Causal Discovery from Subsampled Time Series Data by Constraint Optimization

Abstract

This paper focuses on causal structure estimation from time series data in which measurements are obtained at a coarser timescale than the causal timescale of the underlying system. Previous work has shown that such subsampling can lead to significant errors about the system's causal structure if not properly taken into account. In this paper, we first consider the search for the system timescale causal structures that correspond to a given measurement timescale structure. We provide a constraint satisfaction procedure whose computational performance is several orders of magnitude better than previous approaches. We then consider finite-sample data as input, and propose the first constraint optimization approach for recovering the system timescale causal structure. This algorithm optimally recovers from possible conflicts due to statistical errors. More generally, these advances allow for a robust and non-parametric estimation of system timescale causal structures from subsampled time series data.

Keywords: causal discovery; causality; constraint optimization; constraint satisfaction; graphical models; time series.

Figure 1

Example graphs: a) G¹, b) 𝒢¹, c) G^u, d) 𝒢^u with subsampling rate u = 2.

Figure 2

Running times. Left: for 10-node graphs as a function of graph density (100 graphs per density and a timeout of 100 seconds); Right: for 10%-dense graphs as a function of graph size (100 graphs per density and a timeout of 1 hour).

Figure 3

Left: Influence of input graph density on running times of our approach. Right: Scalability of our approach when enumerating all solutions over u = 1, …, 5.

Figure 4

Accuracy of the optimal solutions with different weighting schemes and parameters (on x-axis). See text for further details.

Figure 5

Scalability of our approach under different settings.