Distributed non-disclosive validation of predictive models by a modified ROC-GLM

The applicability of our algorithms depends on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>ℓ</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:math> sensitivity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>Δ</mml:mi> <mml:mn>2</mml:mn></mml:msub> <mml:mrow><mml:mo>(</mml:mo> <mml:mover><mml:mi>f</mml:mi> <mml:mo>^</mml:mo></mml:mover> <mml:mo>)</mml:mo></mml:mrow> </mml:mrow> </mml:math> of the underlying statistical/predictive model. The simulations carried out have shown that the approximation error is acceptable for the majority of simulated cases. For models with high <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>Δ</mml:mi> <mml:mn>2</mml:mn></mml:msub> <mml:mrow><mml:mo>(</mml:mo> <mml:mover><mml:mi>f</mml:mi> <mml:mo>^</mml:mo></mml:mover> <mml:mo>)</mml:mo></mml:mrow> </mml:mrow> </mml:math> , the privacy parameters must be set accordingly higher to ensure sufficient privacy protection, which affects the approximation error. This work shows that complex measures, as the AUC, are applicable for validation in distributed setups while preserving an individual's privacy.