Deep Gaussian Fuzzy-Mappings
This study introduces a fuzzy theoretic approach to the learning of a deep model formed via a com- position of nonparametric mappings referred to as Gaussian fuzzy-mappings. The fuzzy membership functions are used to represent signals as well as uncertain functions associated to the layers of the deep model. The study suggests a mathematical way to study the propagation of the uncertainty through the layers of the deep model. The learning of the deep model would require a quantification of the uncertainties on the signals while they (i.e. signals) propagate across the layers of the deep model. We derive analytically the mathematical expressions for membership functions using variational optimization to quantify the uncertainties on variables. The most significant feature of the learning approach is that all of the unobserved variables and parameters, associated to the deep model, are averaged out where the averages are computed taking into account the uncertainties (on variables and parameters). The uncertainties are represented by the fuzzy membership functions optimally learned from the observed data. A rigorous mathematical treatment of the learning problem results in the development of a fast, competent, and robust classification algorithm. The study is a theoretical contribution to the field of fuzzy machine learning, nevertheless, offering practical machine learning algorithms.
- M. Kumar and S. Singh, “Deep Gaussian Fuzzy-Mappings,” Annals of Mathematics and Artificial Intelligence, under-review.