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Summary Building on Yu and Kumbier's predictability, computability and stability (PCS) framework and for randomised experiments, we introduce a novel methodology for Stable Discovery of Interpretable Subgroups via Calibration (StaDISC), with large heterogeneous treatment effects. StaDISC was developed during our re‐analysis of the 1999–2000 VIGOR study, an 8076‐patient randomised controlled trial that compared the risk of adverse events from a then newly approved drug, rofecoxib (Vioxx), with that from an older drug naproxen. Vioxx was found to, on average and in comparison with naproxen, reduce the risk of gastrointestinal events but increase the risk of thrombotic cardiovascular events. Applying StaDISC, we fit 18 popular conditional average treatment effect (CATE) estimators for both outcomes and use calibration to demonstrate their poor global performance. However, they are locally well‐calibrated and stable, enabling the identification of patient groups with larger than (estimated) average treatment effects. In fact, StaDISC discovers three clinically interpretable subgroups each for the gastrointestinal outcome (totalling 29.4% of the study size) and the thrombotic cardiovascular outcome (totalling 11.0%). Complementary analyses of the found subgroups using the 2001–2004 APPROVe study, a separate independently conducted randomised controlled trial with 2587 patients, provide further supporting evidence for the promise of StaDISC. 

Modern machine learning has achieved impressive prediction performance, but often sacrifices interpretability, a critical consideration in high-stakes domains such as medicine. In such settings, practitioners often use highly interpretable decision tree models, but these suffer from inductive bias against additive structure. To overcome this bias, we propose Fast Interpretable Greedy-Tree Sums (FIGS), which generalizes the Classification and Regression Trees (CART) algorithm to simultaneously grow a flexible number of trees in summation. By combining logical rules with addition, FIGS adapts to additive structure while remaining highly interpretable. Experiments on real-world datasets show FIGS achieves state-of-the-art prediction performance. To demonstrate the usefulness of FIGS in high-stakes domains, we adapt FIGS to learn clinical decision instruments (CDIs), which are tools for guiding decision-making. Specifically, we introduce a variant of FIGS known as Group Probability-Weighted Tree Sums (G-FIGS) that accounts for heterogeneity in medical data. G-FIGS derives CDIs that reflect domain knowledge and enjoy improved specificity (by up to 20% over CART) without sacrificing sensitivity or interpretability. Theoretically, we prove that FIGS learns components of additive models, a property we refer to as disentanglement. Further, we show (under oracle conditions) that tree-sum models leverage disentanglement to generalize more efficiently than single tree models when fitted to additive regression functions. Finally, to avoid overfitting with an unconstrained number of splits, we develop Bagging-FIGS, an ensemble version of FIGS that borrows the variance reduction techniques of random forests. Bagging-FIGS performs competitively with random forests and XGBoost on real-world datasets. 

Random Forests (RFs) are at the cutting edge of supervised machine learning in terms of prediction performance, especially in genomics. Iterative RFs (iRFs) use a tree ensemble from iteratively modified RFs to obtain predictive and stable nonlinear or Boolean interactions of features. They have shown great promise for Boolean biological interaction discovery that is central to advancing functional genomics and precision medicine. However, theoretical studies into how tree-based methods discover Boolean feature interactions are missing. Inspired by the thresholding behavior in many biological processes, we first introduce a discontinuous nonlinear regression model, called the “Locally Spiky Sparse” (LSS) model. Specifically, the LSS model assumes that the regression function is a linear combination of piecewise constant Boolean interaction terms. Given an RF tree ensemble, we define a quantity called “Depth-Weighted Prevalence” (DWP) for a set of signed features S ± . Intuitively speaking, DWP( S ± ) measures how frequently features in S ± appear together in an RF tree ensemble. We prove that, with high probability, DWP( S ± ) attains a universal upper bound that does not involve any model coefficients, if and only if S ± corresponds to a union of Boolean interactions under the LSS model. Consequentially, we show that a theoretically tractable version of the iRF procedure, called LSSFind, yields consistent interaction discovery under the LSS model as the sample size goes to infinity. Finally, simulation results show that LSSFind recovers the interactions under the LSS model, even when some assumptions are violated. 

Recent deep-learning models have achieved impressive predictive performance by learning complex functions of many variables, often at the cost of interpretability. This chapter covers recent work aiming to interpret models by attributing importance to features and feature groups for a single prediction. Importantly, the proposed attributions assign importance to interactions between features, in addition to features in isolation. These attributions are shown to yield insights across real-world domains, including bio-imaging, cosmology image and natural-language processing. We then show how these attributions can be used to directly improve the generalization of a neural network or to distill it into a simple model. Throughout the chapter, we emphasize the use of reality checks to scrutinize the proposed interpretation techniques. (Code for all methods in this chapter is available at github.com/csinva and github.com/Yu-Group, implemented in PyTorch [54]). 

Decision trees are important both as interpretable models amenable to high-stakes decision making, and as building blocks of ensemble methods such as random forests and gradient boosting. Their statistical properties, however, are not well understood. The most cited prior works have focused on deriving pointwise consistency guarantees for CART in a classical nonparametric regression setting. We take a different approach, and advocate studying the generalization performance of decision trees with respect to different generative regression models. This allows us to elicit their inductive bias, that is, the assumptions the algorithms make (or do not make) to generalize to new data, thereby guiding practitioners on when and how to apply these methods. In this paper, we focus on sparse additive generative models, which have both low statistical complexity and some nonparametric flexibility. We prove a sharp squared error generalization lower bound for a large class of decision tree algorithms fitted to sparse additive models with C component functions. This bound is surprisingly much worse than the minimax rate for estimating such sparse additive models. The inefficiency is due not to greediness, but to the loss in power for detecting global structure when we average responses solely over each leaf, an observation that suggests opportunities to improve tree-based algorithms, for example, by hierarchical shrinkage. To prove these bounds, we develop new technical machinery, establishing a novel connection between decision tree estimation and rate-distortion theory, a sub-field of information theory.