Nonlinear parsimonious modeling based on Copula–LoGo

Herein, we presented a novel methodology for constructing nonlinear parsimonious probabilistic models (Copula–LoGo). Our approach combines Gaussian–Copula with linear LoGo probabilistic models to obtain a nonlinear coefficient matrix, which cannot be accurately estimated using Pearson's correlation coefficients or kernel tricks. Using the Gaussian–Copula obtained from a multivariate normal distribution through the probability integral transform, we applied the triangulated maximally filtered graph algorithm to construct decomposable information filtering networks. By analyzing the topological structure of the networks, we discerned the dependence characteristics for each variable in the regression model. Subsequently, by integrating the Gaussian Markov random field, we computed the estimate of the global sparse inverse covariance J from subparts of the dependence network and constructed the nonlinear, parsimonious model. Thus, our methodology exhibits computational efficiency and statistical robustness, outperforming other regression methods such as Support Vector Machine, Long Short-Term Memory, Principal Components Analysis, and XGBoost models, particularly in the financial domain, as evidenced by improved performance metrics including mean absolute error, root mean square error, and R2 score (prediction accuracy) and reduced execution time.