Benign overfitting and adaptive nonparametric regression
This addresses the challenge of balancing interpolation and optimality in regression for statisticians and machine learning practitioners, representing a theoretical advancement rather than an incremental improvement.
The paper tackles the problem of constructing a nonparametric regression estimator that interpolates data points while achieving minimax optimal rates adaptively to unknown smoothness, resulting in an estimator that attains these rates under mean squared risk on Hölder classes.
In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of Hölder classes adaptively to the unknown smoothness.