Amalgamating evidence of dynamics

Abstract

Many approaches to evidence amalgamation focus on relatively static information or evidence: the data to be amalgamated involve different variables, contexts, or experiments, but not measurements over extended periods of time. However, much of scientific inquiry focuses on dynamical systems; the system's behavior over time is critical. Moreover, novel problems of evidence amalgamation arise in these contexts. First, data can be collected at different measurement timescales, where potentially none of them correspond to the underlying system's causal timescale. Second, missing variables have a significantly different impact on time series measurements than they do in the traditional static setting; in particular, they make causal and structural inference much more difficult. In this paper, we argue that amalgamation should proceed by integrating causal knowledge, rather than at the level of "raw" evidence. We defend this claim by first outlining both of these problems, and then showing that they can be solved only if we operate on causal structures. We therefore must use causal discovery methods that are reliable given these problems. Such methods do exist, but their successful application requires careful consideration of the problems that we highlight.

Keywords: Causal discovery; Causal inference; Dynamical systems; Latent variables; Timescale.

Fig. 1

Undersampling effect on a dynamical causal graph. Superscripts denote measurement time index; subscripts denote causal time index; u is the degree of undersampling.

Fig. 2

An example of obtaining a compressed representation of a Markov order one DBN (bidirected edges not shown).

Fig. 3

Limiting behavior of apparent causal structure for causal time scale interactions described by directed acyclic graphs that allow loops of length one.

Fig. 4

A strongly connected component at a certain undersampling rate may appear as fully connected with all possible edges present.