Fast multi-output relevance vector regression

Abstract

This paper aims to decrease the time complexity of multi-output relevance vector regression from O V M 3 to O V 3 + M 3 , where V is the number of output dimensions, M is the number of basis functions, and V < M . The experimental results demonstrate that the proposed method is more competitive than the existing method, with regard to computation time. MATLAB codes are available at FMRVR ter 6), Thayananthan et al. (2008) uses the Bayes' theorem and the kernel trick to perform regression, but it has the limitation of low computational efficiency. Therefore, a new faster algorithm is proposed in this paper: it uses the matrix normal distribution to model correlated outputs, while the existing algorithm uses the multivariate normal distribution.The contributions of this paper are: • in Section 4, to propose a new algorithm with less time complexity than the existing MRVR algorithm by Thayananthan (2005, Chapter 6), Thayananthan et al. (2008); • in Section 5, to present Monte Carlo simulation results to compare between the existing and the proposed MRVR algorithm in terms of accuracy and computation time.The rest of this paper is organised as follows: Section 2 lists related work. Section 3 and Section 4 describe the existing and proposed algorithms of MRVR, respectively. Section 5 shows the experimental results by using MATLAB, and Section 6 gives the conclusion.

Unified Evaluation Framework for Stochastic Algorithms Applied to Remaining Useful Life Prognosis Problems

“…Some other studies also evaluate the timeliness of the algorithms based on more sophisticated metrics such as the Prognosis Horizon (PH) [17,26], α-λ performance [23], the Convergence of the Relative Accuracy (CRA) [18] or the convergence time [27]. There are also studies that evaluate the computational cost of the algorithm in terms of simulation time [23,28] or in terms of amount of required basic operations (FLOPs) [3].…”