Natural gas is the most important energy source in Italy: it fuels thermoelectric power plants, industrial facilities and domestic heating. Gas demand forecasting is a critical task for any energy provider as it impacts on pipe reservation and stock planning. In this paper, the one-day-ahead forecasting of Italian daily residential gas demand is studied. Five predictors are developed and compared: Ridge Regression, Gaussian Process, k-Nearest Neighbour, Artificial Neural Network, and Torus Model. Preprocessing and feature selection are also discussed in detail. Concerning the prediction error, a theoretical bound on the best achievable root mean square error is worked out assuming ideal conditions, except for the inaccuracy of meteorological temperature forecasts, whose effects are properly propagated. The best predictors, namely the Artificial Neural Network and the Gaussian Process, achieve an RMSE which is twice the performance limit, suggesting that precise predictions of residential gas demand can be achieved at country level.

Forecasting natural gas demand is a key problem for energy providers, as it allows for efficient pipe reservation and power plant allocation, and enables effective price forecasting. We propose a study of Italian gas demand, with particular focus on industrial and thermoelectric components. To the best of our knowledge, this is the first work about these topics. After a preliminary discussion on the characteristics of gas demand, we apply several statistical learning models to perform day-ahead forecasting, including regularized linear models, random forest, support vector regression and neural networks. Moreover, we introduce four simple ensemble models and we compare their performance with the one of basic forecasters. The out-of-sample Mean Absolute Error (MAE) achieved on 2017 by our best ensemble model is 5.16 Millions of Standard Cubic Meters (MSCM), lower than 9.57 MSCM obtained by the predictions issued by SNAM, the Italian Transmission System Operator (TSO).

In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional hyperparameters which need to be tuned in order to achieve optimum predictive performance; this operation can be efficiently performed in an Empirical Bayes fashion by maximizing the posterior marginal likelihood of the observed data. Since the score function of this optimization problem is in general characterized by the presence of local optima, it is necessary to resort to global optimization strategies, which require a large number of function evaluations. Given that the evaluation is usually computationally intensive and badly scaled with respect to the dataset size, the maximum number of observations that can be treated simultaneously is quite limited. In this paper, we consider the case of hyperparameter tuning in Gaussian process regression. A straightforward implementation of the posterior log-likelihood for this model requires O(N^3) operations for every iteration of the optimization procedure, where N is the number of examples in the input dataset. We derive a novel set of identities that allow, after an initial overhead of O(N^3), the evaluation of the score function, as well as the Jacobian and Hessian matrices, in O(N) operations. We prove how the proposed identities, that follow from the eigendecomposition of the kernel matrix, yield a reduction of several orders of magnitude in the computation time for the hyperparameter optimization problem. Notably, the proposed solution provides computational advantages even with respect to state of the art approximations that rely on sparse kernel matrices.

A client-server architecture to simultaneously solve multiple learning tasks from distributed datasets is described. In such architecture, each client is associated with an individual learning task and the associated dataset of examples. The goal of the architecture is to perform information fusion from multiple datasets while preserving privacy of individual data. The role of the server is to collect data in real-time from the clients and codify the information in a common database. The information coded in this database can be used by all the clients to solve their individual learning task, so that each client can exploit the informative content of all the datasets without actually having access to private data of others. The proposed algorithmic framework, based on regularization theory and kernel methods, uses a suitable class of mixed effect kernels. The new method is illustrated through a simulated music recommendation system.