Certain variables of interest in agriculture may preferably be mapped to distributions rather than to real numbers, e.g. the variable “apple (fruit) weight” on an apple tree at sampling times; hence, a stochastic time-series emerges. Since a cumulative probability distribution can be represented by a Type-1 Intervals’ Number (IN) in the mathematical lattice (F1,⪯), this work considers a stochastic time-series F: R → F1 and interprets it as a parametric Type-2 IN, symbolically F(x; t). Given samples F(x; ti), i  k, the problem here is to predict F(x, ti) for i > k, assuming a deterministic relation among samples F(x; ti), i ε {1,…,n}. Prediction is pursued by a novel neural architecture, namely meta-Statistical IN Neural Network, or metaStatINNN for short, consisting of two neural modules in series: The first one, namely lowerNN, induces INs from data using deep learning; whereas, the second one, namely upperNN, is a well known INNN (IN Neural Network) that implements a function f: F1N  F1. This preliminary work considers a benchmark time-series of temperature distributions as well as artificial data sets of increasing cardinality. Computational experiments are demonstrated comparatively to a conventional neural network. The results by metaStatINNN are superior not only in terms of computational speed as well as prediction accuracy but also because a conventional neural network typically predicts only first-order data statistics, whereas the metaStatINNN may predict all-order data statistics; in addition, the metaStatINNN can explain its answers; moreover, an IN can represent big data.


C. Bazinas, C. Lytridis, V. G. Kaburlasos, “Meta-statistical deep learning for stochastic time-series prediction in agricultural applications”, International Joint Conference on Neural Networks (IJCNN 2023). Gold Coast, Queensland, Australia, 18-23 June 2023. 2023 International Neural Network Society (INNS) Workshop on Deep Learning Innovations and Applications (DLIA)