Leibniz Institute of Photonic Technology (IPHT), Jena, Germany.
Institute of Physical Chemistry and Abbe Center of Photonics, Friedrich Schiller University, Jena, Germany.
PLoS One. 2023 Apr 20;18(4):e0284723. doi: 10.1371/journal.pone.0284723. eCollection 2023.
Recently a new family of loss functions called smart error sums has been suggested. These loss functions account for correlations within experimental data and force modeled data to obey these correlations. As a result, multiplicative systematic errors of experimental data can be revealed and corrected. The smart error sums are based on 2D correlation analysis which is a comparably recent methodology for analyzing spectroscopic data that has found broad application. In this contribution we mathematically generalize and break down this methodology and the smart error sums to uncover the mathematic roots and simplify it to craft a general tool beyond spectroscopic modelling. This reduction also allows a simplified discussion about limits and prospects of this new method including one of its potential future uses as a sophisticated loss function in deep learning. To support its deployment, the work includes computer code to allow reproduction of the basic results.
最近，人们提出了一种新的损失函数家族，称为智能误差和。这些损失函数考虑了实验数据中的相关性，并迫使建模数据遵守这些相关性。因此，可以揭示和纠正实验数据的乘法系统误差。智能误差和基于二维相关分析，这是一种相对较新的分析光谱数据的方法，已经得到了广泛的应用。在本贡献中，我们从数学上推广和分解了这种方法和智能误差和，以揭示数学根源，并简化它，以制作超越光谱建模的通用工具。这种简化还允许简化讨论这种新方法的限制和前景，包括将其作为深度学习中复杂损失函数的潜在未来用途之一。为了支持其部署，这项工作包括允许重现基本结果的计算机代码。
