Leveraged non-stationary Gaussian process regression for autonomous robot navigation

In this paper, we propose a novel regression method that can incorporate both positive and negative training data into a single regression framework. In detail, a leveraged kernel function for non-stationary Gaussian process regression is proposed. With this new kernel function, we can vary the correlation betwen two inputs in both positive and negative directions by adjusting leverage parameters. By using this property, the resulting leveraged non-stationary Gaussian process regression can anchor the regressor to the positive data while avoiding the negative data. We first prove the positive semi-definiteness of the leveraged kernel function using Bochner's theorem. Then, we apply the leveraged non-stationary Gaussian process regression to a real-time motion control problem. In this case, the positive data refer to what to do and the negative data indicate what not to do. The results show that the controller using both positive and negative data outperforms the controller using positive data only in terms of the collision rate given training sets of the same size.