Learning with Latent Factors in Time Series

摘要: This paper considers the problem of learning, from samples, depen- dency structure a system linear stochastic differential equations, when some variables are latent. In particular, we observe time evolution variables, and never other variables; this, would like to find dependency between observed vari- ables – separating out spurious interactions caused by (marginal- izing the) latent variables’ series. We develop new method, based on convex optimization, do so in case number is smaller than ones. For sparse, theoretically establish high-dimensional scaling result for re- covery. verify our theoretical with both synthetic real data (from stock market).