关联向量机的预测问题

(3)
i=0
where α is the vector of hyper-parameters. And compute the defined non-informative prior-distributions below by using Bayes’ rule.
p(ω, α, σ2|t) = P (t|ω, α, σ2)p(ω, α, σ2)
∗Corresponding author. Email address: sshuxin@ (Xin SHU).
© 1553–9105 / Copyright 2012 Binary Information Press
January 2012
48
X. Shu et al. /Journal of Computational Information Systems 8: 1 (2012) 47–54
Electricity consumption of a certain province from 2008.12.1 to 2008.12.31 is used to test the performance of the robust relevance vector regression model.In the process of training the robust relevance vector regression model,we employ the relevance vector regression models with the different dimensional input vector to find the optimal robust relevance vector regression model.Here, the robust relevance vector regression models with 3,4,5,6,7,8-dimensional input vector respectively are used in the study.It can be seen that the robust relevance vector regression model with 5-dimensional input vector has the best prediction effects among all the relevance vector regression models,and the prediction effects of the robust relevance vector regression model are better than those of the support vector regression model.
Given a set of input samples {xi, ti}ni=1,the function likelihood of dataset can be written as
p(t|ω,
σ2)
=
1 (√
2πσ2
)nexp{−
1 2σ2
||t
−
ηω||2}
(1)
where η is the design matrix with
2 Robust Relevance Vector Regression Algorithm
2.1 Relevance vector regression algorithm
Relevance vector regression, based on Bayesian evidence framework, is a nonlinear probabilistic model.Generalization performance of relevance vector regression is comparable to that of support vector regression,and relevance vector regression is a higher sparse model.
ηmn = k(xn, xm−1)
(2)
Then,we employ the new higher-level parameters to constrain a Gaussian prior probability distribution over the weights:
∏n
p(ω|α) = N (ωi|0, αi−1)
P
(t|ω,
ρ,
σ2)
=
(2πσ2)−
n 2
√ |P
|exp{−
1 2σ2
(t
−
ηω)′ p(t
−
ηω)}
(6)
where P = diag(ρ1, ρ2, · · · , ρn)
P (ω|t, α,
ρ, σ2)
=
p(ω|α)p(t|ω, ρ, σ2) p(t|ω, ρ, σ2)
=
N (ωal China Grid Company Limited, Wuhan 430077, China
Abstract
Relevance vector regression, based on Bayesian evidence framework, is a nonlinear probabilistic model. Generalization performance of relevance vector regression is comparable to that of support vector regression.In order to solve the QP problem of traditional relevance vector regression effectively, a robust relevance vector regression algorithm is proposed to predict electricity consumption in the paper. Electricity consumption of a certain province from 2008.12.1 to 2008.12.31 is used to test the performance of the robust relevance vector regression model.In the process of training the robust relevance vector regression model,we employ the relevance vector regression models with the different dimensional input vector to find the optimal robust relevance vector regression model. It can be seen that the robust relevance vector regression model with 5-dimensional input vector has the best prediction effects among all the relevance vector regression models,and the prediction effects of the robust relevance vector regression model are better than those of the support vector regression model.
(7)
where △ is the variance matrix and λ is the mean value vector.
Keywords: Robust Relevance Vector Regression; Probabilistic Interpretation;Learning Algorithm; Electricity Consumption
1 Introduction
Artificial neural network is one of the most popular intelligent prediction algorithms[1-3], which is widely applied to predict electricity consumption in the past years.However, artificial neural network needs a lot of training samples[4,5], small training samples are difficult to ensure the prediction accuracy of artificial neural network[6,7].Support vector regression(SVR),based on the statistical theory,is a nonlinear kernel-based learning algorithm,which can minimize an upper bound of the generalization error[8-10]. Relevance vector regression, based on Bayesian evidence framework, is a nonlinear probabilistic model. Generalization performance of relevance vector regression is comparable to that of support vector regression,and relevance vector regression is a higher sparse model.In order to solve the QP problem of traditional relevance vector regression effectively, a robust relevance vector regression algorithm is proposed to predict electricity consumption in the paper.