Marco Carone

Lars van der Laan, Ernesto Ulloa-Pérez, Marco Carone et al.

We propose causal isotonic calibration, a novel nonparametric method for calibrating predictors of heterogeneous treatment effects. Furthermore, we introduce cross-calibration, a data-efficient variant of calibration that eliminates the need for hold-out calibration sets. Cross-calibration leverages cross-fitted predictors and generates a single calibrated predictor using all available data. Under weak conditions that do not assume monotonicity, we establish that both causal isotonic calibration and cross-calibration achieve fast doubly-robust calibration rates, as long as either the propensity score or outcome regression is estimated accurately in a suitable sense. The proposed causal isotonic calibrator can be wrapped around any black-box learning algorithm, providing robust and distribution-free calibration guarantees while preserving predictive performance.

Lars van der Laan, Marco Carone, Alex Luedtke

We introduce efficient plug-in (EP) learning, a novel framework for the estimation of heterogeneous causal contrasts, such as the conditional average treatment effect and conditional relative risk. The EP-learning framework enjoys the same oracle-efficiency as Neyman-orthogonal learning strategies, such as DR-learning and R-learning, while addressing some of their primary drawbacks, including that (i) their practical applicability can be hindered by loss function non-convexity; and (ii) they may suffer from poor performance and instability due to inverse probability weighting and pseudo-outcomes that violate bounds. To avoid these drawbacks, EP-learner constructs an efficient plug-in estimator of the population risk function for the causal contrast, thereby inheriting the stability and robustness properties of plug-in estimation strategies like T-learning. Under reasonable conditions, EP-learners based on empirical risk minimization are oracle-efficient, exhibiting asymptotic equivalence to the minimizer of an oracle-efficient one-step debiased estimator of the population risk function. In simulation experiments, we illustrate that EP-learners of the conditional average treatment effect and conditional relative risk outperform state-of-the-art competitors, including T-learner, R-learner, and DR-learner. Open-source implementations of the proposed methods are available in our R package hte3.

Brian D. Williamson, Peter B. Gilbert, Noah R. Simon et al.

In many applications, it is of interest to assess the relative contribution of features (or subsets of features) toward the goal of predicting a response -- in other words, to gauge the variable importance of features. Most recent work on variable importance assessment has focused on describing the importance of features within the confines of a given prediction algorithm. However, such assessment does not necessarily characterize the prediction potential of features, and may provide a misleading reflection of the intrinsic value of these features. To address this limitation, we propose a general framework for nonparametric inference on interpretable algorithm-agnostic variable importance. We define variable importance as a population-level contrast between the oracle predictiveness of all available features versus all features except those under consideration. We propose a nonparametric efficient estimation procedure that allows the construction of valid confidence intervals, even when machine learning techniques are used. We also outline a valid strategy for testing the null importance hypothesis. Through simulations, we show that our proposal has good operating characteristics, and we illustrate its use with data from a study of an antibody against HIV-1 infection.

Alexander R. Luedtke, Marco Carone, Mark J. van der Laan

We present a novel family of nonparametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a generalization of the maximum mean discrepancy tests described in Gretton et al. [2006], using recent developments from the higher-order pathwise differentiability literature. Despite their complex derivation, the associated test statistics can be expressed rather simply as U-statistics. We study the asymptotic behavior of the proposed tests under the null hypothesis and under both fixed and local alternatives. We provide examples to which our tests can be applied and show that they perform well in a simulation study. As an important special case, our proposed tests can be used to determine whether an unknown function, such as the conditional average treatment effect, is equal to zero almost surely.