  Missing value imputation is an important practical problem. There is a large
body of work on it, but there does not exist any work that formulates the
problem in a structured output setting. Also, most applications have
constraints on the imputed data, for example on the distribution associated
with each variable. None of the existing imputation methods use these
constraints. In this paper we propose a structured output approach for missing
value imputation that also incorporates domain constraints. We focus on large
margin models, but it is easy to extend the ideas to probabilistic models. We
deal with the intractable inference step in learning via a piecewise training
technique that is simple, efficient, and effective. Comparison with existing
state-of-the-art and baseline imputation methods shows that our method gives
significantly improved performance on the Hamming loss measure.
