In the contexts of automated reasoning and formal verification, important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories of practical interest (e.g., linear arithmetic, arrays, bit-vectors). Surprisingly, very few work has been done to extend SMT to deal with optimization problems; in particular, we are not aware of any work on SMT solvers able to produce solutions which minimize cost functions over arithmetical variables. This is unfortunate, since some problems of interest require this functionality. In this paper we start filling this gap. We present and discuss two general procedures for leveraging SMT to handle the minimization of LA(Q) cost functions, combining SMT with standard minimization techniques. We have implemented the procedures within the MathSAT SMT solver. Due to the absence of competitors in AR and SMT domains, we have experimentally evaluated our implementation against state-of-the-art tools for the domain of linear generalized disjunctive programming (LGDP), which is closest in spirit to our domain, on sets of problems which have been previously proposed as benchmarks for the latter tools. The results show that our tool is very competitive with, and often outperforms, these tools on these problems, clearly demonstrating the potential of the approach.

This article presents a new algorithm which is a modified version of the elite ant system (EAS) algorithm. The new version utilizes an effective criterion for escaping from the local optimum points. In contrast to the classical EAC algorithms, the proposed algorithm uses only a global updating, which will increase pheromone on the edges of the best (i.e. the shortest) route and will at the same time decrease the amount of pheromone on the edges of the worst (i.e. the longest) route. In order to assess the efficiency of the new algorithm, some standard traveling salesman problems (TSPs) were studied and their results were compared with classical EAC and other well-known meta-heuristic algorithms. The results indicate that the proposed algorithm has been able to improve the efficiency of the algorithms in all instances and it is competitive with other algorithms.

We study sparse principal components analysis in the high-dimensional setting, where $p$ (the number of variables) can be much larger than $n$ (the number of observations). We prove optimal, non-asymptotic lower and upper bounds on the minimax estimation error for the leading eigenvector when it belongs to an $\ell_q$ ball for $q \in [0,1]$. Our bounds are sharp in $p$ and $n$ for all $q \in [0, 1]$ over a wide class of distributions. The upper bound is obtained by analyzing the performance of $\ell_q$-constrained PCA. In particular, our results provide convergence rates for $\ell_1$-constrained PCA.

A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an infinite Poisson factor analysis model. A finite approximation for the beta process Levy random measure is constructed for convenient implementation. Efficient MCMC computations are performed with data augmentation and marginalization techniques. Encouraging results are shown on document count matrix factorization.

The proposed feature selection method builds a histogram of the most stable features from random subsets of a training set and ranks the features based on a classifier based cross-validation. This approach reduces the instability of features obtained by conventional feature selection methods that occur with variation in training data and selection criteria. Classification results on four microarray and three image datasets using three major feature selection criteria and a naive Bayes classifier show considerable improvement over benchmark results.

A significant challenge to make learning techniques more sui table for general purpose use is to move beyond i) complete supervision, ii) low dimensional data, iii) a single t ask and single view per instance. Solving these challenges a llows working with "Big Data" problems that are typically high dim ensional with multiple (but possibly incomplete) labeling s and views. While other work has addressed each of these probl ems separately, in this paper we show how to address them together, namelysemi-supervised dimension reduction for multi-task and multi-view learning (SSDR-MML), which performs optimization for dimension reduction and label inference in semi-supervised setting. The proposed framework is designed to handle both multi-task and multi-view learning settings, and can be easily adapted to many useful applications. Inform ation obtained from all tasks and views is combined via reconstruction errors in a linear fashion that can be efficiently solvedusing an alternating optimization scheme. Our formulation has a number of advantages. W e explicitly model the information combining mechanism as a data structure (a weight/nearest-nei ghbor matrix) which allows investigating fundamental ques tions in multi-task and multi-view learning. W e address one such question by presenting a general measure to quantify the success of simultaneous learning of multiple tasks or from multiple views. W e show that our SSDR-MML approach can outperform many state-of-the-art baseline methods and demonstrate the effectiveness of connecting dimension reduction and learning.

This paper studies peek arc consistency, a reasoning technique that extends the well-known arc consistency technique for constraint satisfaction. In contrast to other more costly extensions of arc consistency that have been studied in the literature, peek arc consistency requires only linear space and quadratic time and can be parallelized in a straightforward way such that it runs in linear time with a linear number of processors. We demonstrate that for various constraint languages, peek arc consistency gives a polynomial-time decision procedure for the constraint satisfaction problem. We also present an algebraic characterization of those constraint languages that can be solved by peek arc consistency, and study the robustness of the algorithm.

This paper analyses the influence of including agents of different degrees of intelligence in a multiagent system. The goal is to better understand how we can develop intelligence tests that can evaluate social intelligence. We analyse several reinforcement algorithms in several contexts of cooperation and competition. Our experimental setting is inspired by the recently developed Darwin-Wallace distribution.

Many modern data mining applications are concerned with the analysis of datasets in which the observations are described by paired high-dimensional vectorial representations or "views". Some typical examples can be found in web mining and genomics applications. In this article we present an algorithm for data clustering with multiple views, Multi-View Predictive Partitioning (MVPP), which relies on a novel criterion of predictive similarity between data points. We assume that, within each cluster, the dependence between multivariate views can be modelled by using a two-block partial least squares (TB-PLS) regression model, which performs dimensionality reduction and is particularly suitable for high-dimensional settings. The proposed MVPP algorithm partitions the data such that the within-cluster predictive ability between views is maximised. The proposed objective function depends on a measure of predictive influence of points under the TB-PLS model which has been derived as an extension of the PRESS statistic commonly used in ordinary least squares regression. Using simulated data, we compare the performance of MVPP to that of competing multi-view clustering methods which rely upon geometric structures of points, but ignore the predictive relationship between the two views. State-of-art results are obtained on benchmark web mining datasets.

In this paper, we will argue that if we want to understand the function of the brain (or the control in the case of robots), we must understand how the brain is embedded into the physical system, and how the organism interacts with the real world. While embodiment has often been used in its trivial meaning, i.e. 'intelligence requires a body', the concept has deeper and more important implications, concerned with the relation between physical and information (neural, control) processes. A number of case studies are presented to illustrate the concept. These involve animals and robots and are concentrated around locomotion, grasping, and visual perception. A theoretical scheme that can be used to embed the diverse case studies will be presented. Finally, we will establish a link between the low-level sensory-motor processes and cognition. We will present an embodied view on categorization, and propose the concepts of 'body schema' and 'forward models' as a natural extension of the embodied approach toward first representations.