Observational studies have recently received significant attention from the machine learning community due to the increasingly available non-experimental observational data and the limitations of the experimental studies, such as considerable cost, impracticality, small and less representative sample sizes, etc. In observational studies, de-confounding is a fundamental problem of individualised treatment effects (ITE) estimation. This paper proposes disentangled representations with adversarial training to selectively balance the confounders in the binary treatment setting for the ITE estimation. The adversarial training of treatment policy selectively encourages treatment-agnostic balanced representations for the confounders and helps to estimate the ITE in the observational studies via counterfactual inference. Empirical results on synthetic and real-world datasets, with varying degrees of confounding, prove that our proposed approach improves the state-of-the-art methods in achieving lower error in the ITE estimation.
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This paper considers identification and estimation of the causal effect of the time Z until a subject is treated on a survival outcome T. The treatment is not randomly assigned, T is randomly right censored by a random variable C and the time to treatment Z is right censored by min(T,C). The endogeneity issue is treated using an instrumental variable explaining Z and independent of the error term of the model. We study identification in a fully nonparametric framework. We show that our specification generates an integral equation, of which the regression function of interest is a solution. We provide identification conditions that rely on this identification equation. For estimation purposes, we assume that the regression function follows a parametric model. We propose an estimation procedure and give conditions under which the estimator is asymptotically normal. The estimators exhibit good finite sample properties in simulations. Our methodology is applied to find evidence supporting the efficacy of a therapy for burn-out.
A typical desideratum for quantifying the uncertainty from a classification model as a prediction set is class-conditional singleton set calibration. That is, such sets should map to the output of well-calibrated selective classifiers, matching the observed frequencies of similar instances. Recent works proposing adaptive and localized conformal p-values for deep networks do not guarantee this behavior, nor do they achieve it empirically. Instead, we use the strong signals for prediction reliability from KNN-based approximations of Transformer networks to construct data-driven partitions for Mondrian Conformal Predictors, which are treated as weak selective classifiers that are then calibrated via a new Inductive Venn Predictor, the Venn-ADMIT Predictor. The resulting selective classifiers are well-calibrated, in a conservative but practically useful sense for a given threshold. They are inherently robust to changes in the proportions of the data partitions, and straightforward conservative heuristics provide additional robustness to covariate shifts. We compare and contrast to the quantities produced by recent Conformal Predictors on several representative and challenging natural language processing classification tasks, including class-imbalanced and distribution-shifted settings.
In randomized experiments and observational studies, weighting methods are often used to generalize and transport treatment effect estimates to target populations. Traditional methods construct the weights by separately modeling the treatment assignment and study selection probabilities and then multiplying functions (e.g., inverses) of their estimates. In this work, we provide a justification and an implementation for weighting in a single step. We show a formal connection between this one-step method and inverse probability and inverse odds weighting. We demonstrate that the resulting estimator for the target average treatment effect is consistent, asymptotically Normal, multiply robust, and semiparametrically efficient.
This paper provides estimation and inference methods for a conditional average treatment effects (CATE) characterized by a high-dimensional parameter in both homogeneous cross-sectional and unit-heterogeneous dynamic panel data settings. In our leading example, we model CATE by interacting the base treatment variable with explanatory variables. The first step of our procedure is orthogonalization, where we partial out the controls and unit effects from the outcome and the base treatment and take the cross-fitted residuals. This step uses a novel generic cross-fitting method we design for weakly dependent time series and panel data. This method "leaves out the neighbors" when fitting nuisance components, and we theoretically power it by using Strassen's coupling. As a result, we can rely on any modern machine learning method in the first step, provided it learns the residuals well enough. Second, we construct an orthogonal (or residual) learner of CATE -- the Lasso CATE -- that regresses the outcome residual on the vector of interactions of the residualized treatment with explanatory variables. If the complexity of CATE function is simpler than that of the first-stage regression, the orthogonal learner converges faster than the single-stage regression-based learner. Third, we perform simultaneous inference on parameters of the CATE function using debiasing. We also can use ordinary least squares in the last two steps when CATE is low-dimensional. In heterogeneous panel data settings, we model the unobserved unit heterogeneity as a weakly sparse deviation from Mundlak (1978)'s model of correlated unit effects as a linear function of time-invariant covariates and make use of L1-penalization to estimate these models. We demonstrate our methods by estimating price elasticities of groceries based on scanner data. We note that our results are new even for the cross-sectional (i.i.d) case.
With a few exceptions, work in offline reinforcement learning (RL) has so far assumed that there is no confounding. In a classical regression setting, confounders introduce omitted variable bias and inhibit the identification of causal effects. In offline RL, they prevent the identification of a policy's value, and therefore make it impossible to perform policy improvement. Using conventional methods in offline RL in the presence of confounding can therefore not only lead to poor decisions and poor policies, but can also have disastrous effects in applications such as healthcare and education. We provide approaches for both off-policy evaluation (OPE) and local policy optimization in the settings of i.i.d. and global confounders. Theoretical and empirical results confirm the validity and viability of these methods.
We study a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness. Our Bayesian approach involves a correction term for prior distributions adjusted by the propensity score. We prove asymptotic equivalence of our Bayesian estimator and efficient frequentist estimators by establishing a new semiparametric Bernstein-von Mises theorem under double robustness; i.e., the lack of smoothness of conditional mean functions can be compensated by high regularity of the propensity score and vice versa. Consequently, the resulting Bayesian point estimator internalizes the bias correction as the frequentist-type doubly robust estimator, and the Bayesian credible sets form confidence intervals with asymptotically exact coverage probability. In simulations, we find that this corrected Bayesian procedure leads to significant bias reduction of point estimation and accurate coverage of confidence intervals, especially when the dimensionality of covariates is large relative to the sample size and the underlying functions become complex. We illustrate our method in an application to the National Supported Work Demonstration.
We propose an analysis in fair learning that preserves the utility of the data while reducing prediction disparities under the criteria of group sufficiency. We focus on the scenario where the data contains multiple or even many subgroups, each with limited number of samples. As a result, we present a principled method for learning a fair predictor for all subgroups via formulating it as a bilevel objective. Specifically, the subgroup specific predictors are learned in the lower-level through a small amount of data and the fair predictor. In the upper-level, the fair predictor is updated to be close to all subgroup specific predictors. We further prove that such a bilevel objective can effectively control the group sufficiency and generalization error. We evaluate the proposed framework on real-world datasets. Empirical evidence suggests the consistently improved fair predictions, as well as the comparable accuracy to the baselines.
Causal inference in observational studies can be challenging when confounders are subject to missingness. Generally, the identification of causal effects is not guaranteed even under restrictive parametric model assumptions when confounders are missing not at random. To address this, We propose a general framework to establish the identification of causal effects when confounders are subject to treatment-independent missingness, which means that the missing data mechanism is independent of the treatment, given the outcome and possibly missing confounders. We give special consideration to commonly-used models for continuous and binary outcomes and provide counterexamples when identification fails. For estimation, we provide a weighted estimation equation estimating method for model parameters and purpose three estimators for the average causal effect based on the estimated models. We evaluate the finite-sample performance of the estimators via simulations. We further illustrate the proposed method with real data sets from the National Health and Nutrition Examination Survey.
We identify the average dose-response function (ADRF) for a continuously valued error-contaminated treatment by a weighted conditional expectation. We then estimate the weights nonparametrically by maximising a local generalised empirical likelihood subject to an expanding set of conditional moment equations incorporated into the deconvolution kernels. Thereafter, we construct a deconvolution kernel estimator of ADRF. We derive the asymptotic bias and variance of our ADRF estimator and provide its asymptotic linear expansion, which helps conduct statistical inference. To select our smoothing parameters, we adopt the simulation-extrapolation method and propose a new extrapolation procedure to stabilise the computation. Monte Carlo simulations and a real data study illustrate our method's practical performance.
Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.
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