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 [39], 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.

As machine learning procedures become an increasingly popular modeling option among applied researchers, there has been a corresponding interest in developing valid tools for understanding their statistical properties and uncertainty. Tree-based ensembles like random forests remain one such popular option for which several important theoretical advances have been made in recent years by drawing upon a connection between their natural subsampled structure and the classical theory of $U$-statistics. Unfortunately, the procedures for estimating predictive variance resulting from these studies are plagued by severe bias and extreme computational overhead. Here, we argue that the root of these problems lies in the use of subsampling without replacement and that with-replacement subsamples, resulting in $V$-statistics, substantially alleviates these problems. We develop a general framework for analyzing the asymptotic behavior of $V$-statistics, demonstrating asymptotic normality under precise regularity conditions and establishing previously unreported connections to $U$-statistics. Importantly, these findings allow us to produce a natural and efficient means of estimating the variance of a conditional expectation, a problem of wide interest across multiple scientific domains that also lies at the heart of uncertainty quantification for supervised learning ensembles.

We propose a modification that corrects for split-improvement variable importance measures in Random Forests and other tree-based methods. These methods have been shown to be biased towards increasing the importance of features with more potential splits. We show that by appropriately incorporating split-improvement as measured on out of sample data, this bias can be corrected yielding better summaries and screening tools.