Consider a two-class classification problem where the number of features is much larger than the sample size. The features are masked by Gaussian noise with mean zero and covariance matrix $\Sigma$, where the precision matrix $\Omega=\Sigma^{-1}$ is unknown but is presumably sparse. The useful features, also unknown, are sparse and each contributes weakly (i.e., rare and weak) to the classification decision. By obtaining a reasonably good estimate of $\Omega$, we formulate the setting as a linear regression model. We propose a two-stage classification method where we first select features by the method of Innovated Thresholding (IT), and then use the retained features and Fisher's LDA for classification. In this approach, a crucial problem is how to set the threshold of IT. We approach this problem by adapting the recent innovation of Higher Criticism Thresholding (HCT). We find that when useful features are rare and weak, the limiting behavior of HCT is essentially just as good as the limiting behavior of ideal threshold, the threshold one would choose if the underlying distribution of the signals is known (if only). Somewhat surprisingly, when $\Omega$ is sufficiently sparse, its off-diagonal coordinates usually do not have a major influence over the classification decision. Compared to recent work in the case where $\Omega$ is the identity matrix [Proc. Natl. Acad. Sci. USA 105 (2008) 14790-14795; Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 367 (2009) 4449-4470], the current setting is much more general, which needs a new approach and much more sophisticated analysis. One key component of the analysis is the intimate relationship between HCT and Fisher's separation. Another key component is the tight large-deviation bounds for empirical processes for data with unconventional correlation structures, where graph theory on vertex coloring plays an important role.

Many optimization tasks have to be handled in noisy environments, where we cannot obtain the exact evaluation of a solution but only a noisy one. For noisy optimization tasks, evolutionary algorithms (EAs), a kind of stochastic metaheuristic search algorithm, have been widely and successfully applied. Previous work mainly focuses on empirical studying and designing EAs for noisy optimization, while, the theoretical counterpart has been little investigated. In this paper, we investigate a largely ignored question, i.e., whether an optimization problem will always become harder for EAs in a noisy environment. We prove that the answer is negative, with respect to the measurement of the expected running time. The result implies that, for optimization tasks that have already been quite hard to solve, the noise may not have a negative effect, and the easier a task the more negatively affected by the noise. On a representative problem where the noise has a strong negative effect, we examine two commonly employed mechanisms in EAs dealing with noise, the re-evaluation and the threshold selection strategies. The analysis discloses that the two strategies, however, both are not effective, i.e., they do not make the EA more noise tolerant. We then find that a small modification of the threshold selection allows it to be proven as an effective strategy for dealing with the noise in the problem.

Name Reference Comments KS Koller and Sahami (1996) - Not Sound - The first one of this type - Requires specifying MB size in advance GS Margaritis and Thrun (2000) - Sound in theory - Proposed to learn Bayesian network via the induction of neighbors of each variable - First proved such kind of algorithm - Works in two phases: grow and shrink IAMB and its variants Tsamardinos et al (2003) - Sound in theory - Actually variant of GS - Simple to implement - Time efficient - Very poor on data efficiency - IAMB's variants achieve better performance on data efficiency than IAMB HITON-PC/MB Aliferis et al (2003) - Not sound - Another trial to make use of the topology information to enhance data efficiency - Data efficiency comparable to IAMB - Much slower compared to IAMB Fast-IAMB Yaramakala and Margaritis (2005) - Sound in theory - No fundamental difference as compared to IAMB - Adds candidates more greedily to speed up the learning - Still poor on data efficiency performance MMPC/MB Tsamardinos et al (2006) - Not sound - The first to make use of the underling topology information - Much more data efficient compared to IAMB - Much slower compared to IAMB PCMB Peña et al (2007) - Sound in theory - Data efficient by making use of topology information - Poor on time efficiency - Distinguish spouses from parents/children - Distinguish some children from parents/children IPC-MB Fu and Desmarais (2008) - Sound in theory - Most data efficient compared with previous algorithms - Much faster than PCMB on computing - Distinguish spouses from parents/children - Distinguish some children from parents/children - Best tradeoff among this family of algorithms

Symmetric binary matrices representing relations among entities are commonly collected in many areas. Our focus is on dynamically evolving binary relational matrices, with interest being in inference on the relationship structure and prediction. We propose a nonparametric Bayesian dynamic model, which reduces dimensionality in characterizing the binary matrix through a lower-dimensional latent space representation, with the latent coordinates evolving in continuous time via Gaussian processes. By using a logistic mapping function from the probability matrix space to the latent relational space, we obtain a flexible and computational tractable formulation. Employing P\`olya-Gamma data augmentation, an efficient Gibbs sampler is developed for posterior computation, with the dimension of the latent space automatically inferred. We provide some theoretical results on flexibility of the model, and illustrate performance via simulation experiments. We also consider an application to co-movements in world financial markets.

The sigma point (SP) filter, also known as unscented Kalman filter, is an attractive alternative to the extended Kalman filter and the particle filter. Here, we extend the SP filter to nonsequential Bayesian inference corresponding to loopy factor graphs. We propose sigma point belief propagation (SPBP) as a low-complexity approximation of the belief propagation (BP) message passing scheme. SPBP achieves approximate marginalizations of posterior distributions corresponding to (generally) loopy factor graphs. It is well suited for decentralized inference because of its low communication requirements. For a decentralized, dynamic sensor localization problem, we demonstrate that SPBP can outperform nonparametric (particle-based) BP while requiring significantly less computations and communications.

In recent years, Stackelberg Security Games have been successfully applied to solve resource allocation and scheduling problems in several security domains. However, previous work has mostly assumed that the targets are stationary relative to the defender and the attacker, leading to discrete game models with finite numbers of pure strategies. This paper in contrast focuses on protecting mobile targets that leads to a continuous set of strategies for the players. The problem is motivated by several real-world domains including protecting ferries with escort boats and protecting refugee supply lines. Our contributions include: (i) A new game model for multiple mobile defender resources and moving targets with a discretized strategy space for the defender and a continuous strategy space for the attacker.

Algorithmic composition is the partial or total automation of the process of music composition by using computers. Since the 1950s, different computational techniques related to Artificial Intelligence have been used for algorithmic composition, including grammatical representations, probabilistic methods, neural networks, symbolic rule-based systems, constraint programming and evolutionary algorithms. This survey aims to be a comprehensive account of research on algorithmic composition, presenting a thorough view of the field for researchers in Artificial Intelligence.

Many real-world problem domains generate data in the form of graphs or networks. Examples include social networks (e.g., Facebook), recommendation services (e.g., Netflix or Last.fm), biochemical networks, citation graphs and market analysis. The inferential problem in these settings is often one of link prediction. This problem can be formulated in a static setting where one assumes that a fixed but unknown graph is partially observed, and one wishes to assess whether a pair of nodes that are not known to be linked are in fact linked, given an observed linkage pattern among other nodes. Many real-world graphs are often best modeled, however, as dynamic entities, where links can arise and disappear over time. In the dynamic setting the link prediction problem involves assessing whether two nodes will be linked at time t given the linkage patterns at all previous times. Real-world graphs of current interest are often very large, involving many hundreds of thousands or millions of nodes. The dynamic setting involves sequences of such graphs.

This paper outlines some of the inherent difficulties present in large-scale standards-based semantic interoperability in the Oil and Gas industry. This domain in particularly interesting for semantic interoperability, as the complexity is manifold: data sets are large, span many different domains, are modeled and represented differently in various standards, which have evolved considerably over time. We outline the main challenges with respect to sustained interoperability and advocate that the interoperability scenarios could serve as an interesting test bed for evaluating semantic interoperability techniques.

The ability to understand behaviour is a crucial skill for Artificial Intelligence systems that are expected to interact with external agents such as humans or other AI systems. Such systems might be expected to operate in co-operative or team-based scenarios, such as domestic robots capable of helping out with household jobs, or disaster relief robots expected to collaborate and lend assistance to others. Conversely, they may also be required to hinder the activities of malicious agents in adversarial scenarios. In this paper we address the problem of modelling agent behaviour in domains expressed in continuous, quantitative space by applying qualitative, relational spatial abstraction techniques. We employ three common techniques for Qualitative Spatial Reasoning — the Region Connection Calculus, the Qualitative Trajectory Calculus and the Star calculus. We then supply an algorithm based on analysis of Mutual Information that allows us to find the set of abstract, spatial relationships that provide high degrees of information about an agent's future behaviour. We employ the RoboCup soccer simulator as a base for movement-based tasks of our own design and compare the predictions of our system against those of systems utilising solely metric representations. Results show that use of a spatial abstraction-based representation, along with feature selection mechanisms, allows us to outperform metric representations on the same tasks.