Linear Stochastic Dynamical Systems with Latent Factors: High-Dimensional Inference

Details Linear Stochastic Dynamical Systems with Latent Factors: High-Dimensional Inference Linear Stochastic Dynamical Systems with Latent Factors: High-Dimensional Inference

2011-06-09

arxiv.org/abs/1106.1887v3

Computer Science

Learning

Scientific paper

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).

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