A Generalized Multiple Criteria Data-Fitting Model With Sparsity and Entropy With Application to Growth Forecasting

Abstract

In this article, we present an extended data-fitting model which involves different and conflicting criteria, and we propose an algorithm based on a scalarization technique to solve it. Our model integrates in a unique framework three different criteria, namely, a data-fitting term, and the entropy and the sparsity of the set of unknown parameters. This model can be analyzed by means of multiple criteria decision-making techniques. We then validate the proposed modified algorithm using two computational experiments: We analyze the problem of handwritten digit recognition using a logistic regression model and a deep neural network model, respectively. In the final part of the article, we employ this methodology to forecasting instead. Given the importance of forecasting techniques to predict the future, which in turn can lead to positive impacts on firm performance, we propose two numerical experiments focusing on the forecast of the US GDP. In the first one, we proceed by means of a modified iterated function system with grayscale maps-type fractal operator, and, in the second one, we implement a modified neural network-based model.