INVESTIGADOR(ES) PRINCIPAL(ES):

Mauricio Alexander Alvarez Lopez

5 horas

CODIGO CIE

6-15-8

Edgar Alirio Valencia Angulo

Coinvestigador

0 Horas

TIPO DE CONVOCATORIA

2014. Convocatoria 652. Programa De Intercambio De Investigadores Colombia-Francia

TIPO DE PROYECTO

Investigación Básica

OBJETIVO(S)

General goal To develop a general methodology for nonlinearization of autoregressive processes by using Hilbert space embeddings for distributions. Specific goals 1) To develop a non-linear version of an autoregressive process by using covariance operators within the Hilbert space embedding theory, and the Yule-Walker algorithm. 2) To develop an algorithm for solving the pre-image problem in the kernelized version of the autoregressive process. 3. To validate the method proposed over non-linear time-series datasets, and compare its compare its performace against different versions of non-linear autoregressive processes.

RESUMEN

Autoregressive processes are useful probabilistic models for discrete time random processes. The basic idea in an autoregressive process is that the random variable at time n, can be described as a linear combination of the p past random variables associated to the process, plus white Gaussian noise. The value of p determines the order of the autoregressive process (Shanmugan and Breipohl, 1988). Different authors have proposed non-linear extensions of the above model, for example, NARMAX (Non-linear autoregressive moving average model with exogenous inputs) (Shumway and Stoffer, 2011). Other authors have proposed the use of more general nonlinear regression methods for extending the classical autoregressive process to non-linear setups. These general regression methods include neural networks (Nelles, 2001), Gaussian processes (Kocijan et al., 2005), and kernel methods (Kallas et al. 2013). On the other hand, Hilbert space embeddings are a recent trend in kernel methods that map distributions into infinite-dimensional feature spaces using kernels, such that comparisonsand manipulations of these distributions can be performed using standard feature space operations like inner products or projections (Song et al., 2013). Hilbert space embeddings have been succesfully used as alternatives to traditional parametric probabilistic models like hidden Markov models (Song et al., 2010) or linear dynamical systems (Song et al., 2008). They have also been used as nonparametric alternatives to statistical tests (Smola et al., 2007). Motivated by this powerful framework, our objective with this proposal is to use Hilbert space embeddings for nonparametric estimation of an autoregressive process, essentially leading to a non-linear version of the autoregressive model. To the best of our knowledge, this is the first time that the Hilbert space embedding method will be applied to an stochastic process with dependencies that go beyond the Markov assumption.

ESTADO

Concluido

FECHA DE INICIO

18/03/2015

FECHA DE FINALIZACION

18/03/2017

PRODUCTOS

Curso: "Avances on Kernel Methods"

Cursos o talleres de extensión

Short-term time series prediction using Hilbert space embeddings of autoregressive processes

Artículo publicado en Revista de divulgación

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