Emiliano Torre


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Torre

First Name

Emiliano

ORCID

0000-0001-8263-9278

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20196
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Publications 1 - 6 of 6
  • Vine copulas for uncertainty quantification: why and how
    Item type: Other Conference Item
    Torre, Emiliano; Marelli, Stefano; Embrechts, Paul; et al. (2019)
    Systems subject to uncertain inputs produce uncertain responses. Uncertainty quantification (UQ) deals with the estimation of the response statistics of systems for which a runnable computational model is available. Problems of interest are those where the computational model is expensive, making Monte Carlo approaches unfeasible and thus calling for cheaper solutions that require fewer runs. In these settings, an accurate representation of the input statistics, including their mutual dependencies, is critical to obtain accurate output estimates. For instance, tail dependencies among the inputs may strongly affect failure probabilities in reliability analysis. Failing to capture such forms of correlations may render accurate estimation of the output statistics hopeless, regardless of the UQ method used to carry out the analysis. The last decade saw a remarkable extension of copula models that can be effectively used to describe multivariate dependence. Among these models, copulas built by tensor product of simple pair copulas (so-called vine copulas) enable a very flexible representation of high-order dependencies [1,2]. In parallel, novel methods have been proposed to perform inference on these copula models. Here we illustrate how these relatively recent advances in copula modeling can be easily combined with virtually any UQ analysis [3], including those methods that assume the input to have a specific multivariate distribution (such as independent inputs). We showcase the approach on a variety of examples, spanning different simulated problems as well as different UQ techniques used to solve them. The analyses are fully carried out with the UQLab toolbox [4], whose simple syntax is also illustrated. [1] T. Bedford and R.M. Cooke (2002) Vines - A new graphical model for dependent random variables. The Annals of Statistics 30(4): 1031-1068. [2] K. Aas, C. Czado, A. Frigessi and H. Bakken (2009) Pair-Copula constructions of multiple dependence. Insurance, Mathematics and Economics 44:182-198. [3] E. Torre, S. Marelli, P. Embrechts and B. Sudret (2019). A general framework for data-driven uncertainty quantification under complex input dependencies using vine copulas. Probabilistic Engineering Mechanics (55): 1-16. [4] S. Marelli and B. Sudret (2014) UQLab: A framework for uncertainty quantification in Matlab. In: Vulnerability, Uncertainty, and Risk (Proc. 2nd Int. Conf. on Vulnerability, Risk Analysis and Management {(ICVRAM2014), Liverpool, United Kingdom)}, chapter 257: 2554-2563
  • A general framework for data-driven uncertainty quantification under complex input dependencies using vine copulas
    Item type: Journal Article
    Torre, Emiliano; Marelli, Stefano; Embrechts, Paul; et al. (2019)
    Probabilistic Engineering Mechanics
  • 3d-SPADE: Significance evaluation of spatio-temporal patterns of various temporal extents
    Item type: Journal Article
    Stella, Alessandra; Quaglio, Pietro; Torre, Emiliano; et al. (2019)
    Biosystems
    The Spike Pattern Detection and Evaluation (SPADE) analysis is a method to find reoccurring spike patterns in parallel spike train data, and to determine their statistical significance. Here we introduce an extension of the original statistical testing procedure which explicitly accounts for the temporal duration of the patterns. The extension improves the performance in the presence of patterns with different durations, as here demonstrated by application to various synthetic data. We further introduce an implementation of SPADE in form of a sub-module of the Python library Elephant (ELEctroPHysiological ANalysis Toolkit). The code is made publicly available on GitHub, together with detailed documentation, tutorials, and the results presented here.
  • Representation and Inference of Complex dependencies through copulas in UQLab
    Item type: Other Conference Item
    Torre, Emiliano; Marelli, Stefano; Sudret, Bruno (2019)
  • Data-driven polynomial chaos expansion for machine learning regression
    Item type: Journal Article
    Torre, Emiliano; Marelli, Stefano; Embrechts, Paul; et al. (2019)
    Journal of Computational Physics
  • Surrogate modelling meets machine learning
    Item type: Other Conference Item
    Sudret, Bruno; Lataniotis, Christos; Lüthen, Nora; et al. (2019)
    Complex computational models are used nowadays in all fields of applied sciences to predict the behaviour of natural, economic and engineering systems. High-fidelity simulators are able to capture more and more realistic features by including multi-scale or multi-physics aspects in their governing equations, which can result in high complexity. Although computer power has attained unprecedented levels, it is still not possible to use brute force approaches such as Monte Carlo simulation for solving uncertainty propagation, sensitivity or optimization problems with those models. This is the reason why surrogate models such as polynomial chaos expansions (PCE) or Gaussian processes (GP), among others, have gained a lot of attention in the past two decades. In parallel, machine learning and in particular deep neural networks have shown tremendous performance in solving dedicated problems such as image classification or natural language processing. This has raised a lot of interest in the uncertainty quantification community, too. In this lecture, we advocate a sound cross-fertilization of the two worlds. The links between surrogate modelling and supervised learning are first underlined. We show that sparse polynomial chaos expansions can be used as a supervised learning technique in a pure data-driven sense. Through various examples, we show that their predicting capabilities are comparable to, or in some cases better, than neural networks and support vector regression, especially in the context of small data sets. In a second part, we address problems with high-dimensional input vectors for which standard PCE or GP techniques cannot be straightforwardly applied. In this context, we devise an optimal coupling strategy between dimensionality reduction techniques borrowed from machine learning and standard surrogate modelling. This allows us to develop surrogates for computational models where inputs are large time series or maps. We illustrate the performance of this approach on examples in heat conduction and wind turbine dynamics.
Publications 1 - 6 of 6