Causal Inference from Observational Data

Abstract:

Humans tend to have the concept of causality: "If I drink more tea, I will not sleep better." Some schools of thought have asserted that this understanding is natural, while others have claimed that it is something we must learn through empirical observations. Causal inference is an important problem in science and many real-life applications. A major challenge is in estimating the effect of a treatment on causing an outcome, which are usually confounded by a common cause variable, namely the confounder. This leads to several problems to be addressed. First, the confounder may not be a fixed quantity but changes over time. Its time-dependent property might contribute to bias in the estimates of causal effects. Second, the causal effects on different populations may be different. The data is scarce on some populations while more commonly available on others. In this case, a naive combination of the data sources might not be an ideal approach to learn causal effects in the population with scarce data because it would be dominated by the other populations. Third, learning causal effects might be limited by data privacy constraints. Different sets of data might be maintained in different clients, and they cannot be shared to an outsider due to privacy right of the users, and thus limiting access of causal inference algorithms to the data.

This dissertation is concerned with the methodologies of estimating causal effects in the three general contexts as described above, which are common in real life problems.

To incorporate latent factors that change with time, we extend causal inference with stochastic confounders. We propose Causal Modeling with Stochastic Confounders (CausalSC), a new approach to variational estimation for causal inference based on the well-known representer theorem but augmented to include a random input space. The causal effects involving latent confounders that are interdependent and time-varying from sequential, repeated measurements in an observational study are estimated. Our approach extends the recent work that assumes independent, non-temporal latent confounders, with potentially biased estimators. We demonstrate the effectiveness of this method on various benchmark temporal datasets.

To address data scarcity in a target population, we propose an adaptive transfer (AdaTRANS) algorithm which exploits additional data sources to facilitate estimating causal effects for the target population. Specifically, we leverage additional source datasets, which share similar causal mechanisms with the target observations, to help infer causal effects in the target population. We propose three levels of knowledge transfer, including modeling of outcomes, treatments, and confounders. To transfer knowledge based on similarity of the sources and the target observations, we introduce learnable transfer factors that can adaptively control the transfer strength, and thus achieving a fair and balanced transfer of knowledge between the sources and target. This is done through an extension of the representer theorem-based algorithm introduced in the first work (CausalSC). Our proposed method can estimate causal effects in the target population without prior knowledge of the data discrepancy between additional data sources and the target. This contrasts with the cutting edge tools and techniques that usually assume that the data are come from the same distribution. Experiments on both synthetic and real-world datasets show the effectiveness of the proposed method as compared with recent baselines.

To preserve data privacy in causal inference, we present a Federated Causal Inference (FedCI) framework to learn a common causal model, whilst keeping sensitive data at their local sites. This helps assess and integrate local causal effects from different private data sources without centralizing them. In particular, we estimate the treatment effect on individual subjects from observational data using a non-parametric reformulation of a classical potential outcomes framework. Under the strong ignorability assumption in causal modelling, the proposed model can be decomposed into multiple components, each associated with a data fragment. Thus, it enables the model to be efficiently estimated from federated data sources. This naturally allows us to adapt and incorporate observational data of related studies to infer the causal effects of interest. To the best of our knowledge, our proposed FedCI is the first method that infer causal effects while preserving an individual's privacy. We demonstrate the promise of the proposed approach through a set of simulated and real-world benchmark examples.