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In this manuscript we consider the problem of kernel classification. While worst-case bounds on the decay rate of the prediction error with the number of samples are known for some classifiers, they often fail to accurately describe the learning curves of real data sets. In this work, we consider the important class of data sets satisfying the standard source and capacity conditions, comprising a number of real data sets as we show numerically. Under the Gaussian design, we derive the decay rates for the misclassification (prediction) error as a function of the source and capacity coefficients. We do so for two standard kernel classification settings, namely margin-maximizing support vector machines and ridge classification, and contrast the two methods. We find that our rates tightly describe the learning curves for this class of data sets, and are also observed on real data. Our results can also be seen as an explicit prediction of the exponents of a scaling law for kernel classification that is accurate on some real datasets.
Olivier Schneider, Yiming Li, Mingkui Wang, Chao Wang, Tagir Aushev, Sun Hee Kim, Donghyun Kim, Lei Li
Jian Wang, Matthias Finger, Qian Wang, Yiming Li, Matthias Wolf, Varun Sharma, Yi Zhang, Konstantin Androsov, Jan Steggemann, Xin Chen, Rakesh Chawla, Matteo Galli, Anna Mascellani, João Miguel das Neves Duarte, Tagir Aushev, Tian Cheng, Yixing Chen, Werner Lustermann, Andromachi Tsirou, Alexis Kalogeropoulos, Andrea Rizzi, Ioannis Papadopoulos, Paolo Ronchese, Hua Zhang, Siyuan Wang, Tao Huang, David Vannerom, Michele Bianco, Sebastiana Gianì, Sun Hee Kim, Kun Shi, Abhisek Datta, Federica Legger, Gabriele Grosso, Ji Hyun Kim, Donghyun Kim, Zheng Wang, Sanjeev Kumar, Wei Li, Yong Yang, Geng Chen, Ajay Kumar, Ashish Sharma, Georgios Anagnostou, Joao Varela, Csaba Hajdu, Muhammad Ahmad, Ioannis Evangelou, Milos Dordevic, Meng Xiao, Sourav Sen, Xiao Wang, Kai Yi, Jing Li, Rajat Gupta, Zhen Liu, Hui Wang, Seungkyu Ha, Long Wang, Pratyush Das, Anton Petrov, Xin Sun, Valérie Scheurer, Giovanni Mocellin, Muhammad Ansar Iqbal, Lukas Layer
Jian Wang, Lesya Shchutska, Olivier Schneider, Yiming Li, Yi Zhang, Aurelio Bay, Guido Haefeli, Christoph Frei, Frédéric Blanc, Tatsuya Nakada, Michel De Cian, François Fleuret, Elena Graverini, Renato Quagliani, Federico Betti, Andrea Merli, Aravindhan Venkateswaran, Vitalii Lisovskyi, Katharina Müller, Sebastian Schulte, Veronica Sølund Kirsebom, Elisabeth Maria Niel, Mingkui Wang, Zhirui Xu, Chao Wang, Lei Zhang, Ho Ling Li, Mark Tobin, Minh Tâm Tran, Niko Neufeld, Matthew Needham, Marc-Olivier Bettler, Maurizio Martinelli, Vladislav Balagura, Donal Patrick Hill, Liang Sun, Pietro Marino, Mirco Dorigo, Xiaoxue Han, Liupan An, Federico Leo Redi, Plamen Hristov Hopchev, Maxime Schubiger, Hang Yin, Guido Andreassi, Violaine Bellée, Preema Rennee Pais, Pavol Stefko, Tara Nanut, Maria Elena Stramaglia, Yao Zhou, Tommaso Colombo, Vladimir Macko, Guillaume Max Pietrzyk, Evgenii Shmanin, Simone Meloni, Xiaoqing Zhou, Surapat Ek-In, Carina Trippl, Sara Celani, Marco Guarise, Serhii Cholak, Dipanwita Dutta, Zheng Wang, Yong Yang, Yi Wang, Hao Liu, Hans Dijkstra, Gerhard Raven, Peter Clarke, Frédéric Teubert, Giovanni Carboni, Victor Coco, Shuai Liu, Adam Davis, Paolo Durante, Yu Zheng, Renjie Wang, Anton Petrov, Maxim Borisyak, Feng Jiang, Chen Chen, Zhipeng Tang, Xuan Li, Alexey Boldyrev, Almagul Kondybayeva, Hossein Afsharnia