Deep Neural Networks (DNNs) have performed admirably in classification tasks. However, the characterization of their classification uncertainties, required for certain applications, has been lacking. In this work, we investigate the issue by assessing DNNs' ability to estimate conditional probabilities and propose a framework for systematic uncertainty characterization. Denoting the input sample as x and the category as y, the classification task of assigning a category y to a given input x can be reduced to the task of estimating the conditional probabilities p(y|x), as approximated by the DNN at its last layer using the softmax function. Since softmax yields a vector whose elements all fall in the interval (0, 1) and sum to 1, it suggests a probabilistic interpretation to the DNN's outcome. Using synthetic and real-world datasets, we look into the impact of various factors, e.g., probability density f(x) and inter-categorical sparsity, on the precision of DNNs' estimations of p(y|x), and find that the likelihood probability density and the inter-categorical sparsity have greater impacts than the prior probability to DNNs' classification uncertainty.

翻译：深度神经网络（DNN）在分类任务中表现出色。然而，对于某些应用所需的分类不确定性表征，目前仍存在不足。本文通过评估DNN对条件概率的估计能力来探究这一问题，并提出了一种系统性的不确定性表征框架。将输入样本记为x，类别记为y，为给定输入x分配类别y的分类任务可简化为估计条件概率p(y|x)的任务，该概率由DNN在最后一层通过softmax函数近似计算。由于softmax生成的向量元素均落在区间(0,1)内且和为1，这为DNN的输出提供了概率解释。我们利用合成数据集和真实数据集，研究了概率密度f(x)和类别间稀疏性等因素对DNN估计p(y|x)精度的影响，发现似然概率密度和类别间稀疏性对DNN分类不确定性的影响大于先验概率。