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The PC algorithm is a popular method for learning the structure of Gaussian Bayesian networks. It carries out statistical tests to determine absent edges in the network. It is hence governed by two parameters: (i) The type of test, and (ii) its significance level. These parameters are usually set to values recommended by an expert. Nevertheless, such an approach can suffer from human bias, leading to suboptimal reconstruction results. In this paper we consider a more principled approach for choosing these parameters in an automatic way. For this we optimize a reconstruction score evaluated on a set of different Gaussian Bayesian networks. This objective is expensive to evaluate and lacks a closed-form expression, which means that Bayesian optimization (BO) is a natural choice. BO methods use a model to guide the search and are hence able to exploit smoothness properties of the objective surface. We show that the parameters found by a BO method outperform those found by a random search strategy and the expert recommendation. Importantly, we have found that an often overlooked statistical test provides the best over-all reconstruction results.

We propose a novel Metropolis-Hastings algorithm to sample uniformly from the space of correlation matrices. Existing methods in the literature are based on elaborated representations of a correlation matrix, or on complex parametrizations of it. By contrast, our method is intuitive and simple, based the classical Cholesky factorization of a positive definite matrix and Markov chain Monte Carlo theory. We perform a detailed convergence analysis of the resulting Markov chain, and show how it benefits from fast convergence, both theoretically and empirically. Furthermore, in numerical experiments our algorithm is shown to be significantly faster than the current alternative approaches, thanks to its simple yet principled approach.

Esta es la versión de autor de la comunicación de congreso publicada en: This is an author produced version of a paper published in: ABSTRACTThis paper describes a new modelling language for the effective design of Java annotations. Since their inclusion in the 5th edition of Java, annotations have grown from a useful tool for the addition of meta-data to play a central role in many popular software projects. Usually they are conceived as sets with dependency and integrity constraints within them; however, the native support provided by Java for expressing this design is very limited.To overcome its deficiencies and make explicit the rich conceptual model which lies behind a set of annotations, we propose a domain-specific modelling language.The proposal has been implemented as an Eclipse plugin, including an editor and an integrated code generator that synthesises annotation processors. The language has been tested using a real set of annotations from the Java Persistence API (JPA). It has proven to cover a greater scope with respect to other related work in different shared areas of application.

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