Counterfactual explanation of machine learning survival models

A method for counterfactual explanation of machine learning survival models is proposed. One of the difficulties of solving the counterfactual explanation problem is that the classes of examples are implicitly defined through outcomes of a machine learning survival model in the form of survival functions. A condition that establishes the difference between survival functions of the original example and the counterfactual is introduced. This condition is based on using a distance between mean times to event. It is shown that the counterfactual explanation problem can be reduced to a standard convex optimization problem with linear constraints when the explained black-box model is the Cox model. For other black-box models, it is proposed to apply the well-known Particle Swarm Optimization algorithm. A lot of numerical experiments with real and synthetic data demonstrate the proposed method.

A robust algorithm for explaining unreliable machine learning survival models using the Kolmogorov-Smirnov bounds

A new robust algorithm based of the explanation method SurvLIME called SurvLIME-KS is proposed for explaining machine learning survival models. The algorithm is developed to ensure robustness to cases of a small amount of training data or outliers of survival data. The first idea behind SurvLIME-KS is to apply the Cox proportional hazards model to approximate the black-box survival model at the local area around a test example due to the linear relationship of covariates in the model. The second idea is to incorporate the well-known Kolmogorov-Smirnov bounds for constructing sets of predicted cumulative hazard functions. As a result, the robust maximin strategy is used, which aims to minimize the average distance between cumulative hazard functions of the explained black-box model and of the approximating Cox model, and to maximize the distance over all cumulative hazard functions in the interval produced by the Kolmogorov-Smirnov bounds. The maximin optimization problem is reduced to the quadratic program. Various numerical experiments with synthetic and real datasets demonstrate the SurvLIME-KS efficiency.

SurvLIME-Inf: A simplified modification of SurvLIME for explanation of machine learning survival models

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.

SurvLIME: A method for explaining machine learning survival models

A new method called SurvLIME for explaining machine learning survival models is proposed. It can be viewed as an extension or modification of the well-known method LIME. The main idea behind the proposed method is to apply the Cox proportional hazards model to approximate the survival model at the local area around a test example. The Cox model is used because it considers a linear combination of the example covariates such that coefficients of the covariates can be regarded as quantitative impacts on the prediction. Another idea is to approximate cumulative hazard functions of the explained model and the Cox model by using a set of perturbed points in a local area around the point of interest. The method is reduced to solving an unconstrained convex optimization problem. A lot of numerical experiments demonstrate the SurvLIME efficiency.

An explanation method for Siamese neural networks

A new method for explaining the Siamese neural network is proposed. It uses the following main ideas. First, the explained feature vector is compared with the prototype of the corresponding class computed at the embedding level (the Siamese neural network output). The important features at this level are determined as features which are close to the same features of the prototype. Second, an autoencoder is trained in a special way in order to take into account the embedding level of the Si-amese network, and its decoder part is used for reconstructing input data with the corresponding changes. Numerical experiments with the well-known dataset MNIST illustrate the propose method.