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
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Organizer(s):
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)