Bayesian Support Vector Regression Using a Unified Loss Function

Abstract

In this paper, we use a unified loss function, called the soft insensitive loss function, for Bayesian support vector regression. We follow standard Gaussian processes for regression to set up the Bayesian framework, in which the unified loss function is used in the likelihood evaluation. Under this framework, the maximum a posteriori estimate of the function values corresponds to the solution of an extended support vector regression problem. The overall approach has the merits of support vector regression such as convex quadratic programming and sparsity in solution representation. It also has the advantages of Bayesian methods for model adaptation and error bars of its predictions. Experimental results on simulated and real-world data sets indicate that the approach works well even on large data sets.

Bayesian Support Vector Regression for traffic speed prediction with error bars

“…where f k is the relationship function for k th prediction horizon with i.i.d noise samples {δ j } d j=1 [7], [8]. The extension of (2) to Bayesian framework will help us to find optimal hyperparameters for SVR.…”

“…We propose Bayesian Support Vector Regression (BSVR) to provide error bars [7], [8] for the predicted traffic states.…”

“…This technique combines advantages of SVR and Bayesian inference [8]. SVR is highly suitable for traffic prediction as it can map non-linear relationships between past and future traffic conditions for SVR [4], [9].…”

“…Bayesian methods for SVR are useful for selecting suitable hyperparameters [10]. They can also estimate variance (termed as error bar, [7], [8]) associated with each prediction. The estimated variance can be considered as a confidence measure for the corresponding predicted traffic state.…”

“…This increases the computational complexity of such algorithms. BSVR overcomes both these issues [8].…”