This paper presents several novel generalization bounds for the problem of learning kernels based on the analysis of the Rademacher complexity of the corresponding hypothesis sets. Our bound for learning kernels with a convex combination of p base kernels has only a log(p) dependency on the number...
Later, we will observe that the mathematical description of rotation invariant kernels on isotropic distributions reduces to this simple model in each learning stage. In this model, the kernel eigenvalues are equal \({\eta }_{\rho }=\frac{1}{N}\) for a finite number of modes ρ = ...
We define notions of stability for learning algorithms and show how to use these notions to derive generalization error bounds based on the empirical error and the leave-one-out error. The methods we use can be applied in the regression framework as well as in the classification one when the...
Learning theory is rich in bounds that have been derived and that relate quantities such as the empirical error, the true error probability, the number of training vectors, and the VC dimension or a VC related quantity. In his elegant theory of learning, Valiant [Vali 84] proposed to express...
New Generalization Bounds for Learning Kernels This paper presents several novel generalization bounds for the problem of learning kernels based on the analysis of the Rademacher complexity of the corre... C Cortes,M Mohri,A Rostamizadeh 被引量: 143发表: 2009年 ...
Achieving small prediction errorR(α) is the ultimate goal of (quantum) machine learning. AsPis generally not known, the training error{\hat{R}}_{S}({{{\boldsymbol{\alpha }}})is often taken as a proxy forR(α). This strategy can be justified via bounds on thegeneralization error...
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For both datasets, most of the Gaussian kernels yield smaller upper bounds on generalization error Full size table Fig. 2 Experimental test errors and accuracy on the test set at the different steps of the Gradient Descent optimization algorithm for first two classes of CIFAR-10 dataset Full ...
Kernel Fisher discriminant analysis (KDA)[30] is used to find a transformation of data using nonlinear kernels in all source domains. Undo-bias (UB)[7] measures the model of each task with a domain-specific weight and a globally shared weight used for domain generalization. The original UB ...
Generalization bounds for learning the kernel problem - Ying, Campbell - 2009 () Citation Context ... from a data-dependent to a distribution dependent bound. In Section 2 we show that this recovers existing results (Cortes et al., 2010; Kakade et al., 2010; Kloft et al., 2011; Meir ...