تقرير
The Geometry of Mixability
| العنوان: | The Geometry of Mixability |
|---|---|
| المؤلفون: | Pacheco, Armando J. Cabrera, Williamson, Robert C. |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science |
| مصطلحات موضوعية: | Computer Science - Machine Learning |
| الوصف: | Mixable loss functions are of fundamental importance in the context of prediction with expert advice in the online setting since they characterize fast learning rates. By re-interpreting properness from the point of view of differential geometry, we provide a simple geometric characterization of mixability for the binary and multi-class cases: a proper loss function $\ell$ is $\eta$-mixable if and only if the superpredition set $\textrm{spr}(\eta \ell)$ of the scaled loss function $\eta \ell$ slides freely inside the superprediction set $\textrm{spr}(\ell_{\log})$ of the log loss $\ell_{\log}$, under fairly general assumptions on the differentiability of $\ell$. Our approach provides a way to treat some concepts concerning loss functions (like properness) in a ''coordinate-free'' manner and reconciles previous results obtained for mixable loss functions for the binary and the multi-class cases. Comment: 53 pages, 6 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2302.11905 |
| رقم الأكسشن: | edsarx.2302.11905 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |