Learning the Dependence Graph of Time Series with Latent Factors

Abstract

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).

References in corpus (6)

• Latent variable graphical model selection via convex optimization
• Robust Principal Component Analysis?
• High-dimensional covariance estimation by minimizing ${\ell }_1$-penalized log-determinant divergence
• Learning Networks of Stochastic Differential Equations
• Clustering using Max-norm Constrained Optimization
• Low-rank Matrix Recovery from Errors and Erasures

Cited by in corpus (6)

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• Learning Leading Indicators for Time Series Predictions
• Learning Vector Autoregressive Models with Latent Processes
• Single Index Latent Variable Models for Network Topology Inference