A Survey on Causal Inference <s> Unconfoundedness assumption <s> Learning individual-level causal effects from observational data, such as inferring the most effective medication for a specific patient, is a problem of growing importance for policy makers. The most important aspect of inferring causal effects from observational data is the handling of confounders, factors that affect both an intervention and its outcome. A carefully designed observational study attempts to measure all important confounders. However, even if one does not have direct access to all confounders, there may exist noisy and uncertain measurement of proxies for confounders. We build on recent advances in latent variable modeling to simultaneously estimate the unknown latent space summarizing the confounders and the causal effect. Our method is based on Variational Autoencoders (VAE) which follow the causal structure of inference with proxies. We show our method is significantly more robust than existing methods, and matches the state-of-the-art on previous benchmarks focused on individual treatment effects. <s> BIB001 </s> A Survey on Causal Inference <s> Unconfoundedness assumption <s> Counterfactual prediction requires understanding causal relationships between so-called treatment and outcome variables. This paper provides a recipe for augmenting deep learning methods to accurately characterize such relationships in the presence of instrument variables (IVs)—sources of treatment randomization that are conditionally independent from the outcomes. Our IV specification resolves into two prediction tasks that can be solved with deep neural nets: a first-stage network for treatment prediction and a second-stage network whose loss function involves integration over the conditional treatment distribution. This Deep IV framework allows us to take advantage of off-the-shelf supervised learning techniques to estimate causal effects by adapting the loss function. Experiments show that it outperforms existing machine learning approaches. <s> BIB002 </s> A Survey on Causal Inference <s> Unconfoundedness assumption <s> Observational data is increasingly used as a means for making individual-level causal predictions and intervention recommendations. The foremost challenge of causal inference from observational data is hidden confounding, whose presence cannot be tested in data and can invalidate any causal conclusion. Experimental data does not suffer from confounding but is usually limited in both scope and scale. We introduce a novel method of using limited experimental data to correct the hidden confounding in causal effect models trained on larger observational data, even if the observational data does not fully overlap with the experimental data. Our method makes strictly weaker assumptions than existing approaches, and we prove conditions under which it yields a consistent estimator. We demonstrate our method's efficacy using real-world data from a large educational experiment. <s> BIB003 </s> A Survey on Causal Inference <s> Unconfoundedness assumption <s> Counterfactual evaluation of novel treatment assignment functions (e.g., advertising algorithms and recommender systems) is one of the most crucial causal inference problems for practitioners. Traditionally, randomized controlled trials (A/B tests) are performed to evaluate treatment assignment functions. However, such trials can be time-consuming, expensive, and even unethical in some cases. Therefore, offline counterfactual evaluation of treatment assignment functions becomes a pressing issue because a massive amount of observational data is available in today's big data era. Counterfactual evaluation requires handling the hidden confounders -- the unmeasured features which causally influence both the treatment assignment and the outcome. To deal with the hidden confounders, most of the existing methods rely on the assumption of no hidden confounders. However, this assumption can be untenable in the context of massive observational data. When such data comes with network information, the later can be potentially useful to correct hidden confounding bias. As such, we first formulate a novel problem, counterfactual evaluation of treatment assignment functions with networked observational data. Then, we investigate the following research questions: How can we utilize network information in counterfactual evaluation? Can network information improve the estimates in counterfactual evaluation? Toward answering these questions, first, we propose a novel framework, \emph{Counterfactual Network Evaluator} (CONE), which (1) learns partial representations of latent confounders under the supervision of observed treatments and outcomes; and (2) combines them for counterfactual evaluation. Then through extensive experiments, we corroborate the effectiveness of CONE. The results imply that incorporating network information mitigates hidden confounding bias in counterfactual evaluation. <s> BIB004 </s> A Survey on Causal Inference <s> Unconfoundedness assumption <s> We consider causal inference in the presence of unobserved confounding. We study the case where a proxy is available for the unobserved confounding in the form of a network connecting the units. For example, the link structure of a social network carries information about its members. We show how to effectively use the proxy to do causal inference. The main idea is to reduce the causal estimation problem to a semi-supervised prediction of both the treatments and outcomes. Networks admit high-quality embedding models that can be used for this semi-supervised prediction. We show that the method yields valid inferences under suitable (weak) conditions on the quality of the predictive model. We validate the method with experiments on a semi-synthetic social network dataset. Code is available at github.com/vveitch/causal-network-embeddings. <s> BIB005 </s> A Survey on Causal Inference <s> Unconfoundedness assumption <s> The estimation of treatment effects is a pervasive problem in medicine. Existing methods for estimating treatment effects from longitudinal observational data assume that there are no hidden confounders. This assumption is not testable in practice and, if it does not hold, leads to biased estimates. In this paper, we develop the Time Series Deconfounder, a method that leverages the assignment of multiple treatments over time to enable the estimation of treatment effects even in the presence of hidden confounders. The Time Series Deconfounder uses a novel recurrent neural network architecture with multitask output to build a factor model over time and infer substitute confounders that render the assigned treatments conditionally independent. Then it performs causal inference using the substitute confounders. We provide a theoretical analysis for obtaining unbiased causal effects of time-varying exposures using the Time Series Deconfounder. Using simulations we show the effectiveness of our method in deconfounding the estimation of treatment responses in longitudinal data. <s> BIB006
The ignorability assumption is also named as unconfoundedness assumption. Given the background variable, X , the treatment assignment W is independent to the potential outcomes, i.e., W ⊥ ⊥ Y (W = 0), Y (W = 1)|X . With this unconfoundedness assumption, for the units with the same background variable X , their treatment assignment can be viewed as random. Obviously, identifying and collecting all of background variables is impossible, and this assumption is very difficult to satisfy. For example, in an observational study that tries to estimate the individual treatment effect of a medicine, instead of randomized experiments, the medicine is assigned to individuals based on a series of factors. Some factors (e.g., socioeconomic status) are challenging to measure and therefore become hidden confounders. Existing work overwhelmingly relies on the unconfoundedness assumption that all confounders can be measured. However, this assumption might be untenable in practice. In the above example, units' demographic attributes, such as their home address, consumption ability or employment status, may be the proxies for socioeconomic status. Leveraging big data, it is possible to find a proxy for the latent and unobserved confounders. Variational autoencoder has been used to infer the complex non-linear relationships between the observed confounders and joint distribution of the latent confounders, treatment assignment and outcomes BIB001 . The joint distribution of the latent confounders and the observed confounders can be approximately recovered from the observations. An alternative way is to capture their patterns and control their influence by incorporating the underlying network information. Network information is also a reasonable proxy for the unobserved confounding.  applies GCN on network information to get the representation of hidden confounders. Moreover, in BIB004 , graph attention layers are used to map the observed features in networked observational data to the D-dimensional space of partial latent confounders, by capturing the unknown edge weights in the real-world networked observational data. An interesting insight mentioned in BIB005 is that, even if the confounders are observed, it doesn't mean all the information they contain is useful to infer the causal effect. Instead, requiring the part of confounders actually used by the estimator is sufficient. Therefore, if a good predictive model for the treatment can be built, one may only need to plug the outputs into a causal effect estimate directly, without any need to learn the whole true confounders. In BIB005 , the main idea is to reduce the causal estimation problem to a semi-supervised prediction of both the treatments and outcomes. Networks admit high-quality embedding models that can be used for this semi-supervised prediction. In addition, embedding methods can also offer an alternative to fully specified generative models. Only using observational data to solve the confoundings problem is always difficult. Another way is to combine the experimental data and observational data together. In BIB003 , limited experimental data is used to correct the hidden confounding in causal effect models trained on larger observational data, even if the observational data do not fully overlap with the experimental data. This method makes strictly weaker assumptions than existing approaches. For estimating treatment effects from longitudinal observational data, existing methods usually assume that there are no hidden confounders. This assumption is not testable in practice and, if it does not hold, leads to biased estimates. BIB006 infers substitute confounders that render the assigned treatments conditionally independent. Then it performs causal inference using the substitute confounders. This method can help estimate treatment effects for time series data in the presence of hidden confounders. Above methods all aim to solve the problems about the observed and unobserved confounders. Are there any other ways to get around the unconfoundedness assumption and conduct causal inference? One way is to use instrumental variables that only affect treatment assignment but not the outcome variable. Changes in the instrumental variables would lead to the different assignment of treatment, which is independent of the latent variables, and this assignment is as good as randomization for the purposes of causal inference. BIB002 broke instrumental variables analysis into two supervised stages that can each be targeted with deep networks. It models the conditional distribution of the treatment variable given the instruments and covariates, and then employs a loss function involving integration over the conditional treatment distribution. The deep instrumental variables framework also takes advantage of existing supervised learning techniques to estimate causal effects.