Minimax Bounds For Structured Prediction Based On Factor Graphs

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 usually 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 are still limited, even for a specific family of predictors such as factor graphs. In this work, we provide minimax lower bounds for a class of general factor-graph inference models in the context of structured prediction. That is, we characterize the necessary sample complexity for any conceivable algorithm to achieve learning of general factor-graph predictors.