Generalization performance of interpolating models in high dimensions

Fan Yang (ETH Zürich)

Jun 02. 2022, 14:00 — 14:45

Interpolating models have recently gained popularity in the statistical learning community due to common practices in modern machine learning: complex models achieve good generalization performance despite interpolating high-dimensional training data. In this talk, we prove generalization bounds for high-dimensional linear models that interpolate noisy data generated by a sparse ground truth. In particular, we first show that minimum-l1-norm interpolators achieve high-dimensional asymptotic consistency at a logarithmic rate. Further, as opposed to the regularized or noiseless case, for min-lp-norm interpolators with 1<p<2 we surprisingly obtain polynomial rates. Our results suggest a new trade-off for interpolating models: a stronger inductive bias encourages a simpler structure better aligned with the ground truth at the cost of an increased variance.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zürich)
Sara van de Geer (ETH Zürich)
Karen Willcox (U of Texas, Austin)