Causal Discovery with Unobserved Variables: A Proxy Variable Approach
Keywords: causal discovery, unobserved variables, proxy variables, discretization
TL;DR: We propose a proxy-variable-based method to identify causal relations when unobserved variables are present.
Abstract: Discovering causal relations from observational data is important. The existence of unobserved variables, such as latent confounders or mediators, can mislead the causal identification. To address this issue, proximal causal discovery methods were proposed to adjust for the bias with the proxy of the unobserved variable. However, these methods only focused on discrete variables, which limits their real-world application. Besides, the extension to the continuous case is not easy as the naive discretization method can introduce biases due to the discretization error. To tackle this challenge, we propose a new method based on a comprehensive analysis regarding discretization error. We begin by identifying the source of discretization error and how it introduces the bias. We then introduce smoothness conditions under which the discretization error can be reduced to an infinitesimal level, provided the proxy is discretized with sufficiently fine bins. We also find that such conditions can hold for a broad family of causal models, e.g., Additive Noise Model. Based on this, we design a proxy-based hypothesis test that is provable to be consistent for identifying causal relationships within continuous variables. We demonstrate the utility of our method on synthetic and real-world data.
Primary Area: causal reasoning
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Submission Number: 4548
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