Uncertainty Interpretation of the Machine Learning Survival Model Predictions

Abstract

A method for interpreting uncertainty of predictions provided by machine learning survival models is proposed. It is called UncSurvEx and aims to determine which features of an analyzed example lead to uncertain predictions of an explainable black-box survival model. One of the ideas behind the proposed method is to approximate the uncertainty measure of a local black-box survival model prediction by the uncertainty measure of the Cox proportional hazards model at the local area around a test example. The linear relationship between covariates and predictions in the corresponding Cox model allows determining quantitative impacts of covariates on the uncertainty measure. A specific certainty measure of the survival function, taking into account the most uncertain survival function, is introduced to interpret the prediction uncertainty. The $L_{2}$ -norm is used to compute the distance between survival functions. The method leads to an unconstrained non-convex optimization problem which is solved by means of the well-known Broyden–Fletcher–Goldfarb–Shanno algorithm. A lot of numerical experiments demonstrate the uncertainty interpretation method.

Keywords

• Explainable AI
• survival analysis
• uncertainty
• censored data
• the Cox model