# Scaling up Vector Autoregressive Models With Operator-Valued Random Fourier Features

2 S2A - Signal, Statistique et Apprentissage
LTCI - Laboratoire Traitement et Communication de l'Information
Abstract : A nonparametric approach to Vector Autoregressive Modeling consists in working in vector-valued Reproducing Kernel Hilbert Spaces. The main idea is to build vector-valued models (OKVAR) using operator-valued kernels. Similar to scalar-valued kernels, operator-valued kernels enjoy representer theorems and learning algorithms that heavily depends on training data. We present a new approach to scale up OKVAR models... This contribution aims at scaling up non-linear autoregression models based on operator-valued kernel ($K$) by constructing an explicit feature map function (ORFF) that transforms an input data to a Hilbert space 'embed' in the RKHS induced by $K$. ORFF are constructed in the spirit of Random Fourier Features introduced by Rahimi and Recht. We show that ORFF competes with VAR on stationary linear time-series in terms of time and accuracy. Moreover ORFF is able to compete with OVK accuracy on non-stationary, non-linear time-series (being better than VAR) while keeping low execution time, comparable to VAR.
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Conference papers
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https://hal.telecom-paris.fr/hal-02288472
Contributor : Telecomparis Hal <>
Submitted on : Saturday, September 14, 2019 - 6:51:30 PM
Last modification on : Tuesday, June 30, 2020 - 11:56:10 AM

### Identifiers

• HAL Id : hal-02288472, version 1

### Citation

Romain Brault, Néhémy Lim, Florence d'Alché-Buc. Scaling up Vector Autoregressive Models With Operator-Valued Random Fourier Features. 2nd ECML/PKDD Workshop on Advanced Analytics and Learning on Temporal Data (AALTD 2016), Sep 2016, Riva Del Garda, Italy. ⟨hal-02288472⟩

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