Interval predictor models for data with measurement uncertainty

An interval predictor model (IPM) is a computational model that predicts the range of an output variable given input-output data. This paper proposes strategies for constructing IPMs based on semidefinite programming and sum of squares (SOS). The models are optimal in the sense that they yield an interval valued function of minimal spread containing all the observations. Two different scenarios are considered. The first one is applicable to situations where the data is measured precisely whereas the second one is applicable to data subject to biases and random measurement error. In the latter case, the IPMs are designed to fully contain regions in the input-output space where the data is expected to fall. Moreover, we propose an algorithm to reduce the computational cost associated with generating IPMs that enclose all such regions. Numerical examples illustrate the performance of the proposed methods.