Least median of squares (LMS) and least trimmed squares (LTS) fitting for the weighted arithmetic mean

Abstract

We look at different approaches to learning the weights of the weighted arithmetic mean such that the median residual or sum of the smallest half of squared residuals is minimized. The more general problem of multivariate regression has been well studied in statistical literature, however in the case of aggregation functions we have the restriction on the weights and the domain is also usually restricted so that ‘outliers’ may not be arbitrarily large. A number of algorithms are compared in terms of accuracy and speed. Our results can be extended to other aggregation functions.