Multidimensional classification (MDC) is the supervised learning problem where an instance is associated with multiple classes, rather than with a single class, as in traditional classification problems. Since these classes are often strongly correlated, modeling the dependencies between them allows MDC methods to improve their performance - at the expense of an increased computational cost. In this paper we focus on the classifier chains (CC) approach for modeling dependencies, one of the most popular and highestperforming methods for multi-label classification (MLC), a particular case of MDC which involves only binary classes (i.e., labels). The original CC algorithm makes a greedy approximation, and is fast but tends to propagate errors along the chain. Our algorithms remain tractable for high-dimensional data sets and obtain the best predictive performance across several real data sets. Keywords: classifier chains, multidimensional classification, multi-label classification, Monte Carlo methods, Bayesian inference 1. Introduction Multidimensional classification (MDC) is the supervised learning problem where an instance may be associated with multiple classes, rather than Preprint submitted to Pattern Recognition March 22, 2018 with a single class as in traditional binary or multi-class single-dimensional classification (SDC) problems. So-called MDC (e.g., in [1]) is also known in the literature as multi-target, multi-output [2], or multi-objective [3] classification The recently popularised task of multi-label classification (see [4, 5, 6, 7] for overviews) can be viewed as a particular case of the multidimensional problem that only involves binary classes, i.e., labels that can be turned on (1) or off (0) for any data instance. The MDC learning context is receiving increased attention in the literature, since it arises naturally in a wide variety of domains, such as image classification [8, 9], information retrieval and text categorization [10], automated detection of emotions in music [11] or bioinformatics [10, 12].

The use of mixture models for clustering, referred to as model-based clustering, has become increasingly popular since the work of Wolfe (1963). A wide variety of finite mixture models has been studied extensively within the literature to date. Amongst these, the Gaussian mixture model has received special attention due to its mathematical tractability and the relative computational simplicity associated with parameter estimation. However, the Gaussian mixture model is not without limitations; for instance, the component densities are restricted to being symmetric.

Stochastic models such as Continuous-Time Markov Chains (CTMC) and Stochastic Hybrid Automata (SHA) are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity inherent in biological processes. A classical question in formal modelling with clear relevance to biological modelling is the model checking problem. i.e. calculate the probability that a behaviour, expressed for instance in terms of a certain temporal logic formula, may occur in a given stochastic process. However, one may not only be interested in the notion of satisfiability, but also in the capacity of a system to mantain a particular emergent behaviour unaffected by the perturbations, caused e.g. from extrinsic noise, or by possible small changes in the model parameters. To address this issue, researchers from the verification community have recently proposed several notions of robustness for temporal logic providing suitable definitions of distance between a trajectory of a (deterministic) dynamical system and the boundaries of the set of trajectories satisfying the property of interest. The contributions of this paper are twofold. First, we extend the notion of robustness to stochastic systems, showing that this naturally leads to a distribution of robustness scores. By discussing two examples, we show how to approximate the distribution of the robustness score and its key indicators: the average robustness and the conditional average robustness. Secondly, we show how to combine these indicators with the satisfaction probability to address the system design problem, where the goal is to optimize some control parameters of a stochastic model in order to best maximize robustness of the desired specifications.

The purpose of this paper is twofold. On one side, we present a general framework for Bayesian optimization and we compare it with some related fields in active learning and Bayesian numerical analysis. On the other hand, Bayesian optimization and related problems (bandits, sequential experimental design) are highly dependent on the surrogate model that is selected. However, there is no clear standard in the literature. Thus, we present a fast and flexible toolbox that allows to test and combine different models and criteria with little effort. It includes most of the state-of-the-art contributions, algorithms and models. Its speed also removes part of the stigma that Bayesian optimization methods are only good for "expensive functions". The software is free and it can be used in many operating systems and computer languages.

Cognitive radio networks (CRNs) are networks of nodes equipped with cognitive radios that can optimize performance by adapting to network conditions. While cognitive radio networks (CRN) are envisioned as intelligent networks, relatively little research has focused on the network level functionality of CRNs. Although various routing protocols, incorporating varying degrees of adaptiveness, have been proposed for CRNs, it is imperative for the long term success of CRNs that the design of cognitive routing protocols be pursued by the research community. Cognitive routing protocols are envisioned as routing protocols that fully and seamless incorporate AI-based techniques into their design. In this paper, we provide a self-contained tutorial on various AI and machine-learning techniques that have been, or can be, used for developing cognitive routing protocols. We also survey the application of various classes of AI techniques to CRNs in general, and to the problem of routing in particular. We discuss various decision making techniques and learning techniques from AI and document their current and potential applications to the problem of routing in CRNs. We also highlight the various inference, reasoning, modeling, and learning sub tasks that a cognitive routing protocol must solve. Finally, open research issues and future directions of work are identified.

A mixture of common skew-t factor analyzers model is introduced for model-based clustering of high-dimensional data. By assuming common component factor loadings, this model allows clustering to be performed in the presence of a large number of mixture components or when the number of dimensions is too large to be well-modelled by the mixtures of factor analyzers model or a variant thereof. Furthermore, assuming that the component densities follow a skew-t distribution allows robust clustering of skewed data. The alternating expectation-conditional maximization algorithm is employed for parameter estimation. We demonstrate excellent clustering performance when our model is applied to real and simulated data.This paper marks the first time that skewed common factors have been used.

In modern data science problems, techniques for extracting value from big data require performing large-scale optimization over heterogenous, irregularly structured data. Much of this data is best represented as multi-relational graphs, making vertex programming abstractions such as those of Pregel and GraphLab ideal fits for modern large-scale data analysis. In this paper, we describe a vertex-programming implementation of a popular consensus optimization technique known as the alternating direction of multipliers (ADMM). ADMM consensus optimization allows elegant solution of complex objectives such as inference in rich probabilistic models. We also introduce a novel hypergraph partitioning technique that improves over state-of-the-art partitioning techniques for vertex programming and significantly reduces the communication cost by reducing the number of replicated nodes up to an order of magnitude. We implemented our algorithm in GraphLab and measure scaling performance on a variety of realistic bipartite graph distributions and a large synthetic voter-opinion analysis application. In our experiments, we are able to achieve a 50% improvement in runtime over the current state-of-the-art GraphLab partitioning scheme.

Classifiers based on probabilistic graphical models are very effective. In continuous domains, maximum likelihood is usually used to assess the predictions of those classifiers. When data is scarce, this can easily lead to overfitting. In any probabilistic setting, Bayesian averaging (BA) provides theoretically optimal predictions and is known to be robust to overfitting. In this work we introduce Bayesian Conditional Gaussian Network Classifiers, which efficiently perform exact Bayesian averaging over the parameters. We evaluate the proposed classifiers against the maximum likelihood alternatives proposed so far over standard UCI datasets, concluding that performing BA improves the quality of the assessed probabilities (conditional log likelihood) whilst maintaining the error rate. Overfitting is more likely to occur in domains where the number of data items is small and the number of variables is large. These two conditions are met in the realm of bioinformatics, where the early diagnosis of cancer from mass spectra is a relevant task. We provide an application of our classification framework to that problem, comparing it with the standard maximum likelihood alternative, where the improvement of quality in the assessed probabilities is confirmed.

We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed acyclic graph describing the relationships between the variables. In Gaussian structural equation models with linear functions, the graph can be identified from the joint distribution only up to Markov equivalence classes, assuming faithfulness. In this work, we prove full identifiability if all noise variables have the same variances: the directed acyclic graph can be recovered from the joint Gaussian distribution. Our result has direct implications for causal inference: if the data follow a Gaussian structural equation model with equal error variances and assuming that all variables are observed, the causal structure can be inferred from observational data only. We propose a statistical method and an algorithm that exploit our theoretical findings.

A Bayesian factor graph reduced to normal form (Forney, 2001) consists in the interconnection of diverter units (or equal constraint units) and Single-Input/Single-Output (SISO) blocks. In this framework localized adaptation rules are explicitly derived from a constrained maximum likelihood (ML) formulation and from a minimum KL-divergence criterion using KKT conditions. The learning algorithms are compared with two other updating equations based on a Viterbi-like and on a variational approximation respectively. The performance of the various algorithm is verified on synthetic data sets for various architectures. The objective of this paper is to provide the programmer with explicit algorithms for rapid deployment of Bayesian graphs in the applications.