论文标题
迈向基于内核的数据和模型的不确定性分解框架
Towards a Kernel based Uncertainty Decomposition Framework for Data and Models
论文作者
论文摘要
本文介绍了一个新的框架，用于量化数据和模型的预测不确定性，依赖于将数据投影到高斯复制子元素希尔伯特空间（RKHS）中，并以量化其拓扑电位的流程在所有点上量化了梯度的流量，并将数据概率密度函数（PDF）转换为样品空间中的梯度流量。这可以通过将量子物理（特别是Schrodinger的配方）将PDF梯度流的分解作为矩分解问题进行分解。我们在实验上表明，高阶模式系统地聚集了PDF的不同尾部区域，从而提供了具有高认知不确定性的数据区域的前所未有的歧视性分辨率。从本质上讲，这种方法分解了数据PDF的局部实现，从不确定性时刻来看。我们将此框架应用于对点预测神经网络模型的预测不确定性量化的替代工具，从而克服了常规贝叶斯基于贝叶斯的不确定性量化方法的各种局限性。与一些既定方法的实验比较说明了我们框架所表现出的性能优势。
This paper introduces a new framework for quantifying predictive uncertainty for both data and models that relies on projecting the data into a Gaussian reproducing kernel Hilbert space (RKHS) and transforming the data probability density function (PDF) in a way that quantifies the flow of its gradient as a topological potential field quantified at all points in the sample space. This enables the decomposition of the PDF gradient flow by formulating it as a moment decomposition problem using operators from quantum physics, specifically the Schrodinger's formulation. We experimentally show that the higher order modes systematically cluster the different tail regions of the PDF, thereby providing unprecedented discriminative resolution of data regions having high epistemic uncertainty. In essence, this approach decomposes local realizations of the data PDF in terms of uncertainty moments. We apply this framework as a surrogate tool for predictive uncertainty quantification of point-prediction neural network models, overcoming various limitations of conventional Bayesian based uncertainty quantification methods. Experimental comparisons with some established methods illustrate performance advantages exhibited by our framework.
