network, consisting of 3-star counts. Our learning method is fast and is based on simple linear algebraic operations, e.g. singular value decomposition and tensor power iterations. We provide guaranteed recovery of community memberships and model parameters and present a careful finite sample analysis of our learning method. As an important special case, our results match the best known scaling requirements for the (homogeneous) stochastic block model.

We develop an online mechanism for the allocation of an expiring resource to a dynamic agent population. Each agent has a non-increasing marginal valuation function for the resource, and an upper limit on the number of units that can be allocated in any period. We propose two versions on a truthful allocation mechanism. Each modifies the decisions of a greedy online assignment algorithm by sometimes cancelling an allocation of resources. One version makes this modification immediately upon an allocation decision while a second waits until the point at which an agent departs the market. Adopting a prior-free framework, we show that the second approach has better worst-case allocative efficiency and is more scalable. On the other hand, the first approach (with immediate cancellation) may be easier in practice because it does not need to reclaim units previously allocated. We consider an application to recharging plug-in hybrid electric vehicles (PHEVs). Using data from a real-world trial of PHEVs in the UK, we demonstrate higher system performance than a fixed price system, performance comparable with a standard, but non-truthful scheduling heuristic, and the ability to support 50% more vehicles at the same fuel cost than a simple randomized policy.

Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed on the selected kernel. This note contributes to the study of universal, characteristic, and $C_0$-universal kernels. We first give simple and direct description of the difference and relation among these three kinds of universalities of kernels. We then focus on translation-invariant and weighted polynomial kernels. A simple and shorter proof of the known characterization of characteristic translation-invariant kernels will be presented. The main purpose of the note is to give a delicate discussion on the universalities of weighted polynomial kernels.

As humans, we live in a remarkably complex social environment. One cognitive tool which helps us manage all this complexity is our theory of mind, the ability to reason about the mental states of others. By deducing what other people want, feel and think, we can understand their actions, predict how our actions will influence them, and decide how we should behave to be successful. Theory of mind is the cognitive capacity to understand and predict external behavior of others and oneself by attributing internal mental states, such as knowledge, beliefs, and intentions [17]. This is thought to be the pinnacle of social cognition.

This paper presents a novel SAT-based approach for the computation of extensions in abstract argumentation, with focus on preferred semantics, and an empirical evaluation of its performances. The approach is based on the idea of reducing the problem of computing complete extensions to a SAT problem and then using a depth-first search method to derive preferred extensions. The proposed approach has been tested using two distinct SAT solvers and compared with three state-of-the-art systems for preferred extension computation. It turns out that the proposed approach delivers significantly better performances in the large majority of the considered cases.

The chase algorithm is a fundamental tool for query evaluation and for testing query containment under tuple-generating dependencies (TGDs) and equality-generating dependencies (EGDs). So far, most of the research on this topic has focused on cases where the chase procedure terminates. This paper introduces expressive classes of TGDs defined via syntactic restrictions: guarded TGDs (GTGDs) and weakly guarded sets of TGDs (WGT-GDs). For these classes, the chase procedure is not guaranteed to terminate and thus may have an infinite outcome. Nevertheless, we prove that the problems of conjunctive-query answering and query containment under such TGDs are decidable. We provide decision procedures and tight complexity bounds for these problems. Then we show how EGDs can be incorporated into our results by providing conditions under which EGDs do not harmfully interact with TGDs and do not affect the decidability and complexity of query answering. We show applications of the aforesaid classes of constraints to the problem of answering conjunctive queries in F-Logic Lite, an object-oriented ontology language, and in some tractable Description Logics.

Combining information from different sources is a common way to improve classification accuracy in Brain-Computer Interfacing (BCI). For instance, in small sample settings it is useful to integrate data from other subjects or sessions in order to improve the estimation quality of the spatial filters or the classifier. Since data from different subjects may show large variability, it is crucial to weight the contributions according to importance. Many multi-subject learning algorithms determine the optimal weighting in a separate step by using heuristics, however, without ensuring that the selected weights are optimal with respect to classification. In this work we apply Multiple Kernel Learning (MKL) to this problem. MKL has been widely used for feature fusion in computer vision and allows to simultaneously learn the classifier and the optimal weighting. We compare the MKL method to two baseline approaches and investigate the reasons for performance improvement.

We introduce a computationally effective algorithm for a linear model selection consisting of three steps: screening--ordering--selection (SOS). Screening of predictors is based on the thresholded Lasso that is l_1 penalized least squares. The screened predictors are then fitted using least squares (LS) and ordered with respect to their t statistics. Finally, a model is selected using greedy generalized information criterion (GIC) that is l_0 penalized LS in a nested family induced by the ordering. We give non-asymptotic upper bounds on error probability of each step of the SOS algorithm in terms of both penalties. Then we obtain selection consistency for different (n, p) scenarios under conditions which are needed for screening consistency of the Lasso. For the traditional setting (n >p) we give Sanov-type bounds on the error probabilities of the ordering--selection algorithm. Its surprising consequence is that the selection error of greedy GIC is asymptotically not larger than of exhaustive GIC. We also obtain new bounds on prediction and estimation errors for the Lasso which are proved in parallel for the algorithm used in practice and its formal version.

In this work, we propose a PAC-Bayes bound for the generalization risk of the Gibbs classifier in the multi-class classification framework. The novelty of our work is the critical use of the confusion matrix of a classifier as an error measure; this puts our contribution in the line of work aiming at dealing with performance measure that are richer than mere scalar criterion such as the misclassification rate. Thanks to very recent and beautiful results on matrix concentration inequalities, we derive two bounds showing that the true confusion risk of the Gibbs classifier is upper-bounded by its empirical risk plus a term depending on the number of training examples in each class. To the best of our knowledge, this is the first PAC-Bayes bounds based on confusion matrices.

The generic identification problem is to decide whether a stochastic process $(X_t)$ is a hidden Markov process and if yes to infer its parameters for all but a subset of parametrizations that form a lower-dimensional subvariety in parameter space. Partial answers so far available depend on extra assumptions on the processes, which are usually centered around stationarity. Here we present a general solution for binary-valued hidden Markov processes. Our approach is rooted in algebraic statistics hence it is geometric in nature. We find that the algebraic varieties associated with the probability distributions of binary-valued hidden Markov processes are zero sets of determinantal equations which draws a connection to well-studied objects from algebra. As a consequence, our solution allows for algorithmic implementation based on elementary (linear) algebraic routines.