Most Likely Heteroscedastic Gaussian Pro cess Regression

Most Likely Heteroscedastic Gaussian Pro cess Regression
Kristian Kersting - MIT CSAIL, USA Christian Plagemann - University of Freiburg, Germany Patrick Pfaff - University of Freiburg, Germany Wolfram Burgard - University of Freiburg, Germany
This paper presents a novel Gaussian process (GP) approach to regression with inputdependent noise rates. We follow Goldberg et al.’s approach and model the noise variance using a second GP in addition to the GP governing the noise-free output value. In contrast to Goldberg et al., however, we do not use a Markov chain Monte Carlo method to approximate the posterior noise variance but a most likely noise approach. The resulting model is easy to implement and can directly be used in combination with various existing extensions of the standard GPs such as sparse approximations. Extensive experiments on both synthetic and real-world data, including a challenging perception problem in robotics, show the effectiveness of most likely heteroscedastic GP regression.

Kristian Kersting - MIT CSAIL, USA
Christian Plagemann - University of Freiburg, Germany
Patrick Pfaff - University of Freiburg, Germany
Wolfram Burgard - University of Freiburg, Germany

This paper presents a novel Gaussian process (GP) approach to regression with inputdependent noise rates. We follow Goldberg et al.’s approach and model the noise variance using a second GP in addition to the GP governing the noise-free output value. In contrast to Goldberg et al., however, we do not use a Markov chain Monte Carlo method to approximate the posterior noise variance but a most likely noise approach. The resulting model is easy to implement and can directly be used in combination with various existing extensions of the standard GPs such as sparse approximations. Extensive experiments on both synthetic and real-world data, including a challenging perception problem in robotics, show the effectiveness of most likely heteroscedastic GP regression.