  Structured prediction can be considered as a generalization of many standard
supervised learning tasks, and is usually thought as a simultaneous prediction
of multiple labels. One standard approach is to maximize a score function on
the space of labels, which decomposes as a sum of unary and pairwise
potentials, each depending on one or two specific labels, respectively. For
this approach, several learning and inference algorithms have been proposed
over the years, ranging from exact to approximate methods while balancing the
computational complexity. However, in contrast to binary and multiclass
classification, results on the necessary number of samples for achieving
learning is still limited, even for a specific family of predictors such as
factor graphs. In this work, we provide minimax bounds for a class of
factor-graph inference models for structured prediction. That is, we
characterize the necessary sample complexity for any conceivable algorithm to
achieve learning of factor-graph predictors.
