Neural networks present characteristics where the results are strongly dependent on the training data, the weight initialisation, and the hyperparameters chosen. The determination of the distribution of a statistical estimator, as the Mean Squared Error (MSE) or the accuracy, is fundamental to evaluate the performance of a neural network model (NNM). For many machine learning models, as linear regression, it is possible to analytically obtain information as variance or confidence intervals on the results. Neural networks present the difficulty of not being analytically tractable due to their complexity. Therefore, it is impossible to easily estimate distributions of statistical estimators. When estimating the global performance of an NNM by estimating the MSE in a regression problem, for example, it is important to know the variance of the MSE. Bootstrap is one of the most important resampling techniques to estimate averages and variances, between other properties, of statistical estimators. In this tutorial, the application of resampling techniques (including bootstrap) to the evaluation of neural networks’ performance is explained from both a theoretical and practical point of view. The pseudo-code of the algorithms is provided to facilitate their implementation. Computational aspects, as the training time, are discussed, since resampling techniques always require simulations to be run many thousands of times and, therefore, are computationally intensive. A specific version of the bootstrap algorithm is presented that allows the estimation of the distribution of a statistical estimator when dealing with an NNM in a computationally effective way. Finally, algorithms are compared on both synthetically generated and real data to demonstrate their performance.

Background: Several models have been developed to predict mortality in patients with COVID-19 pneumonia, but only a few have demonstrated enough discriminatory capacity. Machine learning algorithms represent a novel approach for the data-driven prediction of clinical outcomes with advantages over statistical modeling. Objective: We aimed to develop a machine learning–based score—the Piacenza score—for 30-day mortality prediction in patients with COVID-19 pneumonia. Methods: The study comprised 852 patients with COVID-19 pneumonia, admitted to the Guglielmo da Saliceto Hospital in Italy from February to November 2020. Patients’ medical history, demographics, and clinical data were collected using an electronic health record. The overall patient data set was randomly split into derivation and test cohorts. The score was obtained through the naïve Bayes classifier and externally validated on 86 patients admitted to Centro Cardiologico Monzino (Italy) in February 2020. Using a forward-search algorithm, 6 features were identified: age, mean corpuscular hemoglobin concentration, PaO2/FiO2 ratio, temperature, previous stroke, and gender. The Brier index was used to evaluate the ability of the machine learning model to stratify and predict the observed outcomes. A user-friendly website was designed and developed to enable fast and easy use of the tool by physicians. Regarding the customization properties of the Piacenza score, we added a tailored version of the algorithm to the website, which enables an optimized computation of the mortality risk score for a patient when some of the variables used by the Piacenza score are not available. In this case, the naïve Bayes classifier is retrained over the same derivation cohort but using a different set of patient characteristics. We also compared the Piacenza score with the 4C score and with a naïve Bayes algorithm with 14 features chosen a priori. Results: The Piacenza score exhibited an area under the receiver operating characteristic curve (AUC) of 0.78 (95% CI 0.74-0.84, Brier score=0.19) in the internal validation cohort and 0.79 (95% CI 0.68-0.89, Brier score=0.16) in the external validation cohort, showing a comparable accuracy with respect to the 4C score and to the naïve Bayes model with a priori chosen features; this achieved an AUC of 0.78 (95% CI 0.73-0.83, Brier score=0.26) and 0.80 (95% CI 0.75-0.86, Brier score=0.17), respectively. Conclusions: Our findings demonstrated that a customizable machine learning–based score with a purely data-driven selection of features is feasible and effective for the prediction of mortality among patients with COVID-19 pneumonia.

Extra virgin olive oil (EVOO) is the highest quality of olive oil and is characterized by highly beneficial nutritional properties. The large increase in both consumption and fraud, for example through adulteration, creates new challenges and an increasing demand for developing new quality assessment methodologies that are easier and cheaper to perform. As of today, the determination of olive oil quality is performed by producers through chemical analysis and organoleptic evaluation. The chemical analysis requires advanced equipment and chemical knowledge of certified laboratories, and has therefore limited accessibility. In this work a minimalist, portable, and low-cost sensor is presented, which can perform olive oil quality assessment using fluorescence spectroscopy. The potential of the proposed technology is explored by analyzing several olive oils of different quality levels, EVOO, virgin olive oil (VOO), and lampante olive oil (LOO). The spectral data were analyzed using a large number of machine learning methods, including artificial neural networks. The analysis performed in this work demonstrates the possibility of performing the classification of olive oil in the three mentioned classes with an accuracy of 100%. These results confirm that this minimalist low-cost sensor has the potential to substitute expensive and complex chemical analysis.