Minimax bounds for structured prediction
This work addresses a gap in theoretical understanding for structured prediction, offering foundational insights for researchers in machine learning, though it is incremental as it builds on existing factor-graph models.
The paper tackles the problem of determining the necessary sample complexity for learning factor-graph predictors in structured prediction, providing minimax bounds that characterize the required number of samples for any algorithm.
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.