The dueling bandit problem is a variation of the classical multi-armed bandit in which the allowable actions are noisy comparisons between pairs of arms. This paper focuses on a new approach for finding the "best" arm according to the Borda criterion using noisy comparisons. We prove that in the absence of structural assumptions, the sample complexity of this problem is proportional to the sum of the inverse squared gaps between the Borda scores of each suboptimal arm and the best arm. We explore this dependence further and consider structural constraints on the pairwise comparison matrix (a particular form of sparsity natural to this problem) that can significantly reduce the sample complexity. This motivates a new algorithm called Successive Elimination with Comparison Sparsity (SECS) that exploits sparsity to find the Borda winner using fewer samples than standard algorithms. We also evaluate the new algorithm experimentally with synthetic and real data. The results show that the sparsity model and the new algorithm can provide significant improvements over standard approaches.

As a technology to read brain states from measurable brain activities, brain decoding are widely applied in industries and medical sciences. In spite of high demands in these applications for a universal decoder that can be applied to all individuals simultaneously, large variation in brain activities across individuals has limited the scope of many studies to the development of individual-specific decoders. In this study, we used deep neural network (DNN), a nonlinear hierarchical model, to construct a subject-transfer decoder. Our decoder is the first successful DNN-based subject-transfer decoder. When applied to a large-scale functional magnetic resonance imaging (fMRI) database, our DNN-based decoder achieved higher decoding accuracy than other baseline methods, including support vector machine (SVM). In order to analyze the knowledge acquired by this decoder, we applied principal sensitivity analysis (PSA) to the decoder and visualized the discriminative features that are common to all subjects in the dataset. Our PSA successfully visualized the subject-independent features contributing to the subject-transferability of the trained decoder.

We consider a set of probabilistic functions of some input variables as a representation of the inputs. We present bounds on how informative a representation is about input data. We extend these bounds to hierarchical representations so that we can quantify the contribution of each layer towards capturing the information in the original data. The special form of these bounds leads to a simple, bottom-up optimization procedure to construct hierarchical representations that are also maximally informative about the data. This optimization has linear computational complexity and constant sample complexity in the number of variables. These results establish a new approach to unsupervised learning of deep representations that is both principled and practical. We demonstrate the usefulness of the approach on both synthetic and real-world data.

Not all NP-complete problems share the same practical hardness with respect to exact computation. Whereas some NP-complete problems are amenable to efficient computational methods, others are yet to show any such sign. It becomes a major challenge to develop a theoretical framework that is more fine-grained than the theory of NP-completeness, and that can explain the distinction between the exact complexities of various NP-complete problems. This distinction is highly relevant for constraint satisfaction problems under natural restrictions, where various shades of hardness can be observed in practice. Acknowledging the NP-hardness of such problems, one has to look beyond polynomial time computation. The theory of subexponential-time complexity provides such a framework, and has been enjoying increasing popularity in complexity theory. An instance of the constraint satisfaction problem with n variables over a domain of d values can be solved by brute-force in dn steps (omitting a polynomial factor). In this paper we study the existence of subexponential-time algorithms, that is, algorithms running in do(n) steps, for various natural restrictions of the constraint satisfaction problem. We consider both the constraint satisfaction problem in which all the constraints are given extensionally as tables, and that in which all the constraints are given intensionally in the form of global constraints. We provide tight characterizations of the subexponential-time complexity of the aforementioned problems with respect to several natural structural parameters, which allows us to draw a detailed landscape of the subexponential-time complexity of the constraint satisfaction problem. Our analysis provides fundamental results indicating whether and when one can significantly improve on the brute-force search approach for solving the constraint satisfaction problem.

A graph is one of the most general data types to represent structured objects, and massive amounts of structured data are now available as graphs across a wide range of domains, such as chemical compounds in PubChem [5], biological pathways in KEGG [16], protein structures in PDB [3], and social networks on the web. Analyzing such databases, that is, graph mining, has evolved into an important branch of data mining and knowledge discovery. Graph databases often include two or more distinct classes of graphs and, in many application domains, the ultimate purpose is to discover significant subgraphs that are statistically significantly enriched in one particular class of graphs. In drug discovery, for instance, chemists try to identify a key substructure of chemical compounds which is significantly associated with a particular activity, e.g., anticancer activity [30]. In a similar fashion, biologists seek substructures of proteins that are required for particular docking events [37]. 1 Finding such significant subgraphs is an open problem, as the large number of candidate subgraphs causes both a computational and a statistical problem: the computational problem is that it is often extremely expensive to check all subgraphs for enrichment, given that their number scales exponentially in the number of nodes of the largest graph in the database.

Identification of the influential clinical symptoms and laboratory features that help in the diagnosis of dengue fever in early phase of the illness would aid in designing effective public health management and virological surveillance strategies. Keeping this as our main objective we develop in this paper, a new computational intelligence based methodology that predicts the diagnosis in real time, minimizing the number of false positives and false negatives. Our methodology consists of three major components (i) a novel missing value imputation procedure that can be applied on any data set consisting of categorical (nominal) and/or numeric (real or integer) (ii) a wrapper based features selection method with genetic search for extracting a subset of most influential symptoms that can diagnose the illness and (iii) an alternating decision tree method that employs boosting for generating highly accurate decision rules. The predictive models developed using our methodology are found to be more accurate than the state-of-the-art methodologies used in the diagnosis of the dengue fever.

We study regularized estimation in high-dimensional longitudinal classification problems, using the lasso and fused lasso regularizers. The constructed coefficient estimates are piecewise constant across the time dimension in the longitudinal problem, with adaptively selected change points (break points). We present an efficient algorithm for computing such estimates, based on proximal gradient descent. We apply our proposed technique to a longitudinal data set on Alzheimer's disease from the Cardiovascular Health Study Cognition Study, and use this data set to motivate and demonstrate several practical considerations such as the selection of tuning parameters, and the assessment of model stability.

The interest in the combination of probability with logics for modeling the world has rapidly increased in the last few years. One of the most effective approaches is the Distribution Semantics which was adopted by many logic programming languages and in Descripion Logics. In this paper, we illustrate the work we have done in this research field by presenting a probabilistic semantics for description logics and reasoning and learning algorithms. In particular, we present in detail the system TRILL P, which computes the probability of queries w.r.t. probabilistic knowledge bases, which has been implemented in Prolog. Note: An extended abstract / full version of a paper accepted to be presented at the Doctoral Consortium of the 30th International Conference on Logic Programming (ICLP 2014), July 19-22, Vienna, Austria

Machine learning (ML) is a powerful data-driven method for learning patterns in high-dimensional spaces via induction, and has had widespread success in many fields including more recent applications in quantum chemistry and materials science [1-9]. Here we are interested in applications of ML to construction of density functionals [10-14], which have focused so far on approximating the kinetic energy (KE) of non-interacting electrons. An accurate, general approximation to this could make orbital-free DFT a practical reality. However, ML methods have been developed within the areas of statistics and computer science, and have been applied to a huge variety of data, including neuroscience, image and text processing, and robotics [15]. Thus, they are quite general and have not been tailored to account for specific details of the quantum problem.

Determining the 3D structures of biological molecules is a key problem for both biology and medicine. Electron Cryomicroscopy (Cryo-EM) is a promising technique for structure estimation which relies heavily on computational methods to reconstruct 3D structures from 2D images. This paper introduces the challenging Cryo-EM density estimation problem as a novel application for stochastic optimization techniques. Structure discovery is formulated as MAP estimation in a probabilistic latent-variable model, resulting in an optimization problem to which an array of seven stochastic optimization methods are applied. The methods are tested on both real and synthetic data, with some methods recovering reasonable structures in less than one epoch from a random initialization. Complex quasi-Newton methods are found to converge more slowly than simple gradient-based methods, but all stochastic methods are found to converge to similar optima. This method represents a major improvement over existing methods as it is significantly faster and is able to converge from a random initialization.