Artificial neural networks (ANNs) have traditionally been seen as black-box models, because, although they are able to find ``hidden'' relations between inputs and outputs with a high approximation capacity, their structure seldom provides any insights on the structure of the functions being approximated. Several research papers have tried to debunk the black-box nature of ANNs, since it limits the potential use of ANNs in many research areas. This paper is framed in this context and proposes a methodology to determine the individual and collective effects of the input variables on the outputs for classification problems based on the ANOVA-functional decomposition. The method is applied after the training phase of the ANN and allows researchers to rank the input variables according to their importance in the variance of the ANN output. The computation of the sensitivity indices for product unit neural networks is straightforward as those indices can be calculated analytically by evaluating the integrals in the ANOVA decomposition. Unfortunately, the sensitivity indices associated with ANNs based on sigmoidal basis functions or radial basis functions cannot be calculated analytically. In this paper, the indices for those kinds of ANNs are proposed to be estimated by the (quasi-) Monte Carlo method.
COVID-19 has had a negative impact on the living conditions of people in all countries worldwide. With a devastating economic crisis where many families are finding it difficult to pay bills and make ends meet, increases in prices of food basket staples can be very worrying. This study examines the relationship between the incidence of the pandemic during the first wave in 16 Eurozone countries with the variation experienced in food prices. We analysed the harmonised index of consumer food prices (included in HICP) and the classification of the degree of pandemic impact by country, the latter established with the index of deaths provided by the Johns Hopkins Center. The procedure used compared actual food prices during the first wave (March to June 2020) with those foreseeable in the absence of the pandemic. Time series analysis was used, dividing the research period into two phases. In both phases, the Holt–Winters model was applied for estimation and subsequent prediction. After a contrast using Kendall’s tau correlation index, it was concluded that in the countries with the highest death rates during the first wave, there was a higher increase in food prices than in the least affected countries of the Eurozone.
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