# Minimax bounds for structured prediction

## TL;DR

This paper establishes fundamental limits on the number of samples needed for learning structured prediction models, specifically factor-graph inference models, providing a theoretical understanding of their sample complexity.

## Contribution

It introduces minimax bounds for factor-graph structured prediction models, revealing the minimal sample size required for any algorithm to successfully learn these predictors.

## Key findings

- Derived minimax bounds for factor-graph models
- Characterized the necessary sample complexity for structured prediction
- Provided theoretical limits applicable to all algorithms

## Abstract

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.