A MOM-based ensemble method for robustness, subsampling and hyperparameter tuning

Hyperparameter tuning and model selection are important steps in machine learning. Unfortunately, classical hyperparameter calibration and model selection procedures are sensitive to outliers and heavy-tailed data. In this work, we construct a selection procedure which can be seen as a robust alternative to cross-validation and is based on a median-ofmeans principle. Using this procedure, we also build an ensemble method which, trained with algorithms and corrupted heavy-tailed data, selects an algorithm, trains it with a large uncorrupted subsample and automatically tunes its hyperparameters. In particular, the approach can transform any procedure into a robust to outliers and to heavy-tailed data procedure while tuning automatically its hyperparameters. The construction relies on a divide-and-conquer methodology, making this method easily scalable even on a corrupted dataset. This method is tested with the LASSO which is known to be highly sensitive to outliers.