We revisit the problem of feature selection in linear discriminant analysis (LDA), that is, when features are correlated. First, we introduce a pooled centroids formulation of the multiclass LDA predictor function, in which the relative weights of Mahalanobis-transformed predictors are given by correlation-adjusted $t$-scores (cat scores). Second, for feature selection we propose thresholding cat scores by controlling false nondiscovery rates (FNDR). Third, training of the classifier is based on James--Stein shrinkage estimates of correlations and variances, where regularization parameters are chosen analytically without resampling. Overall, this results in an effective and computationally inexpensive framework for high-dimensional prediction with natural feature selection. The proposed shrinkage discriminant procedures are implemented in the R package ``sda'' available from the R repository CRAN.

In many applications, such as information retrieval or gene ranking, one is given a finite set of data of interest sharing a particular property, and wishes to find other data sharing the same property. In information retrieval, for example, the finite set can be a user query, or a set of documents known to belong to a specific category, and the goal is to scan a large database of documents to identify new documents related to the query or belonging to the same category. In gene ranking, the query is a finite list of genes known to have a given function or to be associated to a given disease, and the goal is to identify new genes sharing the same property (Aerts et al., 2006). In fact this setting is ubiquitous in many applications where identifying a data of interest is difficult or expensive, e.g., because human intervention is necessary or expensive experiments are needed, while unlabeled data can be easily collected. In such cases there is a clear opportunity to alleviate the burden and cost of interesting data identification with the help of machine learning techniques. More formally, let us assign a binary label to each possible data: positive ( 1) for data of interest, negative ( 1) for other data. Unlabeled data are data for which we do not know whether 1 they are interesting or not. Denoting X the set of data, we assume that the "query" is a finite set of data P {x

We present an exact method of greatly speeding up belief propagation (BP) for a wide variety of potential functions in pairwise MRFs and other graphical models. Specifically, our technique applies whenever the pairwise potentials have been {\em truncated} to a constant value for most pairs of states, as is commonly done in MRF models with robust potentials (such as stereo) that impose an upper bound on the penalty assigned to discontinuities; for each of the $M$ possible states in one node, only a smaller number $m$ of compatible states in a neighboring node are assigned milder penalties. The computational complexity of our method is $O(mM)$, compared with $O(M^2)$ for standard BP, and we emphasize that the method is {\em exact}, in contrast with related techniques such as pruning; moreover, the method is very simple and easy to implement. Unlike some previous work on speeding up BP, our method applies both to sum-product and max-product BP, which makes it useful in any applications where marginal probabilities are required, such as maximum likelihood estimation. We demonstrate the technique on a stereo MRF example, confirming that the technique speeds up BP without altering the solution.

This survey paper categorises, compares, and summarises from almost all published technical and review articles in automated fraud detection within the last 10 years. It defines the professional fraudster, formalises the main types and subtypes of known fraud, and presents the nature of data evidence collected within affected industries. Within the business context of mining the data to achieve higher cost savings, this research presents methods and techniques together with their problems. Compared to all related reviews on fraud detection, this survey covers much more technical articles and is the only one, to the best of our knowledge, which proposes alternative data and solutions from related domains.

The paper presents a scheme for computing lower and upper bounds on the posterior marginals in Bayesian networks with discrete variables. Its power lies in its ability to use any available scheme that bounds the probability of evidence or posterior marginals and enhance its performance in an anytime manner. The scheme uses the cutset conditioning principle to tighten existing bounding schemes and to facilitate anytime behavior, utilizing a fixed number of cutset tuples. The accuracy of the bounds improves as the number of used cutset tuples increases and so does the computation time. We demonstrate empirically the value of our scheme for bounding posterior marginals and probability of evidence using a variant of the bound propagation algorithm as a plug-in scheme.

Noisy probabilistic relational rules are a promising world model representation for several reasons. They are compact and generalize over world instantiations. They are usually interpretable and they can be learned effectively from the action experiences in complex worlds. We investigate reasoning with such rules in grounded relational domains. Our algorithms exploit the compactness of rules for efficient and flexible decision-theoretic planning. As a first approach, we combine these rules with the Upper Confidence Bounds applied to Trees (UCT) algorithm based on look-ahead trees. Our second approach converts these rules into a structured dynamic Bayesian network representation and predicts the effects of action sequences using approximate inference and beliefs over world states. We evaluate the effectiveness of our approaches for planning in a simulated complex 3D robot manipulation scenario with an articulated manipulator and realistic physics and in domains of the probabilistic planning competition. Empirical results show that our methods can solve problems where existing methods fail.

We propose a novel reformulation of the stochastic optimal control problem as an approximate inference problem, demonstrating, that such a interpretation leads to new practical methods for the original problem. In particular we characterise a novel class of iterative solutions to the stochastic optimal control problem based on a natural relaxation of the exact dual formulation. These theoretical insights are applied to the Reinforcement Learning problem where they lead to new model free, off policy methods for discrete and continuous problems.

We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed nodes (or variables) are not constrained to be leaf nodes. Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups using so-called information distances. One of the main contributions of this work is our second algorithm, which we refer to as CLGrouping. CLGrouping starts with a pre-processing procedure in which a tree over the observed variables is constructed. This global step groups the observed nodes that are likely to be close to each other in the true latent tree, thereby guiding subsequent recursive grouping (or equivalent procedures) on much smaller subsets of variables. This results in more accurate and efficient learning of latent trees. We also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions. We compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree graphical models such as hidden Markov models and star graphs. In addition, we demonstrate the applicability of our methods on real-world datasets by modeling the dependency structure of monthly stock returns in the S&P index and of the words in the 20 newsgroups dataset.

Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it represents a natural route to understand the dynamics, as well as to synthesize or optimize the functions, of networks. A broad spectrum of network structural patterns have been respectively reported in the past decade, such as communities, multipartites, hubs, authorities, outliers, bow ties, and others. Here, we show that most individual real-world networks demonstrate multiplex structures. That is, a multitude of known or even unknown (hidden) patterns can simultaneously situate in the same network, and moreover they may be overlapped and nested with each other to collaboratively form a heterogeneous, nested or hierarchical organization, in which different connective phenomena can be observed at different granular levels. In addition, we show that the multiplex structures hidden in exploratory networks can be well defined as well as effectively recognized within an unified framework consisting of a set of proposed concepts, models, and algorithms. Our findings provide a strong evidence that most real-world complex systems are driven by a combination of heterogeneous mechanisms that may col-1 laboratively shape their ubiquitous multiplex structures as we observe currently. This work also contributes a mathematical tool for analyzing different sources of networks from a new perspective of unveiling multiplex structures, which will be beneficial to multiple disciplines including sociology, economics and computer science. 1 Introduction Complex network analysis provides a novel approach to examining how networked systems in nature are originated and evolving according to what basic principles, and moreover armed with such discovered principles, constructing efficient, robust as well as flexible man-made networked systems under different constraints.

Inspired by the hierarchical hidden Markov models (HHMM), we present the hierarchical semi-Markov conditional random field (HSCRF), a generalisation of embedded undirectedMarkov chains tomodel complex hierarchical, nestedMarkov processes. It is parameterised in a discriminative framework and has polynomial time algorithms for learning and inference. Importantly, we consider partiallysupervised learning and propose algorithms for generalised partially-supervised learning and constrained inference. We demonstrate the HSCRF in two applications: (i) recognising human activities of daily living (ADLs) from indoor surveillance cameras, and (ii) noun-phrase chunking. We show that the HSCRF is capable of learning rich hierarchical models with reasonable accuracy in both fully and partially observed data cases.