Generalized Multi-Output Gaussian Process Censored Regression

• Censored data as defining characteristic of numerous domains in science. Heteroscedastic Multi-Output Gaussian Process formulated for censored regression. Generalization arbitrary likelihood functions enabled by devising a variational bound to the marginal log-likelihood. Experiments with synthetic and real-world demonstrate solution approach. When modelling observations (i.e. which value measurement or observation is un-observable beyond given threshold), typical approach current regression methods use censored-Gaussian Tobit) model describe conditional output distribution. In this paper, case missing data, we argue that exploiting correlations between multiple outputs can enable models better address bias introduced data. To do so, introduce heteroscedastic multi-output process combines non-parametric flexibility GPs ability leverage information from correlated under input-dependent noise conditions. resulting inference intractability, further devise log-likelihood suitable stochastic optimization. We empirically evaluate our against other generative on both real world tasks show how it be generalized deal functions. Results added allows estimate underlying non-censored true) potentially complex censoring dynamics.