Classification Loss Function for Parameter Ensembles in Bayesian Hierarchical Models

Parameter ensembles or sets of point estimates constitute one of the cornerstones of modern statistical practice. This is especially the case in Bayesian hierarchical models, where different decision-theoretic frameworks can be deployed to summarize such parameter ensembles. The estimation of these parameter ensembles may thus substantially vary depending on which inferential goals are prioritised by the modeller. In this note, we consider the problem of classifying the elements of a parameter ensemble above or below a given threshold. Two threshold classification losses (TCLs) --weighted and unweighted-- are formulated. The weighted TCL can be used to emphasize the estimation of false positives over false negatives or the converse. We prove that the weighted and unweighted TCLs are optimized by the ensembles of unit-specific posterior quantiles and posterior medians, respectively. In addition, we relate these classification loss functions on parameter ensembles to the concepts of posterior sensitivity and specificity. Finally, we find some relationships between the unweighted TCL and the absolute value loss, which explain why both functions are minimized by posterior medians.Comment: Submitted to Probability and Statistics Letter

Estimating development effort in free/open source software projects by mining software repositories: A case study of OpenStack

Because of the distributed and collaborative nature of free/open source software (FOSS) projects, the development effort invested in a project is usually unknown, even after the software has been released. However, this information is becoming of major interest, especially-but not only-because of the growth in the number of companies for which FOSS has become relevant for their business strategy. In this paper we present a novel approach to estimate effort by considering data from source code management repositories. We apply our model to the OpenStack project, a FOSS project with more than 1,000 authors, in which several tens of companies cooperate. Based on data from its repositories and together with the input from a survey answered by more than 100 developers, we show that the model offers a simple, but sound way of obtaining software development estimations with bounded margins of error.Gregorio Robles, Carlos Cervig on and Jes us M. Gonz alez-Barahona, project SobreSale (TIN2011-28110). and The work of Daniel Izquierdo has been funded in part by the Torres Quevedo program (PTQ-12-05577

An Ensemble Model of QSAR Tools for Regulatory Risk Assessment

Quantitative structure activity relationships (QSARs) are theoretical models that relate a quantitative measure of chemical structure to a physical property or a biological effect. QSAR predictions can be used for chemical risk assessment for protection of human and environmental health, which makes them interesting to regulators, especially in the absence of experimental data. For compatibility with regulatory use, QSAR models should be transparent, reproducible and optimized to minimize the number of false negatives. In silico QSAR tools are gaining wide acceptance as a faster alternative to otherwise time-consuming clinical and animal testing methods. However, different QSAR tools often make conflicting predictions for a given chemical and may also vary in their predictive performance across different chemical datasets. In a regulatory context, conflicting predictions raise interpretation, validation and adequacy concerns. To address these concerns, ensemble learning techniques in the machine learning paradigm can be used to integrate predictions from multiple tools. By leveraging various underlying QSAR algorithms and training datasets, the resulting consensus prediction should yield better overall predictive ability. We present a novel ensemble QSAR model using Bayesian classification. The model allows for varying a cut-off parameter that allows for a selection in the desirable trade-off between model sensitivity and specificity. The predictive performance of the ensemble model is compared with four in silico tools (Toxtree, Lazar, OECD Toolbox, and Danish QSAR) to predict carcinogenicity for a dataset of air toxins (332 chemicals) and a subset of the gold carcinogenic potency database (480 chemicals). Leave-one-out cross validation results show that the ensemble model achieves the best trade-off between sensitivity and specificity (accuracy: 83.8 % and 80.4 %, and balanced accuracy: 80.6 % and 80.8 %) and highest inter-rater agreement [kappa (κ): 0.63 and 0.62] for both the datasets. The ROC curves demonstrate the utility of the cut-off feature in the predictive ability of the ensemble model. This feature provides an additional control to the regulators in grading a chemical based on the severity of the toxic endpoint under study