Recovering Latent Causal Relations from Times Series Data

Discovering causal relationships from data is a challenging problem that is exacerbated when some of the variables of interests are latent. In this talk, we discuss the problem of learning the support of transition matrix between random processes in a Vector Autoregressive (VAR) model from samples when a subset of the processes are latent. It is well known that ignoring the effect of the latent processes may lead to very different estimates of the influences even among observed processes. We are not only interested in identifying the influences among the observed processes, but also aim at learning those between the latent ones, and those from the latent to the observed ones. We show that the support of transition matrix among the observed processes and lengths of all latent paths between any two observed processes can be identified successfully under some conditions on the VAR model. Our results apply to both non-Gaussian and Gaussian cases, and experimental results on various synthetic and real-world datasets validate our theoretical findings.