Uncertainty Interpretation of the Machine Learning Survival Model Predictions

Lev V Utkin,Andrei V Konstantinov,Alexey A Lukashin,Vladimir S Zaborovsky,Maxim S Kovalev,Natalia A Politaeva

doi:10.1109/access.2021.3108341

Lev V Utkin, Andrei V Konstantinov + Show 4 more

Open Access

https://doi.org/10.1109/access.2021.3108341

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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.

Highlights

We propose a method for uncertainty interpretation of the black-box survival model predictions called UncSurvEx, which uses some ideas of the SurvLIME method [14]
UncSurvEx solves the problem of searching for important features of a single example, which impact on uncertainty of the corresponding machine learning survival model predictions represented in the form of precise survival function (SF) or cumulative hazard function (CHF)
Results of experiments for the dataset Stanford2 are shown in Table 7, where three points randomly selected from Xtest are analyzed

Summary

EXPLANATION OF SURVIVAL MODELS AND UNCERTAINTY INTERPRETATION

Survival analysis is one of the important supplements to many applications, including, medicine, reliability, risk analysis, etc. It is important to note that the proposed method of the local uncertainty interpretation like methods SurvLIME [14] and SurvLIME-KS [15] is based on the idea of using the Cox model because this is a unique survival model providing a simple linear relationship between features and the model outcome. UncSurvEx solves the problem of searching for important features of a single example, which impact on uncertainty of the corresponding machine learning survival model predictions represented in the form of precise SFs or CHFs. In other words, UncSurvEx searches for important features which are responsible for the distance between the prediction and the most uncertain probability distributions (the uniform distribution).

RELATED WORK

THE CERTAINTY MEASURE: A FORMAL DEFINITION

COMPUTING OPTIMAL COEFFICIENTS

NUMERICAL EXPERIMENTS WITH SYNTHETIC DATA

THE BLACK-BOX COX MODEL

VIII. CONCLUSION