We propose a framework for the assessment of uncertainty quantification in deep regression. The framework is based on regression problems where the regression function is a linear combination of nonlinear functions. Basically, any level of complexity can be realized through the choice of the nonlinear functions and the dimensionality of their domain. Results of an uncertainty quantification for deep regression are compared against those obtained by a statistical reference method. The reference method utilizes knowledge of the underlying nonlinear functions and is based on a Bayesian linear regression using a reference prior. Reliability of uncertainty quantification is assessed in terms of coverage probabilities, and accuracy through the size of calculated uncertainties. We illustrate the proposed framework by applying it to current approaches for uncertainty quantification in deep regression. The flexibility, together with the availability of a reference solution, makes the framework suitable for defining benchmark sets for uncertainty quantification.
翻译:我们提出深回归的不确定性定量评估框架。框架基于回归问题,其中回归函数是非线性函数的线性组合。基本上,任何复杂程度都可以通过选择非线性函数及其域的维度来实现。深度回归的不确定性量化结果与统计参考方法得出的结果进行比较。参考方法利用对基础非线性函数的知识,并基于先前使用的巴耶斯线性回归。不确定性量化的可靠性以覆盖概率和计算出的不确定性大小的准确性来评估。我们通过将拟议框架应用于当前在深度回归中的不确定性量化方法来说明拟议框架。灵活性加上参考方法的可用性,使得确定不确定性量化基准的框架适合确定。