Machine learning based segmentation models are frequently miscalibrated, producing for each pixel a label prediction whose associated confidence does not accurately reflect the true underlying probability. This limitation is particularly critical in high-stakes applications such as medical image segmentation. Although several calibration methods have been proposed, only a small subset of them provides theoretical guarantees on the calibration error, i.e., they do not typically ensure that, with high probability, the model exhibits a low calibration error. In this work, we develop a post-hoc calibration method for which formal calibration guarantees can be established. To achieve this, we derive from standard concentration inequalities an improved theoretical bound that explicitly accounts for the spatial dependence inherent in binary segmentation outputs. We empirically demonstrate that the proposed calibrator satisfies the derived guarantee and outperforms existing post-hoc calibration approaches.
This work focuses on the analysis of fully connected feed forward ReLU neural networks as they approximate a given, smooth function. In contrast to conventionally studied universal approximation properties under increasing architectures, e.g., in terms of width or depth of the networks, we are concerned with the asymptotic growth of the parameters of approximating networks. Such results are of interest, e.g., for error analysis or consistency results for neural network training. The main result of our work is that, for a ReLU architecture with state of the art approximation error, the realizing parameters grow at most polynomially. The obtained rate with respect to a normalized network size is compared to existing results and is shown to be superior in most cases, in particular for high dimensional input.