arXiv subjects

Jacopo Diquigiovanni

Publications and source records attributed to Jacopo Diquigiovanni.

7 recordsLinked to original sources

arXiv2024

Distribution-Free Prediction Bands for Multivariate Functional Time Series: an Application to the Italian Gas Market

Uncertainty quantification in forecasting represents a topic of great importance in energy trading, as understanding the status of the energy market would enable traders to directly evaluate the impact of their own offers/bids. To this end, we propose a scalable procedure that outputs closed-form simultaneous prediction bands for multivariate functional response variables in a time series setting, which is able to guarantee performance bounds in terms of unconditional coverage and asymptotic exactness, both under some conditions. After evaluating its performance on synthetic data, the method is used to build multivariate prediction bands for daily demand and offer curves in the Italian gas market.

stat.ME↗

arXiv2023

Conformal Prediction Bands for Two-Dimensional Functional Time Series

Time evolving surfaces can be modeled as two-dimensional Functional time series, exploiting the tools of Functional data analysis. Leveraging this approach, a forecasting framework for such complex data is developed. The main focus revolves around Conformal Prediction, a versatile nonparametric paradigm used to quantify uncertainty in prediction problems. Building upon recent variations of Conformal Prediction for Functional time series, a probabilistic forecasting scheme for two-dimensional functional time series is presented, while providing an extension of Functional Autoregressive Processes of order one to this setting. Estimation techniques for the latter process are introduced and their performance are compared in terms of the resulting prediction regions. Finally, the proposed forecasting procedure and the uncertainty quantification technique are applied to a real dataset, collecting daily observations of Sea Level Anomalies of the Black Sea

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arXiv2022

On the dependence in football match outcomes: traditional model assumptions and an alternative proposal

The approaches routinely used to model the outcomes of football matches are characterised by strong assumptions about the dependence between the number of goals scored by the two competing teams and their marginal distribution. In this work, we argue that the assumptions traditionally made are not always based on solid arguments. Although most of these assumptions have been relaxed in the recent literature, the model introduced by Dixon and Coles in 1997 still represents a point of reference in the betting industry. While maintaining its conceptual simplicity, we propose a modification of the dependence structure. A real data application suggests that our model, named Mar-Co, outperforms the Dixon and Coles one in several betting scenarios, and parameter interpretation provides key insights on league dynamics.

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arXiv2022

conformalInference.multi and conformalInference.fd: Twin Packages for Conformal Prediction

Building on top of a regression model, Conformal Prediction methods produce distribution free prediction sets, requiring only i.i.d. data. While R packages implementing such methods for the univariate response framework have been developed, this is not the case with multivariate and functional responses. conformalInference.multi and conformalInference.fd address this void, by extending classical and more advanced conformal prediction methods like full conformal, split conformal, jackknife+ and multi split conformal to deal with the multivariate and functional case. The extreme flexibility of conformal prediction, fully embraced by the structure of the package, which does not require any specific regression model, enables users to pass in any regression function as input while using basic regression models as reference. Finally, the issue of visualisation is addressed by providing embedded plotting functions to visualize prediction regions.

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arXiv2021

Conformal Prediction Bands for Multivariate Functional Data

Motivated by the pressing request of methods able to create prediction sets in a general regression framework for a multivariate functional response and pushed by new methodological advancements in non-parametric prediction for functional data, we propose a set of conformal predictors that produce finite-sample either valid or exact multivariate simultaneous prediction bands under the mild assumption of exchangeable regression pairs. The fact that the prediction bands can be built around any regression estimator and that can be easily found in closed form yields a very widely usable method, which is fairly straightforward to implement. In addition, we first introduce and then describe a specific conformal predictor that guarantees an asymptotic result in terms of efficiency and inducing prediction bands able to modulate their width based on the local behavior and magnitude of the functional data. The method is investigated and analyzed through a simulation study and a real-world application in the field of urban mobility.

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arXiv2021

The Importance of Being a Band: Finite-Sample Exact Distribution-Free Prediction Sets for Functional Data

Functional Data Analysis represents a field of growing interest in statistics. Despite several studies have been proposed leading to fundamental results, the problem of obtaining valid and efficient prediction sets has not been thoroughly covered. Indeed, the great majority of methods currently in the literature rely on strong distributional assumptions (e.g, Gaussianity), dimension reduction techniques and/or asymptotic arguments. In this work, we propose a new nonparametric approach in the field of Conformal Prediction based on a new family of nonconformity measures inducing conformal predictors able to create closed-form finite-sample valid or exact prediction sets under very minimal distributional assumptions. In addition, our proposal ensures that the prediction sets obtained are bands, an essential feature in the functional setting that allows the visualization and interpretation of such sets. The procedure is also fast, scalable, does not rely on functional dimension reduction techniques and allows the user to select different nonconformity measures depending on the problem at hand always obtaining valid bands. Within this family of measures, we propose also a specific measure leading to prediction bands asymptotically no less efficient than those with constant width.

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arXiv2019

Analysis of association football playing styles: an innovative method to cluster networks

In this work we develop an innovative hierarchical clustering method to divide a sample of undirected weighted networks into groups. The methodology consists of two phases: the first phase is aimed at putting the single networks in a broader framework by including the characteristics of the population in the data, while the second phase creates a subdivision of the sample on the basis of the similarity between the community structures of the processed networks. Starting from the representation of the team's playing style as a network, we apply the method to group the Italian Serie A teams' performances and consequently detect the main 15 tactics shown during the 2015-2016 season. The information obtained is used to verify the effect of the styles of play on the number of goals scored, and we prove the key role of one of them by implementing an extension of the Dixon and Coles model (Dixon and Coles, 1997).

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