Beepul Bharti

Jacopo Teneggi, Beepul Bharti, Yaniv Romano et al.

The complex nature of artificial neural networks raises concerns on their reliability, trustworthiness, and fairness in real-world scenarios. The Shapley value -- a solution concept from game theory -- is one of the most popular explanation methods for machine learning models. More traditionally, from a statistical perspective, feature importance is defined in terms of conditional independence. So far, these two approaches to interpretability and feature importance have been considered separate and distinct. In this work, we show that Shapley-based explanation methods and conditional independence testing are closely related. We introduce the SHAPley EXplanation Randomization Test (SHAP-XRT), a testing procedure inspired by the Conditional Randomization Test (CRT) for a specific notion of local (i.e., on a sample) conditional independence. With it, we prove that for binary classification problems, the marginal contributions in the Shapley value provide lower and upper bounds to the expected $p$-values of their respective tests. Furthermore, we show that the Shapley value itself provides an upper bound to the expected $p$-value of a global (i.e., overall) null hypothesis. As a result, we further our understanding of Shapley-based explanation methods from a novel perspective and characterize the conditions under which one can make statistically valid claims about feature importance via the Shapley value.

Beepul Bharti, Paul Yi, Jeremias Sulam

As complex machine learning models continue to find applications in high-stakes decision-making scenarios, it is crucial that we can explain and understand their predictions. Post-hoc explanation methods provide useful insights by identifying important features in an input $\mathbf{x}$ with respect to the model output $f(\mathbf{x})$. In this work, we formalize and study two precise notions of feature importance for general machine learning models: sufficiency and necessity. We demonstrate how these two types of explanations, albeit intuitive and simple, can fall short in providing a complete picture of which features a model finds important. To this end, we propose a unified notion of importance that circumvents these limitations by exploring a continuum along a necessity-sufficiency axis. Our unified notion, we show, has strong ties to other popular definitions of feature importance, like those based on conditional independence and game-theoretic quantities like Shapley values. Crucially, we demonstrate how a unified perspective allows us to detect important features that could be missed by either of the previous approaches alone.

Beepul Bharti, Ambar Pal, Jacopo Teneggi et al.

Uncertainty quantification (UQ) is critical for the deployment of machine learning predictors in real-world scenarios where the data distribution may shift over time (i.e., data may not be exchangeable). Online conformal prediction (OCP) methods address this issue at the expense of either (i) group-wise error control or (ii) learning-rate independent implementation. Group-conditional coverage is essential for fairness across different collections of data points and for providing finer UQ guarantees. Parameter-free optimization is crucial for robustness to adversarial and unknown data shifts. We propose a parameter-free algorithm for group-conditional OCP and demonstrate that it achieves the best group-conditional coverage guarantees.We evaluate our algorithm on synthetic and real-world data, demonstrating that our method not only improves the reliability of existing parameter-free OCP methods but also provides prediction intervals that are comparable in size to well-tuned group-conditional approaches. By unifying group-conditional coverage with parameter-free online algorithms, our work lays a foundation for fair and robust uncertainty quantification in shifting environments.