When solving instances of problem domains that feature a large branching factor, A* may generate a large number of nodes whose cost is greater than the cost of the optimal solution. We designate such nodes as surplus. Generating surplus nodes and adding them to the OPEN list may dominate both time and memory of the search. A recently introduced variant of A* called Partial Expansion A* (PEA*) deals with the memory aspect of this problem. When expanding a node n, PEA* generates all of its children and puts into OPEN only the children with f = f (n). n is re-inserted in the OPEN list with the f -cost of the best discarded child. This guarantees that surplus nodes are not inserted into OPEN. In this paper, we present a novel variant of A* called Enhanced Partial Expansion A* (EPEA*) that advances the idea of PEA* to address the time aspect. Given a priori domain- and heuristic- specific knowledge, EPEA* generates only the nodes with f = f(n). Although EPEA* is not always applicable or practical, we study several variants of EPEA*, which make it applicable to a large number of domains and heuristics. In particular, the ideas of EPEA* are applicable to IDA* and to the domains where pattern databases are traditionally used. Experimental studies show significant improvements in run-time and memory performance for several standard benchmark applications. We provide several theoretical studies to facilitate an understanding of the new algorithm.

Many problems in machine learning and other fields can be (re)for-mulated as linearly constrained separable convex programs. In most of the cases, there are multiple blocks of variables. However, the traditional alternating direction method (ADM) and its linearized version (LADM, obtained by linearizing the quadratic penalty term) are for the two-block case and cannot be naively generalized to solve the multi-block case. So there is great demand on extending the ADM based methods for the multi-block case. In this paper, we propose LADM with parallel splitting and adaptive penalty (LADMPSAP) to solve multi-block separable convex programs efficiently. When all the component objective functions have bounded subgradients, we obtain convergence results that are stronger than those of ADM and LADM, e.g., allowing the penalty parameter to be unbounded and proving the sufficient and necessary conditions} for global convergence. We further propose a simple optimality measure and reveal the convergence rate of LADMPSAP in an ergodic sense. For programs with extra convex set constraints, with refined parameter estimation we devise a practical version of LADMPSAP for faster convergence. Finally, we generalize LADMPSAP to handle programs with more difficult objective functions by linearizing part of the objective function as well. LADMPSAP is particularly suitable for sparse representation and low-rank recovery problems because its subproblems have closed form solutions and the sparsity and low-rankness of the iterates can be preserved during the iteration. It is also highly parallelizable and hence fits for parallel or distributed computing. Numerical experiments testify to the advantages of LADMPSAP in speed and numerical accuracy.

We present a system that demonstrates how the compositional structure of events, in concert with the compositional structure of language, can interplay with the underlying focusing mechanisms in video action recognition, thereby providing a medium, not only for top-down and bottom-up integration, but also for multi-modal integration between vision and language. We show how the roles played by participants (nouns), their characteristics (adjectives), the actions performed (verbs), the manner of such actions (adverbs), and changing spatial relations between participants (prepositions) in the form of whole sentential descriptions mediated by a grammar, guides the activity-recognition process. Further, the utility and expressiveness of our framework is demonstrated by performing three separate tasks in the domain of multi-activity videos: sentence-guided focus of attention, generation of sentential descriptions of video, and query-based video search, simply by leveraging the framework in different manners.

In many real world elections, agents are not required to rank all candidates. We study three of the most common methods used to modify voting rules to deal with such partial votes. These methods modify scoring rules (like the Borda count), elimination style rules (like single transferable vote) and rules based on the tournament graph (like Copeland) respectively. We argue that with an elimination style voting rule like single transferable vote, partial voting does not change the situations where strategic voting is possible. However, with scoring rules and rules based on the tournament graph, partial voting can increase the situations where strategic voting is possible. As a consequence, the computational complexity of computing a strategic vote can change. For example, with Borda count, the complexity of computing a strategic vote can decrease or stay the same depending on how we score partial votes.

Many machine learning models have important structural tuning parameters that cannot be directly estimated from the data. The common tactic for setting these parameters is to use resampling methods, such as cross--validation or the bootstrap, to evaluate a candidate set of values and choose the best based on some pre--defined criterion. Unfortunately, this process can be time consuming. However, the model tuning process can be streamlined by adaptively resampling candidate values so that settings that are clearly sub-optimal can be discarded. The notion of futility analysis is introduced in this context. An example is shown that illustrates how adaptive resampling can be used to reduce training time. Simulation studies are used to understand how the potential speed--up is affected by parallel processing techniques.

INCE the appearance of the seminal paper [1], NMF has become a popular data decomposition technique due to succesful applications in a still growing number of fields where data are nonnegative, such as pixel intensities in computer vision, amplitude spectra in audio signal analysis and EEG signal analysis, term counts in document clustering problems, and item ratings in collaborative filtering. NMF aims at decompositions, where, and are all nonnegative matrices. Throughout this paper will be regarded as a collection of data samples organized columnwise, as a dictionary of features organized columnwise, and as matrix of coefficients when is projected onto the dictionary. Under assumptions of linearity and nonnegativity, when underlying dimensionality is lower than dimensionality of the original space of the data, dimensionality reduction of the data can effectively be achieved this way. Although the decomposition is nonunique in general, NMF is able to produce strictly additive decompositions perceived as part-based by adding additional bias in the model [1], [2]. To this end, different sparsity promoting regularizers have been proposed for divergence-based NMF [3]. Also, to include higher order data descriptions, many other variants have been developed, e.g.

Calculating similarities between objects defined by many heterogeneous data modalities is an important challenge in many multimedia applications. We use a multi-modal topic model as a basis for defining such a similarity between objects. We propose to compare the resulting similarities from different model realizations using the non-parametric Mantel test. The approach is evaluated on a music dataset.

We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving. The intended audience ranges from students interested in logic over historians to logicians. Besides the well-known correction of Herbrand's False Lemma by Goedel and Dreben, we also present the hardly known unpublished correction of Heijenoort and its consequences on Herbrand's Modus Ponens Elimination. Besides Herbrand's Fundamental Theorem and its relation to the Loewenheim-Skolem-Theorem, we carefully investigate Herbrand's notion of intuitionism in connection with his notion of falsehood in an infinite domain. We sketch Herbrand's two proofs of the consistency of arithmetic and his notion of a recursive function, and last but not least, present the correct original text of his unification algorithm with a new translation.

We revisit a pioneer unsupervised learning technique called archetypal analysis, which is related to successful data analysis methods such as sparse coding and non-negative matrix factorization. Since it was proposed, archetypal analysis did not gain a lot of popularity even though it produces more interpretable models than other alternatives. Because no efficient implementation has ever been made publicly available, its application to important scientific problems may have been severely limited. Our goal is to bring back into favour archetypal analysis. We propose a fast optimization scheme using an active-set strategy, and provide an efficient open-source implementation interfaced with Matlab, R, and Python. Then, we demonstrate the usefulness of archetypal analysis for computer vision tasks, such as codebook learning, signal classification, and large image collection visualization.

Kernel methods have revolutionized the fields of pattern recognition and machine learning. Their success, however, critically depends on the choice of kernel parameters. Using Gaussian process (GP) classification as a working example, this paper focuses on Bayesian inference of covariance (kernel) parameters using Markov chain Monte Carlo (MCMC) methods. The motivation is that, compared to standard optimization of kernel parameters, they have been systematically demonstrated to be superior in quantifying uncertainty in predictions. Recently, the Pseudo-Marginal MCMC approach has been proposed as a practical inference tool for GP models. In particular, it amounts in replacing the analytically intractable marginal likelihood by an unbiased estimate obtainable by approximate methods and importance sampling. After discussing the potential drawbacks in employing importance sampling, this paper proposes the application of annealed importance sampling. The results empirically demonstrate that compared to importance sampling, annealed importance sampling can reduce the variance of the estimate of the marginal likelihood exponentially in the number of data at a computational cost that scales only polynomially. The results on real data demonstrate that employing annealed importance sampling in the Pseudo-Marginal MCMC approach represents a step forward in the development of fully automated exact inference engines for GP models.