Abstract:

Overparametrized interpolating models have drawn increasing attention from machine learning. Some recent studies suggest that regularized interpolating models can generalize well. This phenomenon seemingly contradicts the conventional wisdom that interpolation tends to overfit the data and performs poorly on test data, and it further appears to defy the bias-variance trade-off. As one of the shortcomings of the existing theory, the classical notion of model degrees of freedom fails to explain the intrinsic difference among the interpolating models since it focuses on estimation of in-sample prediction error. This motivates an alternative measure of model complexity which can differentiate those interpolating models and take different test points into account. In particular, we propose a measure with a proper adjustment based on the squared covariance between the prediction and observations. Our analysis with least squares method reveals some interesting properties of the measure, which can reconcile the “double descent” phenomenon with the classical theory. This opens the door to an extended definition of model degrees of freedom in modern predictive settings. (Joint work with Bo Luan and Yoonkyung Lee.)

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Topic: Colloquium -- Department of Statistics and Actuarial Science -- University of Iowa
Time: Apr 6, 2023 03:15 PM Central Time (US and Canada)

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Meeting ID: 919 6962 2615