Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Online prediction of time series data with kernels
IEEE Transactions on Signal Processing
Penalized preimage learning in kernel principal component analysis
IEEE Transactions on Neural Networks
Algorithms for learning kernels based on centered alignment
The Journal of Machine Learning Research
IEEE Transactions on Signal Processing
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This paper proposes nonlinear autoregressive (AR) models for time series, within the framework of kernel machines. Two models are investigated. In the first proposed model, the AR model is defined on the mapped samples in the feature space. In order to predict a future sample, this formulation requires to solve a pre-image problem to get back to the input space. We derive an iterative technique to provide a fine-tuned solution to this problem. The second model bypasses the pre-image problem, by defining the AR model with an hybrid model, as a tradeoff considering the computational time and the precision, by comparing it to the iterative, fine-tuned, model. By considering the stationarity assumption, we derive the corresponding Yule-Walker equations for each model, and show the ease of solving these problems. The relevance of the proposed models is studied on several time series, and compared with other well-known models in terms of accuracy and computational complexity.