Privacy Preserving Regression Residual Analysis

Regression analysis is one of the most basic statistical tools for generating predictive models that describe the relationship between variables. Once a model has been generated, numerous goodness-of-fit measures are used to evaluate the degree to which the model characterizes the relationship between the variables under consideration. The analysis of regression residuals is one such measure, where residuals may be subjectively examined for the presence of structure. However, the residual plots reveal substantial information about each participant’s private data. This issue is most pronounced in the two party case, where the violation of privacy is complete. In this work, we describe an algorithmic approach drawn from random graph theory to evaluate the degree of deviation of the regression residuals from an ideal model. We demonstrate that our approach is effective at characterizing accurate and poor models where previously proposed measures remain neutral or are not applicable. Finally, we provide an efficient privacy preserving protocol for computing our proposed goodnessof-fit measure.