Rethinking Chronological Causal Discovery with Signal Processing

TL;DR

It is demonstrated that both classical and recent causal discovery methods exhibit sensitivity to these hyperparameters, and it is discussed how ideas from signal processing may help us understand these phenomena.

Abstract

Causal discovery problems use a set of observations to deduce causality between variables in the real world, typically to answer questions about biological or physical systems. These observations are often recorded at regular time intervals, determined by a user or a machine, depending on the experiment design. There is generally no guarantee that the timing of these recordings matches the timing of the underlying biological or physical events. In this paper, we examine the sensitivity of causal discovery methods to this potential mismatch. We consider empirical and theoretical evidence to understand how causal discovery performance is impacted by changes of sampling rate and window length. We demonstrate that both classical and recent causal discovery methods exhibit sensitivity to these hyperparameters, and we discuss how ideas from signal processing may help us understand these phenomena.

Figures (5)

• Figure 1: Descriptions of a causal system using a window graph and a summary graph, respectively. A summary graph could be induced by a window graph by aggregating over the edges in a window graph.
• Figure 2: Varying the window length Q.
• Figure 3: Varying the downsampling factor, $k$
• Figure 4: F1 score when X is independent of Y while varying Q and k.
• Figure 5: F1 score when X causes Y while varying Q and k.