Multiclass Calibration Assessment and Recalibration of Probability Predictions via the Linear Log Odds Calibration Function

Machine-generated probability predictions are essential in modern classification tasks such as image classification. A model is well calibrated when its predicted probabilities correspond to observed event frequencies. Despite the need for multicategory recalibration methods, existing methods are limited to (i) comparing calibration between two or more models rather than directly assessing the calibration of a single model, (ii) requiring under-the-hood model access, e.g., accessing logit-scale predictions within the layers of a neural network, and (iii) providing output which is difficult for human analysts to understand. To overcome (i)-(iii), we propose Multicategory Linear Log Odds (MCLLO) recalibration, which (i) includes a likelihood ratio hypothesis test to assess calibration, (ii) does not require under-the-hood access to models and is thus applicable on a wide range of classification problems, and (iii) can be easily interpreted. We demonstrate the effectiveness of the MCLLO method through simulations and three real-world case studies involving image classification via convolutional neural network, obesity analysis via random forest, and ecology via regression modeling. We compare MCLLO to four comparator recalibration techniques utilizing both our hypothesis test and the existing calibration metric Expected Calibration Error to show that our method works well alone and in concert with other methods.