Abstract
Causal inference methods based on conditional independence construct Markov equivalent graphs and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal discovery can be inferred for two observations. In our contribution, we pose a challenge to reconcile these two research directions. We study the role of latent variables such as latent instrumental variables and hidden common causes in the causal graphical structures. We show that methods based on the independence of cause and mechanism indirectly contain traces of the existence of the hidden instrumental variables. We derive a novel algorithm to infer causal relationships between two variables, and we validate the proposed method on simulated data and on a benchmark of cause-effect pairs. We illustrate by our experiments that the proposed approach is simple and extremely competitive in terms of empirical accuracy compared to the state-of-the-art methods.
Highlights
The statistical and probabilistic causal inference methods based on assumptions of independence of cause and mechanism appeared relatively recently and achieve very reasonable empirical results
Assuming the existence of the hidden instrumental variables, we propose a novel method of causal inference
Since we consider a bivariate causal inference case where only X and Y are observed, we propose an approach to estimate the latent instrumental variables for cases where the cluster assumption for the observed data holds
Summary
The statistical and probabilistic causal inference methods based on assumptions of independence of cause and mechanism (see [3] for a general overview) appeared relatively recently and achieve very reasonable empirical results. Our main theoretical result is an alternative viewpoint on the recently appeared causal inference algorithms that are based on the independence of cause and mechanism. Since we consider a bivariate causal inference case where only X and Y are observed, we propose an approach to estimate the latent instrumental variables for cases where the cluster assumption for the observed data holds.
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