J. Smola. Kernel methods and the exponential family. In ESANN, pages 447-454, 2005.Kernel methods and the exponential family - Canu, Smola - 2005Canu, S. and Smola, A.J. (2005) `Kernel methods and the exponential family', in ESANN, pp.447-454....
在论文《Kernel methods and the exponential family》中,上面的也称为Parametric exponential families,是因为这个是通过参数 θ 确定的分布族。同样地,存在Non-parametric exponential families,即通过Kernel定义的分布族, f 是Natural Parameter, K(x,⋅) 被当作充分统计量,所以可以定义函数族: pf(x)=q0(x)exp...
Reproducing Kernel Hilbert Spaces In Probability and Statistics. ^abcM. Kanagawa, P. Hennig, D. Sejdinovic, and B. K. Sriperumbudur. Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences. ^abcdV. I. Bogachev. Gaussian measures. ^M. Lifshits. Lectures on Gaussian ...
Fig. 1: Exponential concentration and its implications on kernel methods. The exponential concentration (in the number of qubitsn) of quantum kernels\(\kappa({{{\boldsymbol{x}}},{{{\boldsymbol{x}}}^{{\prime} })\), over all possible input data pairs\({{{\boldsymbol{x}}},{{{\bold...
Until now, it remained an open question whether some advantage could be gained from data re-uploading models, in light of the guarantees of kernel methods. In this work, we introduce a unifying framework for explicit, implicit and data re-uploading quantum models (see Fig. 2). We show ...
Finally, we present a simulation study and an analysis of real-world data that compares the performance of the proposed approach to existing methods. We show empirically that our approach is comparable to current state of the art, and in some cases is even better....
The kernel function and methods for determining the bandwidth were chosen following the methodology proposed by Ayuga et al. (1994) and the Gaussian kernel function was used. This kernel belongs to the Gram–Charlier family of kernel functions, with general expression of Eq. (7). (8)Kx=pxe...
Bayesian methods for estimating multi-segment discharge rating curves This study explores Bayesian methods for handling compound stage–discharge relationships, a problem which arises in many natural rivers. It is assumed: (1... T Reitan,Asgeir Petersen-Overleir - 《Stochastic Environmental Research &...
Generally, these and similar methods have been successful in some cases but may also suffer from epistasis detection power loss. Furthermore, they embed a degree of subjectivity due to the choice of filtering or dimensionality reduction technique; different choices often leading to quite different res...
IndexTerms—Boosting,Fisher’sdiscriminant,kernelmethods, kernelPCA,mathematicalprogrammingmachines,Mercerker- nels,principalcomponentysis(PCA),single-classclassifica- tion,supportvectormachines(SVMs). I.INTRODUCTION NTHElastyears,anumberofpowerfulkernel-based ...