  A large number and diversity of techniques have been offered in the
literature in recent years for solving multi-label classification tasks,
including classifier chains where predictions are cascaded to other models as
additional features. The idea of extending this chaining methodology to
multi-output regression has already been suggested and trialed: regressor
chains. However, this has so-far been limited to greedy inference and has
provided relatively poor results compared to individual models, and of limited
applicability. In this paper we identify and discuss the main limitations,
including an analysis of different base models, loss functions, explainability,
and other desiderata of real-world applications. To overcome the identified
limitations we study and develop methods for regressor chains. In particular we
present a sequential Monte Carlo scheme in the framework of a probabilistic
regressor chain, and we show it can be effective, flexible and useful in
several types of data. We place regressor chains in context in general terms of
multi-output learning with continuous outputs, and in doing this shed
additional light on classifier chains.
