A Survey on Causal Inference <s> Other Applications <s> Observational studies are rising in importance due to the widespread accumulation of data in fields such as healthcare, education, employment and ecology. We consider the task of answering counterfactual questions such as, "Would this patient have lower blood sugar had she received a different medication?". We propose a new algorithmic framework for counterfactual inference which brings together ideas from domain adaptation and representation learning. In addition to a theoretical justification, we perform an empirical comparison with previous approaches to causal inference from observational data. Our deep learning algorithm significantly outperforms the previous state-of-the-art. <s> BIB001 </s> A Survey on Causal Inference <s> Other Applications <s> There is intense interest in applying machine learning to problems of causal inference in fields such as healthcare, economics and education. In particular, individual-level causal inference has important applications such as precision medicine. We give a new theoretical analysis and family of algorithms for predicting individual treatment effect (ITE) from observational data, under the assumption known as strong ignorability. The algorithms learn a "balanced" representation such that the induced treated and control distributions look similar. We give a novel, simple and intuitive generalization-error bound showing that the expected ITE estimation error of a representation is bounded by a sum of the standard generalization-error of that representation and the distance between the treated and control distributions induced by the representation. We use Integral Probability Metrics to measure distances between distributions, deriving explicit bounds for the Wasserstein and Maximum Mean Discrepancy (MMD) distances. Experiments on real and simulated data show the new algorithms match or outperform the state-of-the-art. <s> BIB002 </s> A Survey on Causal Inference <s> Other Applications <s> Learning representations for counterfactual inference from observational data is of high practical relevance for many domains, such as healthcare, public policy and economics. Counterfactual inference enables one to answer "What if...?" questions, such as "What would be the outcome if we gave this patient treatment $t_1$?". However, current methods for training neural networks for counterfactual inference on observational data are either overly complex, limited to settings with only two available treatment options, or both. Here, we present Perfect Match (PM), a method for training neural networks for counterfactual inference that is easy to implement, compatible with any architecture, does not add computational complexity or hyperparameters, and extends to any number of treatments. PM is based on the idea of augmenting samples within a minibatch with their propensity-matched nearest neighbours. Our experiments demonstrate that PM outperforms a number of more complex state-of-the-art methods in inferring counterfactual outcomes across several real-world and semi-synthetic datasets. <s> BIB003 </s> A Survey on Causal Inference <s> Other Applications <s> Estimating individual treatment effect (ITE) is a challenging problem in causal inference, due to missing counterfactuals and the selection bias. Existing ITE estimation methods mainly focus on balancing the distributions of control and treated groups, but ignore the local similarity information that is helpful. In this paper, we propose a local similarity preserved individual treatment effect (SITE) estimation method based on deep representation learning. SITE preserves local similarity and balances data distributions simultaneously, by focusing on several hard samples in each mini-batch. Experimental results on synthetic and three real-world datasets demonstrate the advantages of the proposed SITE method, compared with the state-of-the-art ITE estimation methods. <s> BIB004 </s> A Survey on Causal Inference <s> Other Applications <s> Estimating individualized treatment effects (ITE) is a challenging task due to the need for an individual's potential outcomes to be learned from biased data and without having access to the counterfactuals. We propose a novel method for inferring ITE based on the Generative Adversarial Nets (GANs) framework. Our method, termed Generative Adversarial Nets for inference of Individualized Treatment Effects (GANITE), is motivated by the possibility that we can capture the uncertainty in the counterfactual distributions by attempting to learn them using a GAN. We generate proxies of the counterfactual outcomes using a counterfactual generator, G, and then pass these proxies to an ITE generator, I, in order to train it. By modeling both of these using the GAN framework, we are able to infer based on the factual data, while still accounting for the unseen counterfactuals. We test our method on three real-world datasets (with both binary and multiple treatments) and show that GANITE outperforms state-of-the-art methods. <s> BIB005 </s> A Survey on Causal Inference <s> Other Applications <s> In many important machine learning applications, the training distribution used to learn a probabilistic classifier differs from the distribution on which the classifier will be used to make predictions. Traditional methods correct the distribution shift by reweighting training data with the ratio of the density between test and training data. However, in many applications training takes place without prior knowledge of the testing distribution. Recently, methods have been proposed to address the shift by learning the underlying causal structure, but those methods rely on diversity arising from multiple training data sets, and they further have complexity limitations in high dimensions. In this paper, we propose a novel Deep Global Balancing Regression (DGBR) algorithm to jointly optimize a deep auto-encoder model for feature selection and a global balancing model for stable prediction across unknown environments. The global balancing model constructs balancing weights that facilitate estimation of partial effects of features (holding fixed all other features), a problem that is challenging in high dimensions, and thus helps to identify stable, causal relationships between features and outcomes. The deep auto-encoder model is designed to reduce the dimensionality of the feature space, thus making global balancing easier. We show, both theoretically and with empirical experiments, that our algorithm can make stable predictions across unknown environments. Our experiments on both synthetic and real datasets demonstrate that our algorithm outperforms the state-of-the-art methods for stable prediction across unknown environments. <s> BIB006
The applications of causal inference are not limited to the areas mentioned above, and areas related to effectiveness measurement, decision making, or handling selection bias, are all potential applications. Education. In the education area, by comparing the outcome of different teaching methods on the student population, a better teaching method can be decided. Moreover, ITE estimation can enhance personalized learning by estimating the outcome of each student on different teaching methods. For example, ITE estimation is developed to answer the questions "Would this particular student benefit more from the video hint or the text hint when this student cannot solve a problem?", so that an Intelligent Tutor System (ITS) can decide which hint is more suitable for a specific student  . Political decision. In the politics area, causal inference can provide decision support. For example, various methods BIB001 BIB003 BIB002 BIB004 BIB005 have been developed on the jobs dataset aiming to answer the question"who would benefit most from subsidized job training?". Causal inference can also help with political decisions such as whether a policy should be promoted to large population size. Improving Machine learning methods. In addition to the decision support, various balancing methods that can handle the selection bias ( mentioned in Section 3), can also be extended to improve the stability of machine learning methods. In BIB006 , the reweighting method is adopted to improve the generalization ability of learned models for unknown environments (i.e., unknown test data). To be specific, the weight of each sample is added to the prediction loss function as a regularization, which is formulated as: p j=1 || ϕ(X T ., −j )(R ⊙X ., j ) R T X ., j − ϕ(X T ., −j )(R ⊙(1−X ., j )) R T (1−X ., j ) where p is the number of total features, ϕ(·) is the feature transformation function such as neural network, X ., j is the j-th feature in X , X .,−j is the features in X except the j-th feature, R ∈ R N is the global sample weights with N as the number of total samples. This balancing regularizer extends the CBPS method discussed in 3.1.1, by taking the j-th feature as the treatment and the remaining features as the background variables, and then combining all the features to obtain the global balancing weight.