Causal inference seeks to estimate the effect given a treatment such as a medicine or the dosage of a medication. To reduce the confounding bias caused by the non-randomized treatment assignment, most existing methods reduce the shift between subpopulations receiving different treatments. However, these methods split limited training samples into smaller groups, which cuts down the number of samples in each group, while precise distribution estimation and alignment highly rely on a sufficient number of training samples. In this paper, we propose a distribution alignment paradigm without data splitting, which can be naturally applied in the settings of binary and continuous treatments. To this end, we characterize the confounding bias by considering different probability measures of the same set including all the training samples, and exploit the optimal transport theory to analyze the confounding bias and outcome estimation error. Based on this, we propose to learn balanced representations by reducing the bias between the marginal distribution and the conditional distribution of a treatment. As a result, data reduction caused by splitting is avoided, and the outcome prediction model trained on one treatment group can be generalized to the entire population. The experiments on both binary and continuous treatment settings demonstrate the effectiveness of our method.

Estimating long-term causal effects by combining long-term observational and short-term experimental data is a crucial but challenging problem in many real-world scenarios. In existing methods, several ideal assumptions, e.g. latent unconfoundedness assumption or additive equi-confounding bias assumption, are proposed to address the latent confounder problem raised by the observational data. However, in real-world applications, these assumptions are typically violated which limits their practical effectiveness. In this paper, we tackle the problem of estimating the long-term individual causal effects without the aforementioned assumptions. Specifically, we propose to utilize the natural heterogeneity of data, such as data from multiple sources, to identify latent confounders, thereby significantly avoiding reliance on idealized assumptions. Practically, we devise a latent representation learning-based estimator of long-term causal effects. Theoretically, we establish the identifiability of latent confounders, with which we further achieve long-term effect identification. Extensive experimental studies, conducted on multiple synthetic and semi-synthetic datasets, demonstrate the effectiveness of our proposed method.

Estimating treatment effects from observational data suffers from the issue of confounding bias, which is induced by the imbalanced confounder distributions between the treated and control groups. As an effective approach, re-weighting learns a group of sample weights to balance the confounder distributions. Existing methods of re-weighting highly rely on a propensity score model or moment alignment. However, for complex real-world data, it is difficult to obtain an accurate propensity score prediction. Although moment alignment is free of learning a propensity score model, accurate estimation for high-order moments is computationally difficult and still remains an open challenge, and first and second-order moments are insufficient to align the distributions and easy to be misled by outliers. In this paper, we exploit geometry to capture the intrinsic structure involved in data for balancing the confounder distributions, so that confounding bias can be reduced even with outliers. To achieve this, we construct a connection between treatment effect estimation and optimal transport, a powerful tool to capture geometric information. After that, we propose an optimal transport model to learn sample weights by extracting geometry from confounders, in which geometric information between groups and within groups is leveraged for better confounder balancing. A projected mirror descent algorithm is employed to solve the derived optimization problem. Experimental studies on both synthetic and real-world datasets demonstrate the effectiveness of our proposed method.

Causal effect estimation under networked interference is an important but challenging problem. Available parametric methods are limited in their model space, while previous semiparametric methods, e.g., leveraging neural networks to fit only one single nuisance function, may still encounter misspecification problems under networked interference without appropriate assumptions on the data generation process. To mitigate bias stemming from misspecification, we propose a novel doubly robust causal effect estimator under networked interference, by adapting the targeted learning technique to the training of neural networks. Specifically, we generalize the targeted learning technique into the networked interference setting and establish the condition under which an estimator achieves double robustness. Based on the condition, we devise an end-to-end causal effect estimator by transforming the identified theoretical condition into a targeted loss. Moreover, we provide a theoretical analysis of our designed estimator, revealing a faster convergence rate compared to a single nuisance model. Extensive experimental results on two real-world networks with semisynthetic data demonstrate the effectiveness of our proposed estimators.

Most studies on causal inference tackle the issue of confounding bias by reducing the distribution shift between the control and treated groups. However, it remains an open question to adopt an appropriate metric for distribution shift in practice. In this paper, we define a generic balancing error on reweighted samples to characterize the confounding bias, and study the connection between the balancing error and the Wasserstein discrepancy derived from the theory of optimal transport. We not only regard the Wasserstein discrepancy as the metric of distribution shift, but also explore the association between the balancing error and the underlying cost function involved in the Wasserstein discrepancy. Motivated by this, we propose to reduce the balancing error under the framework of optimal transport with learnable marginal distributions and the cost function, which is implemented by jointly learning weights and representations associated with factual outcomes. The experiments on both synthetic and real-world datasets demonstrate the effectiveness of our proposed method.

Estimating causal effects from observational network data is a significant but challenging problem. Existing works in causal inference for observational network data lack an analysis of the generalization bound, which can theoretically provide support for alleviating the complex confounding bias and practically guide the design of learning objectives in a principled manner. To fill this gap, we derive a generalization bound for causal effect estimation in network scenarios by exploiting 1) the reweighting schema based on joint propensity score and 2) the representation learning schema based on Integral Probability Metric (IPM). We provide two perspectives on the generalization bound in terms of reweighting and representation learning, respectively. Motivated by the analysis of the bound, we propose a weighting regression method based on the joint propensity score augmented with representation learning. Extensive experimental studies on two real-world networks with semi-synthetic data demonstrate the effectiveness of our algorithm.