Neural network model for imprecise regression with interval dependent variables.

Tretiak, Krasymyr, Schollmeyer, Georg and Ferson, Scott ORCID: 0000-0002-2613-0650 (2023) Neural network model for imprecise regression with interval dependent variables. Neural networks : the official journal of the International Neural Network Society, 161. pp. 550-564.

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Official URL: http://dx.doi.org/10.1016/j.neunet.2023.02.005

Abstract

This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalization of regression analysis to account for epistemic uncertainty in the output variables. The new iterative method uses machine learning algorithms to fit an imprecise regression model to data that consist of intervals rather than point values. The method is based on a single-layer interval neural network which can be trained to produce an interval prediction. It seeks parameters for the optimal model that minimizes the mean squared error between the actual and predicted interval values of the dependent variable using a first-order gradient-based optimization and interval analysis computations to model the measurement imprecision of the data. An additional extension to a multi-layer neural network is also presented. We consider the explanatory variables to be precise point values, but the measured dependent values are characterized by interval bounds without any probabilistic information. The proposed iterative method estimates the lower and upper bounds of the expectation region, which is an envelope of all possible precise regression lines obtained by ordinary regression analysis based on any configuration of real-valued points from the respective y-intervals and their x-values.

Item Type:	Article
Uncontrolled Keywords:	Imprecise regression, Interval data, Neural network, Uncertainty
Divisions:	Faculty of Science and Engineering > School of Engineering
Depositing User:	Symplectic Admin
Date Deposited:	03 Mar 2023 10:52
Last Modified:	05 Apr 2023 12:16
DOI:	10.1016/j.neunet.2023.02.005
Open Access URL:	https://doi.org/10.1016/j.neunet.2023.02.005
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3168731