Class-wise and reduced calibration methods
This work addresses the challenge of reliable calibration for high-dimensional classifiers, which is crucial for applications requiring accurate probability estimates, though it appears incremental as it builds on existing calibration concepts.
The paper tackles the problem of calibrating probabilistic classifiers with many classes by proposing two techniques: a reduced calibration method that simplifies the problem while preserving calibration properties, and class-wise calibration methods that recalibrate each class separately, showing improved performance especially on imbalanced datasets.
For many applications of probabilistic classifiers it is important that the predicted confidence vectors reflect true probabilities (one says that the classifier is calibrated). It has been shown that common models fail to satisfy this property, making reliable methods for measuring and improving calibration important tools. Unfortunately, obtaining these is far from trivial for problems with many classes. We propose two techniques that can be used in tandem. First, a reduced calibration method transforms the original problem into a simpler one. We prove for several notions of calibration that solving the reduced problem minimizes the corresponding notion of miscalibration in the full problem, allowing the use of non-parametric recalibration methods that fail in higher dimensions. Second, we propose class-wise calibration methods, based on intuition building on a phenomenon called neural collapse and the observation that most of the accurate classifiers found in practice can be thought of as a union of K different functions which can be recalibrated separately, one for each class. These typically out-perform their non class-wise counterparts, especially for classifiers trained on imbalanced data sets. Applying the two methods together results in class-wise reduced calibration algorithms, which are powerful tools for reducing the prediction and per-class calibration errors. We demonstrate our methods on real and synthetic datasets and release all code as open source at https://github.com/appliedAI-Initiative