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This paper considers the problem of learning, from samples, the dependencystructure of a system of linear stochastic differential equations, when some ofthe variables are latent. In particular, we observe the time evolution of somevariables, and never observe other variables; from this, we would like to findthe dependency structure between the observed variables - separating out thespurious interactions caused by the (marginalizing out of the) latentvariables' time series. We develop a new method, based on convex optimization,to do so in the case when the number of latent variables is smaller than thenumber of observed ones. For the case when the dependency structure between theobserved variables is sparse, we theoretically establish a high-dimensionalscaling result for structure recovery. We verify our theoretical result withboth synthetic and real data (from the stock market).

Learning the Dependence Graph of Time Series with Latent Factors