Gabriele Maroni

Gabriele Maroni, Loris Cannelli, Dario Piga

Common regularization algorithms for linear regression, such as LASSO and Ridge regression, rely on a regularization hyperparameter that balances the tradeoff between minimizing the fitting error and the norm of the learned model coefficients. As this hyperparameter is scalar, it can be easily selected via random or grid search optimizing a cross-validation criterion. However, using a scalar hyperparameter limits the algorithm's flexibility and potential for better generalization. In this paper, we address the problem of linear regression with l2-regularization, where a different regularization hyperparameter is associated with each input variable. We optimize these hyperparameters using a gradient-based approach, wherein the gradient of a cross-validation criterion with respect to the regularization hyperparameters is computed analytically through matrix differential calculus. Additionally, we introduce two strategies tailored for sparse model learning problems aiming at reducing the risk of overfitting to the validation data. Numerical examples demonstrate that our multi-hyperparameter regularization approach outperforms LASSO, Ridge, and Elastic Net regression. Moreover, the analytical computation of the gradient proves to be more efficient in terms of computational time compared to automatic differentiation, especially when handling a large number of input variables. Application to the identification of over-parameterized Linear Parameter-Varying models is also presented.

Raffaele Giuseppe Cestari, Gabriele Maroni, Loris Cannelli et al.

The calibration and training of a neural network is a complex and time-consuming procedure that requires significant computational resources to achieve satisfactory results. Key obstacles are a large number of hyperparameters to select and the onset of overfitting in the face of a small amount of data. In this framework, we propose an innovative training strategy for feed-forward architectures - called split-boost - that improves performance and automatically includes a regularizing behaviour without modeling it explicitly. Such a novel approach ultimately allows us to avoid explicitly modeling the regularization term, decreasing the total number of hyperparameters and speeding up the tuning phase. The proposed strategy is tested on a real-world (anonymized) dataset within a benchmark medical insurance design problem.

Dario Piga, Matteo Rufolo, Gabriele Maroni et al.

This paper addresses the challenge of overfitting in the learning of dynamical systems by introducing a novel approach for the generation of synthetic data, aimed at enhancing model generalization and robustness in scenarios characterized by data scarcity. Central to the proposed methodology is the concept of knowledge transfer from systems within the same class. Specifically, synthetic data is generated through a pre-trained meta-model that describes a broad class of systems to which the system of interest is assumed to belong. Training data serves a dual purpose: firstly, as input to the pre-trained meta model to discern the system's dynamics, enabling the prediction of its behavior and thereby generating synthetic output sequences for new input sequences; secondly, in conjunction with synthetic data, to define the loss function used for model estimation. A validation dataset is used to tune a scalar hyper-parameter balancing the relative importance of training and synthetic data in the definition of the loss function. The same validation set can be also used for other purposes, such as early stopping during the training, fundamental to avoid overfitting in case of small-size training datasets. The efficacy of the approach is shown through a numerical example that highlights the advantages of integrating synthetic data into the system identification process.