Most likely heteroscedastic gaussian process regression

This paper presents a novel Gaussian pro-cess (GP) approach to regression with input-dependent noise rates. We follow Gold-berg 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 re-sulting 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 experi-ments on both synthetic and real-world data, including a challenging perception problem in robotics, show the effectiveness of most likely heteroscedastic GP regression. 1