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A key to causal inference with observational data is achieving balance in predictive features associated with each treatment type. Recent literature has explored representation learning to achieve this goal. In this work, we discuss the pitfalls of these strategies - such as a steep trade-off between achieving balance and predictive power - and present a remedy via the integration of balancing weights in causal learning. Specifically, we theoretically link balance to the quality of propensity estimation, emphasize the importance of identifying a proper target population, and elaborate on the complementary roles of feature balancing and weight adjustments. Using these concepts, we then develop an algorithm for flexible, scalable and accurate estimation of causal effects. Finally, we show how the learned weighted representations may serve to facilitate alternative causal learning procedures with appealing statistical features. We conduct an extensive set of experiments on both synthetic examples and standard benchmarks, and report encouraging results relative to state-of-the-art baselines.
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One fundamental problem in the learning treatment effect from observational data is confounder identification and balancing. Most of the previous methods realized confounder balancing by treating all observed variables as confounders, ignoring the identification of confounders and non-confounders. In general, not all the observed variables are confounders which are the common causes of both the treatment and the outcome, some variables only contribute to the treatment and some contribute to the outcome. Balancing those non-confounders would generate additional bias for treatment effect estimation. By modeling the different relations among variables, treatment and outcome, we propose a synergistic learning framework to 1) identify and balance confounders by learning decomposed representation of confounders and non-confounders, and simultaneously 2) estimate the treatment effect in observational studies via counterfactual inference. Our empirical results demonstrate that the proposed method can precisely identify and balance confounders, while the estimation of the treatment effect performs better than the state-of-the-art methods on both synthetic and real-world datasets.
Deep learning models exhibit a preference for statistical fitting over logical reasoning. Spurious correlations might be memorized when there exists statistical bias in training data, which severely limits the model performance especially in small data scenarios. In this work, we introduce Counterfactual Adversarial Training framework (CAT) to tackle the problem from a causality perspective. Particularly, for a specific sample, CAT first generates a counterfactual representation through latent space interpolation in an adversarial manner, and then performs Counterfactual Risk Minimization (CRM) on each original-counterfactual pair to adjust sample-wise loss weight dynamically, which encourages the model to explore the true causal effect. Extensive experiments demonstrate that CAT achieves substantial performance improvement over SOTA across different downstream tasks, including sentence classification, natural language inference and question answering.
A standard introduction to online learning might place Online Gradient Descent at its center and then proceed to develop generalizations and extensions like Online Mirror Descent and second-order methods. Here we explore the alternative approach of putting Exponential Weights (EW) first. We show that many standard methods and their regret bounds then follow as a special case by plugging in suitable surrogate losses and playing the EW posterior mean. For instance, we easily recover Online Gradient Descent by using EW with a Gaussian prior on linearized losses, and, more generally, all instances of Online Mirror Descent based on regular Bregman divergences also correspond to EW with a prior that depends on the mirror map. Furthermore, appropriate quadratic surrogate losses naturally give rise to Online Gradient Descent for strongly convex losses and to Online Newton Step. We further interpret several recent adaptive methods (iProd, Squint, and a variation of Coin Betting for experts) as a series of closely related reductions to exp-concave surrogate losses that are then handled by Exponential Weights. Finally, a benefit of our EW interpretation is that it opens up the possibility of sampling from the EW posterior distribution instead of playing the mean. As already observed by Bubeck and Eldan, this recovers the best-known rate in Online Bandit Linear Optimization.
A common statistical problem in econometrics is to estimate the impact of a treatment on a treated unit given a control sample with untreated outcomes. Here we develop a generative learning approach to this problem, learning the probability distribution of the data, which can be used for downstream tasks such as post-treatment counterfactual prediction and hypothesis testing. We use control samples to transform the data to a Gaussian and homoschedastic form and then perform Gaussian process analysis in Fourier space, evaluating the optimal Gaussian kernel via non-parametric power spectrum estimation. We combine this Gaussian prior with the data likelihood given by the pre-treatment data of the single unit, to obtain the synthetic prediction of the unit post-treatment, which minimizes the error variance of synthetic prediction. Given the generative model the minimum variance counterfactual is unique, and comes with an associated error covariance matrix. We extend this basic formalism to include correlations of primary variable with other covariates of interest. Given the probabilistic description of generative model we can compare synthetic data prediction with real data to address the question of whether the treatment had a statistically significant impact. For this purpose we develop a hypothesis testing approach and evaluate the Bayes factor. We apply the method to the well studied example of California (CA) tobacco sales tax of 1988. We also perform a placebo analysis using control states to validate our methodology. Our hypothesis testing method suggests 5.8:1 odds in favor of CA tobacco sales tax having an impact on the tobacco sales, a value that is at least three times higher than any of the 38 control states.
Counterfactual inference has become a ubiquitous tool in online advertisement, recommendation systems, medical diagnosis, and econometrics. Accurate modeling of outcome distributions associated with different interventions -- known as counterfactual distributions -- is crucial for the success of these applications. In this work, we propose to model counterfactual distributions using a novel Hilbert space representation called counterfactual mean embedding (CME). The CME embeds the associated counterfactual distribution into a reproducing kernel Hilbert space (RKHS) endowed with a positive definite kernel, which allows us to perform causal inference over the entire landscape of the counterfactual distribution. Based on this representation, we propose a distributional treatment effect (DTE) that can quantify the causal effect over entire outcome distributions. Our approach is nonparametric as the CME can be estimated under the unconfoundedness assumption from observational data without requiring any parametric assumption about the underlying distributions. We also establish a rate of convergence of the proposed estimator which depends on the smoothness of the conditional mean and the Radon-Nikodym derivative of the underlying marginal distributions. Furthermore, our framework allows for more complex outcomes such as images, sequences, and graphs. Our experimental results on synthetic data and off-policy evaluation tasks demonstrate the advantages of the proposed estimator.
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