Post-hoc Calibration of Neural Networks by g-Layers

• URL: http://arxiv.org/abs/2006.12807v2
• Date: Mon, 21 Feb 2022 12:08:52 GMT
• Title: Post-hoc Calibration of Neural Networks by g-Layers
• Authors: Amir Rahimi, Thomas Mensink, Kartik Gupta, Thalaiyasingam Ajanthan, Cristian Sminchisescu, Richard Hartley
• Abstract summary: In recent years, there is a surge of research on neural network calibration. It is known that minimizing Negative Log-Likelihood (NLL) will lead to a calibrated network on the training set if the global optimum is attained. We prove that even though the base network ($f$) does not lead to the global optimum of NLL, by adding additional layers ($g$) and minimizing NLL by optimizing the parameters of $g$ one can obtain a calibrated network.
• Score: 51.42640515410253
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Calibration of neural networks is a critical aspect to consider when incorporating machine learning models in real-world decision-making systems where the confidence of decisions are equally important as the decisions themselves. In recent years, there is a surge of research on neural network calibration and the majority of the works can be categorized into post-hoc calibration methods, defined as methods that learn an additional function to calibrate an already trained base network. In this work, we intend to understand the post-hoc calibration methods from a theoretical point of view. Especially, it is known that minimizing Negative Log-Likelihood (NLL) will lead to a calibrated network on the training set if the global optimum is attained (Bishop, 1994). Nevertheless, it is not clear learning an additional function in a post-hoc manner would lead to calibration in the theoretical sense. To this end, we prove that even though the base network ($f$) does not lead to the global optimum of NLL, by adding additional layers ($g$) and minimizing NLL by optimizing the parameters of $g$ one can obtain a calibrated network $g \circ f$. This not only provides a less stringent condition to obtain a calibrated network but also provides a theoretical justification of post-hoc calibration methods. Our experiments on various image classification benchmarks confirm the theory.

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