Calibrated Structured Prediction

In user-facing applications, displaying calibrated confidence measures---probabilities that correspond to true frequency---can be as important as obtaining high accuracy. We are interested in calibration for structured prediction problems such as speech recognition, optical character recognition, and medical diagnosis. Structured prediction presents new challenges for calibration: the output space is large, and users may issue many types of probability queries (e.g., marginals) on the structured output. We extend the notion of calibration so as to handle various subtleties pertaining to the structured setting, and then provide a simple recalibration method that trains a binary classifier to predict probabilities of interest. We explore a range of features appropriate for structured recalibration, and demonstrate their efficacy on three real-world datasets.