On Sensitivity of Data Models w.r.t. Training Data.

In this article, we suggest a way how to quantify the sensitivity of a data model w.r.t. training data at a certain input by using a derived model having a single data point as artificial parameter, and we relate our definition of sensitivity w.r.t. training data to the complexity of a data model. In case of linear regression and ridge regression we give an explicit expression for the so defined sensitivity w.r.t. training data and study the properties. Moreover, we discuss the numerical approximation of sensitivity w.r.t. training data for neural networks and provide an application of this numerical approximation to remote sensing in the environmental sciences.