论文标题
正规风险最小化的分配变化中的单调风险关系
Monotonic Risk Relationships under Distribution Shifts for Regularized Risk Minimization
论文作者
论文摘要
机器学习系统通常应用于与训练分布不同的分布中得出的数据。最近的工作表明，对于各种分类和信号重建问题，分布式性能与分布性能密切相关。如果这种关系或更通常是单调的关系，则会产生重要的后果。例如，它允许在一个分布上优化性能，以作为另一个分布的代理。在本文中，我们研究了预计模型对两个分布的性能之间的单调关系。我们证明了平方误差的确切渐近线性关系和在协变量偏移下ridge调查的通用线性模型错误分类误差的单调关系，以及线性反向问题的近似线性关系。
Machine learning systems are often applied to data that is drawn from a different distribution than the training distribution. Recent work has shown that for a variety of classification and signal reconstruction problems, the out-of-distribution performance is strongly linearly correlated with the in-distribution performance. If this relationship or more generally a monotonic one holds, it has important consequences. For example, it allows to optimize performance on one distribution as a proxy for performance on the other. In this paper, we study conditions under which a monotonic relationship between the performances of a model on two distributions is expected. We prove an exact asymptotic linear relation for squared error and a monotonic relation for misclassification error for ridge-regularized general linear models under covariate shift, as well as an approximate linear relation for linear inverse problems.
