%0 Journal Article %1 ZHANG2022128 %A Zhang, Weiping %A Kumar, Mohit %A Ding, Weiping %A Li, Xiujuan %A Yu, Junfeng %D 2022 %J Neurocomputing %K deep-learning fuzzy image mappings neural-networks %P 128-145 %R https://doi.org/10.1016/j.neucom.2022.07.029 %T Variational learning of deep fuzzy theoretic nonparametric model %U https://www.sciencedirect.com/science/article/pii/S0925231222008839 %V 506 %X Nonparametric approaches are a good choice for function approximation as they are flexible, robust to overfitting, and provide well calibrated predictive uncertainty. The nonparametric form of fuzzy modeling can be promising, however, not analytically studied to compete with the Gaussian processes-based Bayesian framework in statistics and machine learning. In this work, a fuzzy modeling framework is built for data analysis of both supervised and unsupervised learning task, as a deterministic fuzzy analogous against the probabilistic Gaussian process, which defines a fuzzy membership over possible membership functions and is updated in light of data via the rules of variational inference. A fast variational inference framework has been suggested to study the propagation of the uncertainty through the layers of the deep model which can jointly infers the inducing inputs and the hyperparameters. The maximization problem is analytically solved using variational optimization with derived lower bound. We provide the sufficient number of experiments to support our argument that the proposed approach works well in practice for the problem which has the requirements to update the model dynamically. In addition, the application potential of the proposed methodology in data representation learning is also investigated, the “auxiliary inducing points” are used to express general features of tasks with smaller datasets. Nevertheless, this study offers new contents to the theory of nonparametric model and presents the potential for the design of practical fuzzy machine learning method.

@article{ZHANG2022128, abstract = {Nonparametric approaches are a good choice for function approximation as they are flexible, robust to overfitting, and provide well calibrated predictive uncertainty. The nonparametric form of fuzzy modeling can be promising, however, not analytically studied to compete with the Gaussian processes-based Bayesian framework in statistics and machine learning. In this work, a fuzzy modeling framework is built for data analysis of both supervised and unsupervised learning task, as a deterministic fuzzy analogous against the probabilistic Gaussian process, which defines a fuzzy membership over possible membership functions and is updated in light of data via the rules of variational inference. A fast variational inference framework has been suggested to study the propagation of the uncertainty through the layers of the deep model which can jointly infers the inducing inputs and the hyperparameters. The maximization problem is analytically solved using variational optimization with derived lower bound. We provide the sufficient number of experiments to support our argument that the proposed approach works well in practice for the problem which has the requirements to update the model dynamically. In addition, the application potential of the proposed methodology in data representation learning is also investigated, the “auxiliary inducing points” are used to express general features of tasks with smaller datasets. Nevertheless, this study offers new contents to the theory of nonparametric model and presents the potential for the design of practical fuzzy machine learning method.}, added-at = {2023-05-02T13:59:22.000+0200}, author = {Zhang, Weiping and Kumar, Mohit and Ding, Weiping and Li, Xiujuan and Yu, Junfeng}, biburl = {https://www.bibsonomy.org/bibtex/202a024e4209c64f8c05c1b1f3e801137/scch}, doi = {https://doi.org/10.1016/j.neucom.2022.07.029}, interhash = {b807c8f667c6af415ed36d3a48668127}, intrahash = {02a024e4209c64f8c05c1b1f3e801137}, issn = {0925-2312}, journal = {Neurocomputing}, keywords = {deep-learning fuzzy image mappings neural-networks}, pages = {128-145}, timestamp = {2023-05-02T13:59:22.000+0200}, title = {Variational learning of deep fuzzy theoretic nonparametric model}, url = {https://www.sciencedirect.com/science/article/pii/S0925231222008839}, volume = 506, year = 2022 }