Person: Leonelli, Manuele
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Manuele
Last Name
Leonelli
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IE University
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IE School of Science & Technology
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Computer Science and AI
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Publication A geometric characterization of sensitivity analysis in monomial models(Elsevier Inc., 2022) Riccomagno, Eva; Leonelli, Manuele; https://ror.org/02jjdwm75Sensitivity analysis in probabilistic discrete graphical models is usually conducted by varying one probability at a time and observing how this affects output probabilities of interest. When one probability is varied,then others are proportionally covaried to respect the sum-to-one condition of probabilities. The choice of proportional covariation is justified by multiple optimality conditions,under which the original and the varied distributions are as close as possible under different measures. For variations of more than one parameter at a time and for the large class of discrete statistical models entertaining a regular monomial parametrisation,we demonstrate the optimality of newly defined proportional multi-way schemes with respect to an optimality criterion based on the I-divergence. We demonstrate that there are varying parameters' choices for which proportional covariation is not optimal and identify the sub-family of distributions where the distance between the original distribution and the one where probabilities are covaried proportionally is minimum. This is shown by adopting a new geometric characterization of sensitivity analysis in monomial models,which include most probabilistic graphical models. We also demonstrate the optimality of proportional covariation for multi-way analyses in Naive Bayes classifiers. © 2022 The Author(s)Publication Sensitivity and robustness analysis in Bayesian networks with the bnmonitor R package(Elsevier, 2023-10-25) Leonelli, Manuele; Ramanathan, Ramsiya; Wilkerson, Rachel; https://ror.org/02jjdwm75Bayesian networks are a class of models that are widely used for the diagnosis, prediction, and risk assessment of complex operational systems. Multiple approaches, as well as implemented software, now guide their construction via learning from data or expert elicitation. However, current software only includes minimal functionalities to explore the assumptions, quality of fit, and sensitivity to learned parameters of a constructed Bayesian network. Here, we illustrate the usage of the bnmonitor R package: the first comprehensive software for model-checking of a Bayesian network. An applied data analysis using bnmonitor is carried out over a medical dataset to illustrate the use of its wide array of functions.Publication Model-Preserving Sensitivity Analysis for Families of Gaussian Distributions(JMLR, 2020) Leonelli, Manuele; G¨orgen, Christiane; Peter Spirtes; https://ror.org/02jjdwm75The accuracy of probability distributions inferred using machine-learning algorithms heavily depends on data availability and quality. In practical applications it is therefore fundamental to investigate the robustness of a statistical model to misspecification of some of its underlying probabilities. In the context of graphical models, investigations of robustness fall under the notion of sensitivity analyses. These analyses consist in varying some of the model’s probabilities or parameters and then assessing how far apart the original and the varied distributions are. However, for Gaussian graphical models, such variations usually make the original graph an incoherent representation of the model’s conditional independence structure. Here we develop an approach to sensitivity analysis which guarantees the original graph remains valid after any probability variation and we quantify the effect of such variations using different measures. To achieve this we take advantage of algebraic techniques to both concisely represent conditional independence and to provide a straightforward way of checking the validity of such relationships. Our methods are demonstrated to be robust and comparable to standard ones, which can break the conditional independence structure of the model, using an artificial example and a medical real-world application.Publication A change-point approach for the identification of financial extreme regimes(Project euclid, 2021-11) Leonelli, Manuele; Lattanzi, ChiaraInference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme value mixture models have been defined to estimate the threshold using the full dataset and to give accurate tail estimates. Such models assume that the tail behavior is constant for all observations. However, the extreme behavior of financial returns often changes considerably in time and such changes occur by sudden shocks of the market. Here the extreme value mixture model class is extended to formally take into account distributional extreme change-points, by allowing for the presence of regime-dependent parameters modelling the tail of the distribution. This extension formally uses the full dataset to both estimate the thresholds and the extreme changepoint locations, giving uncertainty measures for both quantities. Estimation of functions of interest in extreme value analyses is performed via MCMC algorithms. Our approach is evaluated through a series of simulations, applied to real data sets and assessed against competing approaches. Evidence demonstrates that the inclusion of different extreme regimes outperforms both static and dynamic competing approaches in financial applications.Publication The R Package stagedtrees for Structural Learning of Stratified Staged Trees(Stratified Staged Trees, 2022-04) Leonelli, Manuele; Carli, Federico; Riccomagno, Eva; Varando, Gherardo; https://ror.org/02jjdwm75Stagedtrees is an R package which includes several algorithms for learning the structure of staged trees and chain event graphs from data. Score-based and clustering-based algorithms are implemented, as well as various functionalities to plot the models and perform inference. The capabilities of stagedtrees are illustrated using mainly two datasets both included in the package or bundled in RPublication The curved exponential family of a staged tree(Project euclid, 2022-04-08) Leonelli, Manuele; G¨orgen, Christiane; Marigliano, Orlando; https://ror.org/02jjdwm75Staged tree models are a discrete generalization of Bayesian networks. We show that these form curved exponential families and derive their natural parameters, sufficient statistic, and cumulant-generating function as functions of their graphical representation. We give necessary and sufficient graphical criteria for classifying regular subfamilies and discuss implications for model selection.Publication A geometric characterization of sensitivity analysis in monomial models(Elsevier, 2022-12) Leonelli, Manuele; Riccomagno, Eva; https://ror.org/02jjdwm75Sensitivity analysis in probabilistic discrete graphical models is usually conducted by varying one probability at a time and observing how this affects output probabilities of interest. When one probability is varied, then others are proportionally covaried to respect the sum-to-one condition of probabilities. The choice of proportional covariation is justified by multiple optimality conditions, under which the original and the varied distributions are as close as possible under different measures. For variations of more than one parameter at a time and for the large class of discrete statistical models entertaining a regular monomial parametrisation, we demonstrate the optimality of newly defined proportional multi-way schemes with respect to an optimality criterion based on the I-divergence. We demonstrate that there are varying parameters’ choices for which proportional covariation is not optimal and identify the sub-family of distributions where the distance between the original distribution and the one where probabilities are covaried proportionally is minimum. This is shown by adopting a new geometric characterization of sensitivity analysis in monomial models, which include most probabilistic graphical models. We also demonstrate the optimality of proportional covariation for multi-way analyses in Naive Bayes classifiers.