Causal learning is the key to obtaining stable predictions and answering \textit{what if} problems in decision-makings. In causal learning, it is central to seek methods to estimate the average treatment effect (ATE) from observational data. The Double/Debiased Machine Learning (DML) is one of the prevalent methods to estimate ATE. However, the DML estimators can suffer from an \textit{error-compounding issue} and even give extreme estimates when the propensity scores are close to 0 or 1. Previous studies have overcome this issue through some empirical tricks such as propensity score trimming, yet none of the existing works solves it from a theoretical standpoint. In this paper, we propose a \textit{Robust Causal Learning (RCL)} method to offset the deficiencies of DML estimators. Theoretically, the RCL estimators i) satisfy the (higher-order) orthogonal condition and are as \textit{consistent and doubly robust} as the DML estimators, and ii) get rid of the error-compounding issue. Empirically, the comprehensive experiments show that: i) the RCL estimators give more stable estimations of the causal parameters than DML; ii) the RCL estimators outperform traditional estimators and their variants when applying different machine learning models on both simulation and benchmark datasets, and a mimic consumer credit dataset generated by WGAN.
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Estimation of heterogeneous causal effects - i.e., how effects of policies and treatments vary across subjects - is a fundamental task in causal inference, playing a crucial role in optimal treatment allocation, generalizability, subgroup effects, and more. Many flexible methods for estimating conditional average treatment effects (CATEs) have been proposed in recent years, but questions surrounding optimality have remained largely unanswered. In particular, a minimax theory of optimality has yet to be developed, with the minimax rate of convergence and construction of rate-optimal estimators remaining open problems. In this paper we derive the minimax rate for CATE estimation, in a nonparametric model where distributional components are Holder-smooth, and present a new local polynomial estimator, giving high-level conditions under which it is minimax optimal. More specifically, our minimax lower bound is derived via a localized version of the method of fuzzy hypotheses, combining lower bound constructions for nonparametric regression and functional estimation. Our proposed estimator can be viewed as a local polynomial R-Learner, based on a localized modification of higher-order influence function methods; it is shown to be minimax optimal under a condition on how accurately the covariate distribution is estimated. The minimax rate we find exhibits several interesting features, including a non-standard elbow phenomenon and an unusual interpolation between nonparametric regression and functional estimation rates. The latter quantifies how the CATE, as an estimand, can be viewed as a regression/functional hybrid. We conclude with some discussion of a few remaining open problems.
Often in public health, we are interested in the treatment effect of an intervention on a population that is systemically different from the experimental population the intervention was originally evaluated in. When treatment effect heterogeneity is present in a randomized controlled trial, generalizing the treatment effect from this experimental population to a target population of interest is a complex problem; it requires the characterization of both the treatment effect heterogeneity and the baseline covariate mismatch between the two populations. Despite the importance of this problem, the literature for variable selection in this context is limited. In this paper, we present a Group LASSO-based approach to variable selection in the context of treatment effect generalization, with an application to generalize the treatment effect of very low nicotine content cigarettes to the overall U.S. smoking population.
Machine learning methods can be unreliable when deployed in domains that differ from the domains on which they were trained. There are a wide range of proposals for mitigating this problem by learning representations that are ``invariant'' in some sense.However, these methods generally contradict each other, and none of them consistently improve performance on real-world domain shift benchmarks. There are two main questions that must be addressed to understand when, if ever, we should use each method. First, how does each ad hoc notion of ``invariance'' relate to the structure of real-world problems? And, second, when does learning invariant representations actually yield robust models? To address these issues, we introduce a broad formal notion of what it means for a real-world domain shift to admit invariant structure. Then, we characterize the causal structures that are compatible with this notion of invariance.With this in hand, we find conditions under which method-specific invariance notions correspond to real-world invariant structure, and we clarify the relationship between invariant structure and robustness to domain shifts. For both questions, we find that the true underlying causal structure of the data plays a critical role.
Privacy auditing techniques for differentially private (DP) algorithms are useful for estimating the privacy loss to compare against analytical bounds, or empirically measure privacy in settings where known analytical bounds on the DP loss are not tight. However, existing privacy auditing techniques usually make strong assumptions on the adversary (e.g., knowledge of intermediate model iterates or the training data distribution), are tailored to specific tasks and model architectures, and require retraining the model many times (typically on the order of thousands). These shortcomings make deploying such techniques at scale difficult in practice, especially in federated settings where model training can take days or weeks. In this work, we present a novel "one-shot" approach that can systematically address these challenges, allowing efficient auditing or estimation of the privacy loss of a model during the same, single training run used to fit model parameters. Our privacy auditing method for federated learning does not require a priori knowledge about the model architecture or task. We show that our method provides provably correct estimates for privacy loss under the Gaussian mechanism, and we demonstrate its performance on a well-established FL benchmark dataset under several adversarial models.
Personalized treatment effect estimates are often of interest in high-stakes applications -- thus, before deploying a model estimating such effects in practice, one needs to be sure that the best candidate from the ever-growing machine learning toolbox for this task was chosen. Unfortunately, due to the absence of counterfactual information in practice, it is usually not possible to rely on standard validation metrics for doing so, leading to a well-known model selection dilemma in the treatment effect estimation literature. While some solutions have recently been investigated, systematic understanding of the strengths and weaknesses of different model selection criteria is still lacking. In this paper, instead of attempting to declare a global `winner', we therefore empirically investigate success- and failure modes of different selection criteria. We highlight that there is a complex interplay between selection strategies, candidate estimators and the DGP used for testing, and provide interesting insights into the relative (dis)advantages of different criteria alongside desiderata for the design of further illuminating empirical studies in this context.
We consider transfer learning approaches that fine-tune a pretrained deep neural network on a target task. We study the generalization properties of fine-tuning to understand the problem of overfitting, which commonly occurs in practice. Previous works have shown that constraining the distance from the initialization of fine-tuning improves generalization. Using a PAC-Bayesian analysis, we observe that besides distance from initialization, Hessians affect generalization through the noise stability of deep neural networks against noise injections. Motivated by the observation, we develop Hessian distance-based generalization bounds for a wide range of fine-tuning methods. Additionally, we study the robustness of fine-tuning in the presence of noisy labels. We design an algorithm incorporating consistent losses and distance-based regularization for fine-tuning, along with a generalization error guarantee under class conditional independent noise in the training set labels. We perform a detailed empirical study of our algorithm on various noisy environments and architectures. On six image classification tasks whose training labels are generated with programmatic labeling, we find a 3.26% accuracy gain over prior fine-tuning methods. Meanwhile, the Hessian distance measure of the fine-tuned model decreases by six times more than existing approaches.
Causal inference on populations embedded in social networks poses technical challenges, since the typical no interference assumption may no longer hold. For instance, in the context of social research, the outcome of a study unit will likely be affected by an intervention or treatment received by close neighbors. While inverse probability-of-treatment weighted (IPW) estimators have been developed for this setting, they are often highly inefficient. In this work, we assume that the network is a union of disjoint components and propose doubly robust (DR) estimators combining models for treatment and outcome that are consistent and asymptotically normal if either model is correctly specified. We present empirical results that illustrate the DR property and the efficiency gain of DR over IPW estimators when both the outcome and treatment models are correctly specified. Simulations are conducted for networks with equal and unequal component sizes and outcome data with and without a multilevel structure. We apply these methods in an illustrative analysis using the Add Health network, examining the impact of maternal college education on adolescent school performance, both direct and indirect.
Heterogeneous treatment effects (HTE) based on patients' genetic or clinical factors are of significant interest to precision medicine. Simultaneously modeling HTE and corresponding main effects for randomized clinical trials with high-dimensional predictive markers is challenging. Motivated by the modified covariates approach, we propose a two-stage statistical learning procedure for estimating HTE with optimal efficiency augmentation, generalizing to arbitrary interaction model and exploiting powerful extreme gradient boosting trees (XGBoost). Target estimands for HTE are defined in the scale of mean difference for quantitative outcomes, or risk ratio for binary outcomes, which are the minimizers of specialized loss functions. The first stage is to estimate the main-effect equivalency of the baseline markers on the outcome, which is then used as an augmentation term in the second stage estimation for HTE. The proposed two-stage procedure is robust to model mis-specification of main effects and improves efficiency for estimating HTE through nonparametric function estimation, e.g., XGBoost. A permutation test is proposed for global assessment of evidence for HTE. An analysis of a genetic study in Prostate Cancer Prevention Trial led by the SWOG Cancer Research Network, is conducted to showcase the properties and the utilities of the two-stage method.
In the domain generalization literature, a common objective is to learn representations independent of the domain after conditioning on the class label. We show that this objective is not sufficient: there exist counter-examples where a model fails to generalize to unseen domains even after satisfying class-conditional domain invariance. We formalize this observation through a structural causal model and show the importance of modeling within-class variations for generalization. Specifically, classes contain objects that characterize specific causal features, and domains can be interpreted as interventions on these objects that change non-causal features. We highlight an alternative condition: inputs across domains should have the same representation if they are derived from the same object. Based on this objective, we propose matching-based algorithms when base objects are observed (e.g., through data augmentation) and approximate the objective when objects are not observed (MatchDG). Our simple matching-based algorithms are competitive to prior work on out-of-domain accuracy for rotated MNIST, Fashion-MNIST, PACS, and Chest-Xray datasets. Our method MatchDG also recovers ground-truth object matches: on MNIST and Fashion-MNIST, top-10 matches from MatchDG have over 50% overlap with ground-truth matches.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
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