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.
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Notes
- 1.
All fitting performed in R [6] with details available at http://aggregationfunctions.wordpress.com.
- 2.
Achieved in R using solve(), provided the matrix is non-singular. In the event of singular matrices, the particular iteration contributed nothing to the output.
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Beliakov, G., Gagolewski, M., James, S. (2018). Least Median of Squares (LMS) and Least Trimmed Squares (LTS) Fitting for the Weighted Arithmetic Mean. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 854. Springer, Cham. https://doi.org/10.1007/978-3-319-91476-3_31
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