[Paper Review] SurvLIME-Inf: A simplified modification of SurvLIME for explanation of machine learning survival models

Lev V. Utkin, Maxim S. Kovalev+1 more|arXiv (Cornell University)|May 5, 2020

Explainable Artificial Intelligence (XAI)57 references4 citations

TL;DR

This paper proposes SurvLIME-Inf, a simplified modification of SurvLIME that uses the $L_{\ackslash infty}$-norm (Chebyshev distance) to measure the discrepancy between cumulative hazard functions in explaining black-box survival models. By reformulating the explanation task as a linear programming problem, SurvLIME-Inf achieves faster computation and superior performance on small training datasets compared to SurvLIME, which relies on $L_2$-norm optimization.

ABSTRACT

A new modification of the explanation method SurvLIME called SurvLIME-Inf for explaining machine learning survival models is proposed. The basic idea behind SurvLIME as well as SurvLIME-Inf is to apply the Cox proportional hazards model to approximate the black-box survival model at the local area around a test example. The Cox model is used due to the linear relationship of covariates. In contrast to SurvLIME, the proposed modification uses $L_{\infty }$-norm for defining distances between approximating and approximated cumulative hazard functions. This leads to a simple linear programming problem for determining important features and for explaining the black-box model prediction. Moreover, SurvLIME-Inf outperforms SurvLIME when the training set is very small. Numerical experiments with synthetic and real datasets demonstrate the SurvLIME-Inf efficiency.

Motivation & Objective

• To address the challenge of explaining black-box machine learning survival models, particularly when training data is limited.
• To improve upon SurvLIME by simplifying its optimization framework for better computational efficiency and robustness.
• To enable local, post-hoc explanation of survival predictions using the Cox proportional hazards model as a surrogate.
• To enhance interpretability in survival analysis by leveraging the $L_{\infty}$-norm for distance measurement between cumulative hazard functions.
• To support applications in healthcare and risk assessment where model transparency is critical.

Proposed method

• The method uses the Cox proportional hazards model as a local surrogate to explain predictions of a black-box survival model at a test instance.
• It generates synthetic instances around the test point and computes their cumulative hazard functions using the black-box model.
• The $L_{\infty}$-norm (Chebyshev distance) is used to measure the maximum absolute difference between the black-box and approximating Cox model's cumulative hazard functions.
• This transforms the explanation problem into a linear programming optimization task to estimate the Cox model coefficients.
• The approach is model-agnostic and applies to any survival model, including random survival forests and deep learning models.
• The method is validated on synthetic data and real-world datasets (Veteran, LUNG, PBC) with censored survival outcomes.

Experimental results

Research questions

• RQ1 Can replacing the $L_2$-norm with the $L_{\infty}$-norm in SurvLIME improve explanation accuracy and computational efficiency?
• RQ2 Does SurvLIME-Inf outperform SurvLIME when training data is scarce?
• RQ3 How well does SurvLIME-Inf preserve the shape of survival and cumulative hazard functions in local approximation?
• RQ4 Can SurvLIME-Inf provide reliable, interpretable feature importance rankings for individual survival predictions?
• RQ5 Is the linear programming formulation of SurvLIME-Inf more robust to data imprecision than the convex optimization used in SurvLIME?

Key findings

• SurvLIME-Inf significantly outperforms SurvLIME on small training sets, achieving lower RMSE for both model-approximated and true cumulative hazard functions when $n = 10$ and $n = 20$.
• For $n = 10$, SurvLIME-Inf reduces $RMSE_{\text{model}}$ from 0.719 (SurvLIME) to 0.290, and $RMSE_{\text{true}}$ from 0.809 to 0.575.
• For $n = 20$, $RMSE_{\text{model}}$ drops from 0.659 to 0.358, and $RMSE_{\text{true}}$ from 0.664 to 0.460.
• The performance advantage of SurvLIME-Inf diminishes as training set size increases, with both methods converging at $n = 30$ and $n = 40$.
• Numerical results on real datasets (Veteran, LUNG, PBC) confirm that SurvLIME-Inf produces accurate and visually consistent survival function approximations.
• The use of $L_{\infty}$-norm enables a linear programming formulation, simplifying computation and improving scalability for small-data scenarios.