A time-series prediction framework using sequential learning algorithms and dimensionality reduction within a sparsification approach

Abstract

The adaptive kernel filters are sequential learning algorithms that operate in a particular functional space called a reproducing kernel Hilbert space. However, their performance depends on the selection of two hyper-parameters, i.e., kernel bandwidth and learning-rate. Besides, as these algorithms train the model using a sequence of input vectors, their computation scales with the number of samples. In this work, we propose to address the previous challenges of these sequential learning algorithms. The proposed framework, unlike similar methods, maximizes the correntropy function to optimize the bandwidth and learning-rate parameters. Further, we introduce a sparsification strategy based on dimensionality reduction to remove redundant samples. The framework is tested on both synthetic and real-world data sets, showing convergence to relatively low values of mean-square-error.