A Generalized Bridge Regression in Fuzzy Environment and Its Numerical Solution by a Capable Recurrent Neural Network

Abstract

Bridge regression is a special family of penalized regressions using a penalty function ${\displaystyle \sum {\left|A_j\right|}^{\gamma }}$ with $\gamma \ge 1$ that for $\gamma =1$ and $\gamma =2$ , it concludes lasso and ridge regression, respectively. In case where the output variable in the regression model was imprecise, we developed a bridge regression model in a fuzzy environment. We also exhibited penalized fuzzy estimates for this model when the input variables were crisp. So, we perform the presented optimization problem for the model that leads to a multiobjective program. Also, we try to determine the shrinkage parameter and the tuning parameter from the same optimization problem. In order to estimate fuzzy coefficients of the proposed model, we introduce a hybrid scheme based on recurrent neural networks. The suggested neural network model is constructed based on some concepts of convex optimization and stability theory which guarantees to find the approximate parameters of the proposed model. We use a simulation study to depict the performance of the proposed bridge technique in the presence of multicollinear data. Furthermore, real data analysis is used to show the performance of the proposed method. A comparison between the fuzzy bridge regression model and several other shrinkage models is made with three different well-known fuzzy criteria. In this study, we visualize the performance of the model by Taylor’s diagram and Bubble plot. Also, we examine the predictive ability of the model, thus, obtained by cross validation. The numerical results clearly showed higher accuracy of the proposed fuzzy bridge method compared to the other existing fuzzy regression models: fuzzy bridge regression model, multiobjective optimization, recurrent neural network, stability convergence, and goodness-of-fit measure.