Deep patch learning algorithms with high interpretability for regression problems

Abstract

Improving the performance of machine learning algorithms to overcome the curse of dimensionality while maintaining interpretability is still a challenging issue for researchers in artificial intelligence. Patch learning (PL), based on the improved adaptive network-based fuzzy inference system (ANFIS) and continuous local optimization for the input domain, is characterized by high accuracy. However, PL can only handle low-dimensional data set regression. Based on the parallel and serial ensembles, two deep patch learning algorithms with embedded adaptive fuzzy systems (DPLFSs) are proposed in this paper. First, using the maximum information coefficient (MIC) and Pearson's correlation coefficients for feature selection, the variables with the least relationship (linear or nonlinear) are excluded. Second, principal component analysis is used to reduce the complexity further of DPLFSs. Meanwhile, fuzzy C-means clustering is used to enhance the interpretability of DPLFSs. Then, an improved PL method is put forward for the training of each sub-fuzzy system in a fashion of bottom-up layer-by-layer, and finally, the structure optimization is performed to significantly improve the interpretability of DPLFSs. Experiments on several benchmark data sets show the advantages of a DPLFS: (1) it can handle medium-scale data sets; (2) it can overcome the curse of dimensionality faced by PL; (3) its precision and generalization are greatly improved; and (4) it can overcome the poor interpretability of deep learning networks. Compared with shallow and deep learning algorithms, DPLFSs have the advantages of interpretability, self-learning, and high precision. DPLFS1 is superior for medium-scale data; DPLFS2 is more efficient and effective for high-dimensional problems, has a faster convergence, and is more interpretable.