3 years ago

# Is my model any good: differentially private regression diagnostics

Ashwin Machanavajjhala, Yan Chen, Andrés F. Barrientos, Jerome P. Reiter

### Abstract

Linear and logistic regression are popular statistical techniques for analyzing multi-variate data. Typically, analysts do not simply posit a particular form of the regression model, estimate its parameters, and use the results for inference or prediction. Instead, they first use a variety of diagnostic techniques to assess how well the model fits the relationships in the data and how well it can be expected to predict outcomes for out-of-sample records, revising the model as necessary to improve fit and predictive power. In this article, we develop $$\epsilon$$ -differentially private diagnostics tools for regression, beginning to fill a gap in privacy-preserving data analysis. Specifically, we create differentially private versions of residual plots for linear regression and of receiver operating characteristic (ROC) curves as well as binned residual plot for logistic regression. The residual plot and binned residual plot help determine whether or not the data satisfy the assumptions underlying the regression model, and the ROC curve is used to assess the predictive power of the logistic regression model. These diagnostics improve the usefulness of algorithms for computing differentially private regression output, which alone does not allow analysts to assess the quality of the posited model. Our empirical studies show that these algorithms can be effective tools for allowing users to evaluate the quality of their models.

DOI: 10.1007/s10115-017-1128-z

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