Backward Inference in Probabilistic Regressor Chains with Distributional Constraints

State-of-the-art approaches for multi-target prediction, such as Regressor Chains, can exploit interdependencies among the targets and model the outputs jointly, by flowing predictions from the first output to the last. While these models are very useful in applications where targets are highly interdependent and should be modeled jointly, they are however unable to answer queries in situations when targets are not only mutually dependent but also have joint constraints over the output. In addition, existing models are unsuitable when certain target values are fixed or manually imputed prior to inference, and as a result, the flow of predictions cannot cascade backward from an already-imputed output. Here we present a solution to the aforementioned problem as a backward inference algorithm for Regressor Chains via Metropolis-Hastings sampling. We evaluate the proposed approach via different metrics using both synthetic and real-world data. We show that our approach notably reduces errors when compared to traditional marginal inference methods that overlook joint modeling. Furthermore, we show that the proposed method can provide useful insights into a problem in conservation science in predicting the distribution of potential natural vegetation.