Density ratio estimation (DRE) is at the core of various machine learning tasks such as anomaly detection and domain adaptation. In existing studies on DRE, methods based on Bregman divergence (BD) minimization have been extensively studied. However, BD minimization when applied with highly flexible models, such as deep neural networks, tends to suffer from what we call train-loss hacking, which is a source of overfitting caused by a typical characteristic of empirical BD estimators. In this paper, to mitigate train-loss hacking, we propose a non-negative correction for empirical BD estimators. Theoretically, we confirm the soundness of the proposed method through a generalization error bound. Through our experiments, the proposed methods show a favorable performance in inlier-based outlier detection.

翻译：密度比率估计(DRE)是各种机器学习任务的核心,如异常探测和域适应。在现有的关于DRE的研究中,对基于Bregman差异(BD)最小化的方法进行了广泛研究。然而,在运用高度灵活的模型(如深神经网络)时,BD最小化往往会受到我们称之为火车损失黑客的损害,这是经验性BD测算器的典型特征造成的超标。在本文中,为了减少火车损失黑客,我们建议对经验性BD估计器进行非负校正。理论上,我们通过约束一般化错误来确认拟议方法的健全性。通过我们的实验,拟议方法显示了基于内向外探测的优异性表现。