Nonlinear Parsimonious Models for IoT Consumer Electronics: Leveraging Normal Distribution Transformations in Information Filtering Networks

Qingyang Liu, Hongjiu Liu, Ying Zhang, Jijing Cai

Abstract: In this paper, we evaluated various normal distribution transformation methods for converting non-normally distributed data into a normal distribution. These transformations facilitate the computation of the correlation matrix by ensuring linear relationships between variables and observations. We integrated these methods with the Triangulated Maximally Filtered Graph (TMFG) network and Gaussian Markov Random Field (GMRF) to construct nonlinear parsimonious probabilistic models. By leveraging the dependence characteristics of each variable derived from the TMFG network’s topological structure, GMRF can estimate the global sparse inverse covariance matrix J from subparts of the dependence network, resulting in computationally efficient and statistically robust models. We explored several common transformation methods, including high-order polynomial fitting, exponential family transformation, Gaussian mixture models, Gaussian Copula, and others. Through extensive testing of over a dozen methods, we identified the most effective for fitting nonlinear parsimonious models. Our results indicate that half of the tested methods exhibit very low or even negative accuracy in regression models using stock price data. In contrast, several methods—such as Box-Cox, Rank, and Polynomial—achieved accuracies above 90%, with the Polynomial transformation reaching the highest at 98.69%, albeit with the longest execution time of 679.1 ms. Notably, the Gaussian Copula method demonstrates the best trade-off between accuracy and efficiency, attaining an accuracy of 98.67% with an execution time of only 352.7 ms. Compared with traditional models such as LSTM (accuracy 91.12%, time 1578.3 ms) and SVR (89.87%, 964.6 ms), our proposed framework significantly improves both prediction quality and speed. These findings highlight the benefits of integrating normal distribution transformations with parsimonious modeling, especially for nonlinear and high dimensional data. This method provides a practical and scalable solution for the real-world applications such as IoT sensor prediction and financial forecasting.

External IDs:dblp:journals/tce/LiuLZC25