Learning Curves for Noisy Heterogeneous Feature-Subsampled Ridge Ensembles
This work addresses the double-descent phenomenon in machine learning, offering a computationally efficient ensembling method for practitioners dealing with noisy data, though it is incremental as it builds on existing feature-bagging techniques.
The paper tackled the problem of double-descent in linear predictors by developing a theory for feature-bagging in noisy ridge ensembles, showing that subsampling shifts the double-descent peak and introducing heterogeneous feature ensembling as an efficient mitigation method, with qualitative insights validated on image classification tasks using deep learning features.
Feature bagging is a well-established ensembling method which aims to reduce prediction variance by combining predictions of many estimators trained on subsets or projections of features. Here, we develop a theory of feature-bagging in noisy least-squares ridge ensembles and simplify the resulting learning curves in the special case of equicorrelated data. Using analytical learning curves, we demonstrate that subsampling shifts the double-descent peak of a linear predictor. This leads us to introduce heterogeneous feature ensembling, with estimators built on varying numbers of feature dimensions, as a computationally efficient method to mitigate double-descent. Then, we compare the performance of a feature-subsampling ensemble to a single linear predictor, describing a trade-off between noise amplification due to subsampling and noise reduction due to ensembling. Our qualitative insights carry over to linear classifiers applied to image classification tasks with realistic datasets constructed using a state-of-the-art deep learning feature map.