Multi-Output Bayesian Support Vector Regression Considering Dependent Outputs

Multi-output regression aims to utilize the correlation between outputs to achieve information transfer between dependent outputs, thus improving the accuracy of predictive models. Although the Bayesian support vector machine (BSVR) can provide both the mean and the predicted variance distribution of the data to be labeled, which has a large potential application value, its standard form is unable to handle multiple outputs at the same time. To solve this problem, this paper proposes a multi-output Bayesian support vector machine model (MBSVR), which uses a covariance matrix to describe the relationship between outputs and outputs and outputs and inputs simultaneously by introducing a semiparametric latent factor model (SLFM) in BSVR, realizing knowledge transfer between outputs and improving the accuracy of the model. MBSVR integrates and optimizes the parameters in BSVR and those in SLFM through Bayesian derivation to effectively deal with the multi-output problem on the basis of inheriting the advantages of BSVR. The effectiveness of the method is verified using two function cases and four high-dimensional real-world data with multi-output.