Distributed processing over networks relies on in-network processing and cooperation among neighboring agents. Cooperation is beneficial when agents share a common objective. However, in many applications agents may belong to different clusters that pursue different objectives. Then, indiscriminate cooperation will lead to undesired results. In this work, we propose an adaptive clustering and learning scheme that allows agents to learn which neighbors they should cooperate with and which other neighbors they should ignore. In doing so, the resulting algorithm enables the agents to identify their clusters and to attain improved learning and estimation accuracy over networks. We carry out a detailed mean-square analysis and assess the error probabilities of Types I and II, i.e., false alarm and mis-detection, for the clustering mechanism. Among other results, we establish that these probabilities decay exponentially with the step-sizes so that the probability of correct clustering can be made arbitrarily close to one.

A difficult task in modeling with Bayesian networks is the elicitation of numerical parameters of Bayesian networks. A large number of parameters is needed to specify a conditional probability table (CPT) that has a larger parent set. In this paper we show that, most CPTs from real applications of Bayesian networks can actually be very well approximated by tables that require substantially less parameters. This observation has practical consequence not only for model elicitation but also for efficient probabilistic reasoning with these networks.

Variational inference is a powerful concept that underlies many iterative approximation algorithms; expectation propagation, mean-field methods and belief propagations were all central themes at the school that can be perceived from this unifying framework. The lectures of Manfred Opper introduce the archetypal example of Expectation Propagation, before establishing the connection with the other approximation methods. Corrections by expansion about the expectation propagation are then explained. Finally some advanced inference topics and applications are explored in the final sections.

Many signal processing and machine learning methods share essentially the same linear-in-the-parameter model, with as many parameters as available samples as in kernel-based machines. Sparse approximation is essential in many disciplines, with new challenges emerging in online learning with kernels. To this end, several sparsity measures have been proposed in the literature to quantify sparse dictionaries and constructing relevant ones, the most prolific ones being the distance, the approximation, the coherence and the Babel measures. In this paper, we analyze sparse dictionaries based on these measures. By conducting an eigenvalue analysis, we show that these sparsity measures share many properties, including the linear independence condition and inducing a well-posed optimization problem. Furthermore, we prove that there exists a quasi-isometry between the parameter (i.e., dual) space and the dictionary's induced feature space.

Many machine learning frameworks, such as resource-allocating networks, kernel-based methods, Gaussian processes, and radial-basis-function networks, require a sparsification scheme in order to address the online learning paradigm. For this purpose, several online sparsification criteria have been proposed to restrict the model definition on a subset of samples. The most known criterion is the (linear) approximation criterion, which discards any sample that can be well represented by the already contributing samples, an operation with excessive computational complexity. Several computationally efficient sparsification criteria have been introduced in the literature, such as the distance, the coherence and the Babel criteria. In this paper, we provide a framework that connects these sparsification criteria to the issue of approximating samples, by deriving theoretical bounds on the approximation errors. Moreover, we investigate the error of approximating any feature, by proposing upper-bounds on the approximation error for each of the aforementioned sparsification criteria. Two classes of features are described in detail, the empirical mean and the principal axes in the kernel principal component analysis.

A new nonparametric approach for system identification has been recently proposed where the impulse response is seen as the realization of a zero--mean Gaussian process whose covariance, the so--called stable spline kernel, guarantees that the impulse response is almost surely stable. Maximum entropy properties of the stable spline kernel have been pointed out in the literature. In this paper we provide an independent proof that relies on the theory of matrix extension problems in the graphical model literature and leads to a closed form expression for the inverse of the first order stable spline kernel as well as to a new factorization in the form $UWU^\top$ with $U$ upper triangular and $W$ diagonal. Interestingly, all first--order stable spline kernels share the same factor $U$ and $W$ admits a closed form representation in terms of the kernel hyperparameter, making the factorization computationally inexpensive. Maximum likelihood properties of the stable spline kernel are also highlighted. These results can be applied both to improve the stability and to reduce the computational complexity associated with the computation of stable spline estimators.

Large-scale annotated corpora are a prerequisite to developing high-performance NLP systems. Such corpora are expensive to produce, limited in size, often demanding linguistic expertise. In this paper we use text rewriting as a means of increasing the amount of labeled data available for model training. Our method uses automatically extracted rewrite rules from comparable corpora and bitexts to generate multiple versions of sentences annotated with gold standard labels. We apply this idea to semantic role labeling and show that a model trained on rewritten data outperforms the state of the art on the CoNLL-2009 benchmark dataset.

Before deploying a software system we need to assure ourselves (and stakeholders) that the system will behave correctly. This assurance is usually done by testing the system. However, it is intuitively obvious that adaptive systems, including agent-based systems, can exhibit complex behaviour, and are thus harder to test. In this paper we examine this "obvious intuition" in the case of Belief-Desire-Intention (BDI) agents. We analyse the size of the behaviour space of BDI agents and show that although the intuition is correct, the factors that influence the size are not what we expected them to be. Specifically, we found that the introduction of failure handling had a much larger effect on the size of the behaviour space than we expected. We also discuss the implications of these findings on the testability of BDI agents.

Diagnosing the execution of a Multiagent Plan (MAP) means identifying and explaining action failures (i.e., actions that did not reach their expected effects). Current approaches to MAP diagnosis are substantially centralized, and assume that action failures are independent of each other. In this paper, the diagnosis of MAPs, executed in a dynamic and partially observable environment, is addressed in a fully distributed and asynchronous way; in addition, action failures are no longer assumed as independent of each other. The paper presents a novel methodology, named Cooperative Weak-Committed Monitoring (CWCM), enabling agents to cooperate while monitoring their own actions. Cooperation helps the agents to cope with very scarcely observable environments: what an agent cannot observe directly can be acquired from other agents. CWCM exploits nondeterministic action models to carry out two main tasks: detecting action failures and building trajectory-sets (i.e., structures representing the knowledge an agent has about the environment in the recent past). Relying on trajectory-sets, each agent is able to explain its own action failures in terms of exogenous events that have occurred during the execution of the actions themselves. To cope with dependent failures, CWCM is coupled with a diagnostic engine that distinguishes between primary and secondary action failures. An experimental analysis demonstrates that the CWCM methodology, together with the proposed diagnostic inferences, are effective in identifying and explaining action failures even in scenarios where the system observability is significantly reduced.

These notes review six lectures given by Prof. Andrea Montanari on the topic of statistical estimation for linear models. The first two lectures cover the principles of signal recovery from linear measurements in terms of minimax risk. Subsequent lectures demonstrate the application of these principles to several practical problems in science and engineering. Specifically, these topics include denoising of error-laden signals, recovery of compressively sensed signals, reconstruction of low-rank matrices, and also the discovery of hidden cliques within large networks. These are notes from the lecture of Andrea Montanari given at the autumn school "Statistical Physics, Optimization, Inference, and Message-Passing Algorithms", that took place in Les Houches, France from Monday September 30th, 2013, till Friday October 11th, 2013.