Calibrating neural networks is of utmost importance when employing them in safety-critical applications where the downstream decision making depends on the predicted probabilities. Measuring calibration error amounts to comparing two empirical distributions. In this work, we introduce a binning-free calibration measure inspired by the classical Kolmogorov-Smirnov (KS) statistical test in which the main idea is to compare the respective cumulative probability distributions. From this, by approximating the empirical cumulative distribution using a differentiable function via splines, we obtain a recalibration function, which maps the network outputs to actual (calibrated) class assignment probabilities. The spine-fitting is performed using a held-out calibration set and the obtained recalibration function is evaluated on an unseen test set. We tested our method against existing calibration approaches on various image classification datasets and our spline-based recalibration approach consistently outperforms existing methods on KS error as well as other commonly used calibration measures.

本文提出基于KS统计测试的无binning校准方法，使用样条逼近累积分布函数进行重新校准神经网络的输出结果，并在多个图像分类数据集上的实验结果表明，该方法优于现有的校准方法。

利用样条插值法对神经网络进行校准