Timezone: »

 
Poster
Fast rates for noisy interpolation require rethinking the effect of inductive bias
Konstantin Donhauser · Nicolò Ruggeri · Stefan Stojanovic · Fanny Yang

Thu Jul 21 03:00 PM -- 05:00 PM (PDT) @ Hall E #1109
in Poster Session 3 »
Good generalization performance on high-dimensional data crucially hinges on a simple structure of the ground truth and a corresponding strong inductive bias of the estimator. Even though this intuition is valid for regularized models, in this paper we caution against a strong inductive bias for interpolation in the presence of noise: While a stronger inductive bias encourages a simpler structure that is more aligned with the ground truth, it also increases the detrimental effect of noise. Specifically, for both linear regression and classification with a sparse ground truth, we prove that minimum $\ell_p$-norm and maximum $\ell_p$-margin interpolators achieve fast polynomial rates close to order $1/n$ for $p > 1$ compared to a logarithmic rate for $p = 1$. Finally, we provide preliminary experimental evidence that this trade-off may also play a crucial role in understanding non-linear interpolating models used in practice.
Keywords: T: Deep Learning · T: Learning Theory · MISC: Supervised Learning

Author Information

Konstantin Donhauser (ETH Zurich)
Nicolò Ruggeri (ETH)
Stefan Stojanovic (ETH Zurich)
Fanny Yang (ETH Zurich)

Related Events (a corresponding poster, oral, or spotlight)

More from the Same Authors