A Hybrid Causal Search Algorithm for Latent Variable Models

Abstract

Existing score-based causal model search algorithms such as GES (and a speeded up version, FGS) are asymptotically correct, fast, and reliable, but make the unrealistic assumption that the true causal graph does not contain any unmeasured confounders. There are several constraint-based causal search algorithms (e.g RFCI, FCI, or FCI+) that are asymptotically correct without assuming that there are no unmeasured confounders, but often perform poorly on small samples. We describe a combined score and constraint-based algorithm, GFCI, that we prove is asymptotically correct. On synthetic data, GFCI is only slightly slower than RFCI but more accurate than FCI, RFCI and FCI+.

Figures

Figure 1

Markov Equivalence Class and Pattern

Figure 2

Markov Equivalence Class and PAG

Figure 3

Output of FGS when given a data from a system with latents

Figure 4

Average estimation errors of the various algorithms in the 100 variable cases, across different alpha levels for the independence test.

Figure 5

Average estimation errors of the various algorithms in the 1000 variable cases, across different alpha levels for the independence test.