Conditional multi-output regression

In multi-output regression, the goal is to establish a mapping from inputs to multivariate outputs that are often assumed unknown. However, in practice, some outputs may become available. How can we use this extra information to improve our prediction on the remaining outputs? For example, can we use the job data released today to better predict the house sales data to be released tomorrow? Most previous approaches use a single generative model to model the joint predictive distribution of all outputs, based on which unknown outputs are inferred conditionally from the known outputs. However, learning such a joint distribution for all outputs is very challenging and also unnecessary if our goal is just to predict each of the unknown outputs. We propose a conditional model to directly model the conditional probability of a target output on both inputs and all other outputs. A simple generative model is used to infer other outputs if they are unknown. Both models only consist of standard regression predictors, for example, Gaussian process, which can be easily learned.