Kernel-Based Autoregressive Modeling with a Pre-Image Technique

Maya Kallas (1) , Paul Honeine (1) , Cédric Richard (2) , Clovis Francis (3) , Hassan Amoud (3)

1 LM2S - Laboratoire Modélisation et Sûreté des Systèmes
2 FIZEAU - Laboratoire Hippolyte Fizeau
3 LU / ULB - الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth]

Autoregressive (AR) modeling is a very popular method for time series analysis. Being linear by nature, it obviously fails to adequately describe nonlinear systems. In this paper, we propose a kernel-based AR modeling, by combining two main concepts in kernel machines. One the one hand, we map samples to some nonlinear feature space, where an AR model is considered. We show that the model parameters can be determined without the need to exhibit the nonlinear map, by computing inner products thanks to the kernel trick. On the other hand, we propose a prediction scheme, where the prediction in the feature space is mapped back into the input space, the original samples space. For this purpose, a pre-image technique is derived to predict the future back in the input space. The efficiency of the proposed method is illustrated on real-life time-series, by comparing it to other linear and nonlinear time series prediction techniques.

Mots clés: pre-image problem; adaptive filtering; autoregressive processes; time series; kernel-based autoregressive modeling; pre-image technique; nonlinear system; kernel-based AR modeling; kernel machines; nonlinear map; kernel trick; feature space; nonlinear time series prediction; Kernel; Time series analysis; Predictive models; Machine learning; Support vector machines; Mathematical model; Kalman filters; pre-image; kernel machine; autoregressive modeling; pattern recognition; prediction

Domaines: Apprentissage [cs.LG]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Maya Kallas, Paul Honeine, Cédric Richard, Clovis Francis, Hassan Amoud. Kernel-Based Autoregressive Modeling with a Pre-Image Technique. Proc. IEEE workshop on Statistical Signal Processing (SSP), 2011, Nice, France. pp.281 - 284, ⟨10.1109/SSP.2011.5967681⟩. ⟨hal-01966028⟩