Neural network model for imprecise regression with interval dependent variables

TL;DR

This paper introduces a novel neural network-based method for imprecise regression that computes rigorous bounds on interval-dependent variables, effectively handling epistemic uncertainty without probabilistic assumptions.

Contribution

It proposes an iterative training approach for interval neural networks that can produce interval predictions and extend to multi-layer architectures, addressing data imprecision.

Findings

The method accurately estimates bounds on regression outputs with interval data.

It effectively models measurement imprecision without probabilistic information.

The approach is computationally feasible for practical applications.

Abstract

This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalisation 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.