Optimal multiclass overfitting by sequence reconstruction from Hamming queries
This work addresses a theoretical problem in machine learning regarding dataset reuse and overfitting, with implications for understanding multiclass classification robustness.
The paper resolves an open problem from COLT 2019 by characterizing the overfitting bias in multiclass classification, showing it scales as $ ilde{\Theta}(\max\{\sqrt{k/(mn)}, k/n\})$ and providing efficient algorithms that match known upper bounds.
A primary concern of excessive reuse of test datasets in machine learning is that it can lead to overfitting. Multiclass classification was recently shown to be more resistant to overfitting than binary classification. In an open problem of COLT 2019, Feldman, Frostig, and Hardt ask to characterize the dependence of the amount of overfitting bias with the number of classes $m$, the number of accuracy queries $k$, and the number of examples in the dataset $n$. We resolve this problem and determine the amount of overfitting possible in multi-class classification. We provide computationally efficient algorithms that achieve overfitting bias of $\tildeΘ(\max\{\sqrt{{k}/{(mn)}}, k/n\})$, matching the known upper bounds.