Unobserved confounding is a key challenge when estimating causal effects from a treatment on an outcome in scientific applications. In this work, we assume that we observe a single, potentially multi-dimensional proxy variable of the unobserved confounder and that we know the mechanism that generates the proxy from the confounder. Under a completeness assumption on this mechanism, which we call Single Proxy Identifiability of Causal Effects or simply SPICE, we prove that causal effects are identifiable. We extend the proxy-based causal identifiability results by Kuroki and Pearl (2014); Pearl (2010) to higher dimensions, more flexible functional relationships and a broader class of distributions. Further, we develop a neural network based estimation framework, SPICE-Net, to estimate causal effects, which is applicable to both discrete and continuous treatments.

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