227 citations · 355 across the 8 of their papers we have counts for
7 papers · 1 filter
Bootstrap SGD: Algorithmic Stability and Robustness
Andreas Christmann, Yunwen Lei
In this paper some methods to use the empirical bootstrap approach for stochastic gradient descent (SGD) to minimize the empirical risk over a separable Hilbert space are investiga…
Total Stability of SVMs and Localized SVMs
Hannes Köhler, Andreas Christmann
Regularized kernel-based methods such as support vector machines (SVMs) typically depend on the underlying probability measure (respectively an empirical measure $\mat…
On the robustness of kernel-based pairwise learning
Patrick Gensler, Andreas Christmann
It is shown that many results on the statistical robustness of kernel-based pairwise learning can be derived under basically no assumptions on the input and output spaces. In parti…
Total stability of kernel methods
Andreas Christmann, Daohong Xiang, Ding-Xuan Zhou
Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the ac…
Universal Consistency and Robustness of Localized Support Vector Machines
Florian Dumpert
The massive amount of available data potentially used to discover patters in machine learning is a challenge for kernel based algorithms with respect to runtime and storage capacit…
A short note on extension theorems and their connection to universal consistency in machine learning
Andreas Christmann, Florian Dumpert, Dao-Hong Xiang
Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent a…