Granular regression with a gradient descent method

The regression is one of classical models in machine learning. Traditional regression algorithms involve operations of real values, which are difficult to handle the discrete or set data in information systems. Granules are structural objects on which agents perform complex computations. The structural objects are forms of sets that can measure the uncertainty of data. In order to deal with uncertain and vague data in the real world, we propose a set-based regression model: granular regression. Granules are constructed by introducing a distance metric on single-atom features. Meanwhile, we establish conditional granular vectors, weight granular vectors and decision granules. The operations among them induce a granular regression model. Furthermore, we propose a gradient descent method for the granular regression model, and the optimal solution of granular regression is achieved. We prove the convergence of granular regression and design a gradient descent algorithm. Finally, several UCI data sets are used to test and verify the granular regression model. We compare our proposed model with popular regression models from three aspects of convergence, fitting and prediction. The results show that the granular regression model is valid and effective. (C) 2020 Elsevier Inc. All rights reserved.