Kernelized Elastic Net Regularization Based on Markov Selective Sampling

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Chen, Weijian; Xu, Chen; Zou, Bin; Jin, Warren; Xu, Jie


2019-01-01


Journal Article


Knowledge-based System


163


57-68


This paper extends the Kernelized Elastic Net Regularization (KENReg) algorithm from the assumption of independent and identically distributed (i.i.d.) samples to the case of non-i.i.d. samples. We first establish the generalization bounds of KENReg algorithm with uniformly ergodic Markov chain samples and then we prove that the KENReg algorithm with uniformly ergodic Markov chain samples is consistent and obtain the fast learning rate of KENReg algorithm with uniformly ergodic Markov chain samples. We also introduce the KENReg algorithm based on Markov selective sampling. Using Gaussian kernels, the advantages of KENReg algorithm against the traditional one with i.i.d. samples are demonstrated on various real-world data sets. Experimental results show that the KENReg algorithm based on Markov selective sampling compared to that of randomly independent sampling not only has much higher prediction accuracy in terms of mean square errors and generates simpler models in terms of the number of non-zero regression parameters, but also has shorter total time of sampling and training. We compare the algorithm proposed in this paper with these known regularization algorithms, kernelized ridge regression and kernelized Least Absolute Shrinkage and Selection Operator (LASSO)


Springer


Elastic net, Markov sampling, Kernelized


Applied Statistics ; Pattern Recognition and Data Mining


https://doi.org/10.1016/j.knosys.2018.08.013


EP187158


Journal article - Refereed


English


0950-7051


Chen, Weijian; Xu, Chen; Zou, Bin; Jin, Warren; Xu, Jie. Kernelized Elastic Net Regularization Based on Markov Selective Sampling. Knowledge-based System. 2019; 163:57-68.https://doi.org/10.1016/j.knosys.2018.08.013



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