Longitudinal Counterfactuals: Constraints and Opportunities

Counterfactual explanations are a common approach to providing recourse to data subjects. However, current methodology can produce counterfactuals that cannot be achieved by the subject, making the use of counterfactuals for recourse difficult to justify in practice. Though there is agreement that plausibility is an important quality when using counterfactuals for algorithmic recourse, ground truth plausibility continues to be difficult to quantify. In this paper, we propose using longitudinal data to assess and improve plausibility in counterfactuals. In particular, we develop a metric that compares longitudinal differences to counterfactual differences, allowing us to evaluate how similar a counterfactual is to prior observed changes. Furthermore, we use this metric to generate plausible counterfactuals. Finally, we discuss some of the inherent difficulties of using counterfactuals for recourse.

Provably Stable Feature Rankings with SHAP and LIME

Feature attributions are ubiquitous tools for understanding the predictions of machine learning models. However, popular methods for scoring input variables such as SHAP and LIME suffer from high instability due to random sampling. Leveraging ideas from multiple hypothesis testing, we devise attribution methods that correctly rank the most important features with high probability. Our algorithm RankSHAP guarantees that the $K$ highest Shapley values have the proper ordering with probability exceeding $1-\alpha$. Empirical results demonstrate its validity and impressive computational efficiency. We also build on previous work to yield similar results for LIME, ensuring the most important features are selected in the right order.

Stabilizing Estimates of Shapley Values with Control Variates

Shapley values are among the most popular tools for explaining predictions of blackbox machine learning models. However, their high computational cost motivates the use of sampling approximations, inducing a considerable degree of uncertainty. To stabilize these model explanations, we propose ControlSHAP, an approach based on the Monte Carlo technique of control variates. Our methodology is applicable to any machine learning model and requires virtually no extra computation or modeling effort. On several high-dimensional datasets, we find it can produce dramatic reductions in the Monte Carlo variability of Shapley estimates.

A Generic Approach for Reproducible Model Distillation

Model distillation has been a popular method for producing interpretable machine learning. It uses an interpretable "student" model to mimic the predictions made by the black box "teacher" model. However, when the student model is sensitive to the variability of the data sets used for training, the corresponded interpretation is not reliable. Existing strategies stabilize model distillation by checking whether a large enough corpus of pseudo-data is generated to reliably reproduce student models, but methods to do so have so far been developed for a specific student model. In this paper, we develop a generic approach for stable model distillation based on central limit theorem for the average loss. We start with a collection of candidate student models and search for candidates that reasonably agree with the teacher. Then we construct a multiple testing framework to select a corpus size such that the consistent student model would be selected under different pseudo sample. We demonstrate the application of our proposed approach on three commonly used intelligible models: decision trees, falling rule lists and symbolic regression. Finally, we conduct simulation experiments on Mammographic Mass and Breast Cancer datasets and illustrate the testing procedure throughout a theoretical analysis with Markov process.

A Generic Approach for Statistical Stability in Model Distillation

Model distillation has been a popular method for producing interpretable machine learning. It uses an interpretable "student" model to mimic the predictions made by the black box "teacher" model. However, when the student model is sensitive to the variability of the data sets used for training, the corresponded interpretation is not reliable. Existing strategies stabilize model distillation by checking whether a large enough corpus of pseudo-data is generated to reliably reproduce student models, but methods to do so have so far been developed for a specific student model. In this paper, we develop a generic approach for stable model distillation based on central limit theorem for the average loss. We start with a collection of candidate student models and search for candidates that reasonably agree with the teacher. Then we construct a multiple testing framework to select a corpus size such that the consistent student model would be selected under different pseudo sample. We demonstrate the application of our proposed approach on three commonly used intelligible models: decision trees, falling rule lists and symbolic regression. Finally, we conduct simulation experiments on Mammographic Mass and Breast Cancer datasets and illustrate the testing procedure throughout a theoretical analysis with Markov process.

S-LIME: Stabilized-LIME for Model Explanation

An increasing number of machine learning models have been deployed in domains with high stakes such as finance and healthcare. Despite their superior performances, many models are black boxes in nature which are hard to explain. There are growing efforts for researchers to develop methods to interpret these black-box models. Post hoc explanations based on perturbations, such as LIME, are widely used approaches to interpret a machine learning model after it has been built. This class of methods has been shown to exhibit large instability, posing serious challenges to the effectiveness of the method itself and harming user trust. In this paper, we propose S-LIME, which utilizes a hypothesis testing framework based on central limit theorem for determining the number of perturbation points needed to guarantee stability of the resulting explanation. Experiments on both simulated and real world data sets are provided to demonstrate the effectiveness of our method.

Generalised Boosted Forests

This paper extends recent work on boosting random forests to model non-Gaussian responses. Given an exponential family $\mathbb{E}[Y|X] = g^{-1}(f(X))$ our goal is to obtain an estimate for $f$. We start with an MLE-type estimate in the link space and then define generalised residuals from it. We use these residuals and some corresponding weights to fit a base random forest and then repeat the same to obtain a boost random forest. We call the sum of these three estimators a \textit{generalised boosted forest}. We show with simulated and real data that both the random forest steps reduces test-set log-likelihood, which we treat as our primary metric. We also provide a variance estimator, which we can obtain with the same computational cost as the original estimate itself. Empirical experiments on real-world data and simulations demonstrate that the methods can effectively reduce bias, and that confidence interval coverage is conservative in the bulk of the covariate distribution.

Bridging Breiman's Brook: From Algorithmic Modeling to Statistical Learning

In 2001, Leo Breiman wrote of a divide between "data modeling" and "algorithmic modeling" cultures. Twenty years later this division feels far more ephemeral, both in terms of assigning individuals to camps, and in terms of intellectual boundaries. We argue that this is largely due to the "data modelers" incorporating algorithmic methods into their toolbox, particularly driven by recent developments in the statistical understanding of Breiman's own Random Forest methods. While this can be simplistically described as "Breiman won", these same developments also expose the limitations of the prediction-first philosophy that he espoused, making careful statistical analysis all the more important. This paper outlines these exciting recent developments in the random forest literature which, in our view, occurred as a result of a necessary blending of the two ways of thinking Breiman originally described. We also ask what areas statistics and statisticians might currently overlook.

Asymptotic Normality and Variance Estimation For Supervised Ensembles

Ensemble methods based on bootstrapping have improved the predictive accuracy of base learners, but fail to provide a framework in which formal statistical inference can be conducted. Recent theoretical developments suggest taking subsamples without replacement and analyze the resulting estimator in the context of a U-statistic, thus demonstrating asymptotic normality properties. However, we observe that current methods for variance estimation exhibit severe bias when the number of base learners is not large enough, compromising the validity of the resulting confidence intervals or hypothesis tests. This paper shows that similar asymptotics can be achieved by means of V-statistics, corresponding to taking subsamples with replacement. Further, we develop a bias correction algorithm for estimating variance in the limiting distribution, which yields satisfactory results with moderate size of base learners.