Learning Curves for Noisy Heterogeneous Feature-Subsampled Ridge Ensembles

Abstract

Feature bagging is a well-established ensembling method which aims to reduceprediction variance by combining predictions of many estimators trained on subsetsor projections of features. Here, we develop a theory of feature-bagging in noisyleast-squares ridge ensembles and simplify the resulting learning curves in the specialcase of equicorrelated data. Using analytical learning curves, we demonstratethat subsampling shifts the double-descent peak of a linear predictor. This leadsus to introduce heterogeneous feature ensembling, with estimators built on varyingnumbers of feature dimensions, as a computationally efficient method to mitigatedouble-descent. Then, we compare the performance of a feature-subsamplingensemble to a single linear predictor, describing a trade-off between noise amplificationdue to subsampling and noise reduction due to ensembling. Our qualitativeinsights carry over to linear classifiers applied to image classification tasks withrealistic datasets constructed using a state-of-the-art deep learning feature map.