Detailed Instructions: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Problem:This paper considers the problem of learning, from samples, the depen-<lb>dency structure of a system of linear stochastic differential equations,<lb>when some of the variables are latent. In particular, we observe the time<lb>evolution of some variables, and never observe other variables; from this,<lb>we would like to find the dependency structure between the observed vari-<lb>ables separating out the spurious interactions caused by the (marginal-<lb>izing out of the) latent variables' time series. We develop a new method,<lb>based on convex optimization, to do so in the case when the number of<lb>latent variables is smaller than the number of observed ones. For the case<lb>when the dependency structure between the observed variables is sparse,<lb>we theoretically establish a high-dimensional scaling result for structure re-<lb>covery. We verify our theoretical result with both synthetic and real data<lb>(from the stock market).
Solution:
Learning with Latent Factors in Time Series