This paper considers the problem of learning, from samples, the dependency
structure of a system of linear stochastic differential equations, when some of
the variables are latent. In particular, we observe the time evolution of some
variables, and never observe other variables; from this, we would like to find
the dependency structure between the observed variables - separating out the
spurious interactions caused by the (marginalizing out of the) latent
variables' 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 the
number of observed ones. For the case when the dependency structure between the
observed variables is sparse, we theoretically establish a high-dimensional
scaling result for structure recovery. We verify our theoretical result with
both synthetic and real data (from the stock market).

本文考虑学习基于样本的线性随机微分方程系统的依赖结构，特别是当一些变量是潜在变量时。我们开发了一种基于凸优化的新方法来解决这个问题。针对观测变量之间的依赖关系稀疏的情况，我们理论上建立了结构恢复的高维缩放结果，并通过合成和真实数据（来自股票市场）验证了我们的理论结果。