Fuzzy Theoretic Nonparametric Deep Learning
This study introduces a fuzzy theoretic approach to the learning of a nonparametric deep model formed via a composition of uncertain non-linear functions. The fuzzy membership functions are used to rep- resent signals as well as uncertain functions associated to 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 significance 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) being represented by the fuzzy membership functions optimally learned from the observed data. A rigorous mathematical analysis 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, S. Chatterjee, W. Zhang, and L. M. Kolbe, “Fuzzy Theoretic Data Models,” Information Sciences, under-preparation.