Learning with known operators reduces maximum error bounds
Learning with known operators reduces maximum error bounds
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DOI：
10.1038/s42256-019-0077-5
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发表时间：
2019-08-01
影响因子：
23.8
通讯作者：
Christiansen, Silke
中科院分区：
文献类型：
--
作者：
Maier, Andreas K.;Syben, Christopher;Christiansen, Silke
我们描述了一种将先验知识融入机器学习算法的方法。我们的目标是在物理和信号处理中的应用，我们知道，某些操作必须嵌入到算法中。任何允许计算其输入的梯度或子梯度的操作都适合我们的框架。我们推导出了深度网络的最大误差界，表明包含先验知识会导致其减少。此外，我们的实验表明，已知的运营商减少自由参数的数量。我们将这种方法应用于各种任务，从计算机断层扫描图像重建血管分割到以前未知的成像算法的推导。因此，该概念广泛适用于物理，成像和信号处理领域的许多研究人员。我们假设，我们的分析将支持进一步调查已知的运营商在其他领域的物理，成像和信号处理。深度神经网络可以包含任意的数学运算符，只要它们是可导出的。作者研究了如何通过使用与问题相关的算子将有关问题的知识纳入机器学习。
We describe an approach for incorporating prior knowledge into machine learning algorithms. We aim at applications in physics and signal processing in which we know that certain operations must be embedded into the algorithm. Any operation that allows computation of a gradient or sub-gradient towards its inputs is suited for our framework. We derive a maximal error bound for deep nets that demonstrates that inclusion of prior knowledge results in its reduction. Furthermore, we show experimentally that known operators reduce the number of free parameters. We apply this approach to various tasks ranging from computed tomography image reconstruction over vessel segmentation to the derivation of previously unknown imaging algorithms. As such, the concept is widely applicable for many researchers in physics, imaging and signal processing. We assume that our analysis will support further investigation of known operators in other fields of physics, imaging and signal processing. Deep neural networks can contain arbitrary mathematical operators, as long as they are derivable. The authors investigate how knowledge about a problem can be incorporated into machine learning through the use of operators that are related to the problem.