We consider the question of learning in general topological vector spaces. By exploiting known (or parametrized) covariance structures, our Main Theorem demonstrates that any continuous linear map corresponds to a certain isomorphism of embedded Hilbert spaces. By inverting this isomorphism and extending continuously, we construct a version of the Ordinary Least Squares estimator in absolute generality. Our Gauss-Markov theorem demonstrates that OLS is a "best linear unbiased estimator", extending the classical result. We construct a stochastic version of the OLS estimator, which is a continuous disintegration exactly for the class of "uncorrelated implies independent" (UII) measures. As a consequence, Gaussian measures always exhibit continuous disintegrations through continuous linear maps, extending a theorem of the first author. Applying this framework to some problems in machine learning, we prove a useful representation theorem for covariance tensors, and show that OLS defines a good kriging predictor for vector-valued arrays on general index spaces. We also construct a support-vector machine classifier in this setting. We hope that our article shines light on some deeper connections between probability theory, statistics and machine learning, and may serve as a point of intersection for these three communities.

The Clustered Vehicle Routing Problem (CluVRP) is a variant of the Capacitated Vehicle Routing Problem in which customers are grouped into clusters. Each cluster has to be visited once, and a vehicle entering a cluster cannot leave it until all customers have been visited. This article presents two alternative hybrid metaheuristic algorithms for the CluVRP. The first algorithm is based on an Iterated Local Search algorithm, in which only feasible solutions are explored and problem-specific local search moves are utilized. The second algorithm is a Hybrid Genetic Search, for which the shortest Hamiltonian path between each pair of vertices within each cluster should be precomputed. Using this information, a sequence of clusters can be used as a solution representation and large neighborhoods can be efficiently explored by means of bi-directional dynamic programming, sequence concatenations, by using appropriate data structures. Extensive computational experiments are performed on benchmark instances from the literature, as well as new large scale ones. Recommendations on promising algorithm choices are provided relatively to average cluster size.

Archetypal analysis (AA) represents observations as composition of pure patterns, i.e., archetypes, or equivalently convex combinations of extreme values (Cutler and Breiman, 1994). Although AA bears resemblance with many well established prototypical analysis tools, such as principal component analysis (PCA, Mohamed et al, 2009), nonnegative matrix factorization (NMF, F evotte and Idier, 2011), probabilistic latent semantic analysis (Hofmann, 2013), andk -means (Steinley, 2006); AA is arguably unique, both conceptually and computationally . Conceptually, AA imitates the human tendency of representing a group of objects by its extreme elements (Davis and Love, 2010): this makes AA an interesting exploratory tool for applied scientists (e.g., Eugster, 2012; Seiler and Wohlrabe, 2013). Computationally, AA is data-driven, and requires the factors to be probability vectors: these make AA a computationally demanding tool, yet brings better interpretability . The concept of AA was originally formulated by Cutler and Breiman (1994).

Geographical location is vital to geospatial applications like local search and event detection. In this paper, we investigate and improve on the task of text-based geolocation prediction of Twitter users. Previous studies on this topic have typically assumed that geographical references (e.g., gazetteer terms, dialectal words) in a text are indicative of its authors location. However, these references are often buried in informal, ungrammatical, and multilingual data, and are therefore non-trivial to identify and exploit. We present an integrated geolocation prediction framework and investigate what factors impact on prediction accuracy. First, we evaluate a range of feature selection methods to obtain location indicative words. We then evaluate the impact of non-geotagged tweets, language, and user-declared metadata on geolocation prediction. In addition, we evaluate the impact of temporal variance on model generalisation, and discuss how users differ in terms of their geolocatability. We achieve state-of-the-art results for the text-based Twitter user geolocation task, and also provide the most extensive exploration of the task to date. Our findings provide valuable insights into the design of robust, practical text-based geolocation prediction systems.

Mach Learn manuscript No. (will be inserted by the editor) Abstract We present a new application and covering number bound for the framework of "Machine Learning with Operational Costs (MLOC)," which is an exploratory form of decision theory. The MLOC framework incorporates knowledge about how a predictive model will be used for a subsequent task, thus combining machine learning with the decision that is made afterwards. In this work, we use the MLOC framework to study a problem that has implications for power grid reliability and maintenance, called the Machine Learning and Traveling Repairman Problem (ML&TRP). The goal of the ML&TRP is to determine a route for a "repair crew," which repairs nodes on a graph. The repair crew aims to minimize the cost of failures at the nodes, but as in many real situations, the failure probabilities are not known and must be estimated. The MLOC framework allows us to understand how this uncertainty influences the repair route. Keywords decision theory · generalization bound · constrained linear function classes · covering numbers · traveling repairman · mixed-integer programming 1 Introduction In many domains, it is essential to understand how uncertainty in predictions influences decision-making. Funding for Theja Tulabandhula was provided by a Fulbright Fellowship and Xerox Fellowship. Cynthia Rudin's work on this project was funded in part by Con Edison, by the MIT Energy Initiative Seed Fund, and NSF grant IIS-1053407. The new framework of Machine Learning with Operational Costs (MLOC) (Tulabandhula and Rudin, 2013) provides a mechanism to do this, and is a type of exploratory decision theory. Where usual decision theories provide a single policy that minimizes expected costs, the MLOC framework is able to produce a range of reasonable policies that span the full set of reasonable costs. To do this, the operational cost becomes a regularization term within the machine learning model, and adjusting the regularization constant allows us to explore solutions for all reasonable costs. This gives decision makers a way to understand the uncertainty in their predictive model in terms of something they can grasp - uncertainty in the cost to solve the problem. The MLOC framework can also be used in another way, namely to incorporate prior knowledge about the cost to produce a better predictive model.

This paper proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this paper we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and inconsistency in the style of the so-called Logics of Formal Inconsistency (LFIs). The main novelty of the present approach is the definition of postulates for this type of operators over MTL-algebras, leading to the definition and axiomatization of a family of logics, expansions of MTL, whose degree-preserving counterpart are paraconsistent and moreover LFIs.

Support Vector Machine (SVM) is powerful classification technique based on the idea of structural risk minimization. Use of kernel function enables curse of dimensionality to be addressed. However, proper kernel function for certain problem is dependent on specific dataset and as such there is no good method on choice of kernel function. In this paper, SVM is used to build empirical models of currency crisis in Argentina. An estimation technique is developed by training model on real life data set which provides reasonably accurate model outputs and helps policy makers to identify situations in which currency crisis may happen. The third and fourth order polynomial kernel is generally best choice to achieve high generalization of classifier performance. SVM has high level of maturity with algorithms that are simple, easy to implement, tolerates curse of dimensionality and good empirical performance. The satisfactory results show that currency crisis situation is properly emulated using only small fraction of database and could be used as an evaluation tool as well as an early warning system. To the best of knowledge this is the first work on SVM approach for currency crisis evaluation of Argentina.

Distributional semantic models derive computational representations of word meaning from the patterns of co-occurrence of words in text. Such models have been a success story of computational linguistics, being able to provide reliable estimates of semantic relatedness for the many semantic tasks requiring them. However, distributional models extract meaning information exclusively from text, which is an extremely impoverished basis compared to the rich perceptual sources that ground human semantic knowledge. We address the lack of perceptual grounding of distributional models by exploiting computer vision techniques that automatically identify discrete visual words in images, so that the distributional representation of a word can be extended to also encompass its co-occurrence with the visual words of images it is associated with. We propose a flexible architecture to integrate text- and image-based distributional information, and we show in a set of empirical tests that our integrated model is superior to the purely text-based approach, and it provides somewhat complementary semantic information with respect to the latter.

We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. A multiclass extension is introduced using the Gibbs simplex, with the functional's double-well potential modified to handle the multiclass case. The first algorithm minimizes the functional using a convex splitting numerical scheme. The second algorithm is a uses a graph adaptation of the classical numerical Merriman-Bence-Osher (MBO) scheme, which alternates between diffusion and thresholding. We demonstrate the performance of both algorithms experimentally on synthetic data, grayscale and color images, and several benchmark data sets such as MNIST, COIL and WebKB. We also make use of fast numerical solvers for finding the eigenvectors and eigenvalues of the graph Laplacian, and take advantage of the sparsity of the matrix. Experiments indicate that the results are competitive with or better than the current state-of-the-art multiclass segmentation algorithms.

Springs, NY. ICCBR is the annual meeting of the CBR community and the ICCBR also featured a workshop program consisting of three workshops. The main conference track featured 16 research paper presentations, nine posters, and two invited speakers. The papers and posters reflected the state of the art of case-based reasoning, dealing both with open problems at the core of CBR (especially in similarity assessment, case adaptation, and case-based maintenance), as well as trending applications of CBR (especially recommender systems and computer games) and the intersections of CBR with other areas such as multiagent systems. The first invited speaker, Igor Jurisica from the Ontario Cancer Institute and the University of Toronto, spoke about how to scale up case-based reasoning for "big data" applications. The Case-Based Reasoning in Health Sciences workshop, organized by Isabelle Bichindaritz, Cindy Marling, and Stefania Montani, and the EXPPORT workshop (Experience Reuse: Provenance, Process-Orientation and Traces), organized by David Leake, Béatrice Fuchs, Juan A. Recio Garcia, and Stefania Montani, were held jointly and dealt with how to deal with data represented CDPHP, was the local chair; William E. University, and Jonathan Rubin, from Registration information is available at www.aaai.org/Symposia/ the Palo Alto Research Center, were the Spring/ sss14.php.