Seppo Karrila

pp. 241 - 248

Abstract

A measurement result often dictates an interval containing the correct value. Interval data is also created by roundoff, truncation, and binning. We focus on such common interval uncertainty in data. Inaccuracy in model inputs is typically
ignored on model fitting. We provide a practical approach for regression with inaccurate data: the mathematics is easy, and
the linear programming formulations simple to use even in a spreadsheet. This self-contained elementary presentation
introduces interval linear systems and requires only basic knowledge of algebra. Feature selection is automatic; but can be
controlled to find only a few most relevant inputs; and joint feature selection is enabled for multiple modeled outputs. With
more features than cases, a novel connection to compressed sensing emerges: robustness against interval errors-in-variables
implies model parsimony, and the input inaccuracies determine the regularization term. A small numerical example highlights
counterintuitive results and a dramatic difference to total least squares.