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

该研究提出了两种技术，一种是简化校准方法，将原问题转化为更简单的问题，并使用非参数重新校准方法进行解决，另一种是基于神经崩溃现象和大多数精确分类器可以被认为是K个不同函数的组合的观察来提出针对每个类别独立重新校准的方法。将这两种方法应用在一起可以减少预测和每个类别的校准误差。

基于类别和降维的校准方法