Metalearning for robust regression: Robustness and variable selection

Abstrakt

Metalearning represents a useful computational methodology for selecting and recommending a suitable algorithm (e.g. estimation method) for a new dataset, based on information learned over a training database of datasets. While the popularity of metalearning is gradually increasing, practitioners seem not to be aware of common limitations of metalearning, namely its instability and vulnerability with respect to noise, outlying values, or presence of redundant variables in the data. We perform a metalearning study for recommending the best linear regression estimator for a new dataset, which is not included in the training database of 30 datasets. The estimators under consideration include the least squares together with several robust estimators with a high breakdown point. We investigate the e ect of variable selection on the metalearning results. If the training as well as validation data are considered after a proper robust variable selection, the metalearning performance is improved remarkably, especially if a robust prediction error is used.