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Estimation in Autoregressive Processes with Partial Observations

Citation Author(s):
Milind Rao, Tara Javidi, Yonina C. Eldar, Andrea Goldsmith
Submitted by:
Milind Rao
Last updated:
10 March 2017 - 4:48pm
Document Type:
Poster
Document Year:
2017
Event:
Presenters:
Milind Rao
Paper Code:
3470
 

We consider the problem of estimating the covariance matrix and the transition matrix of vector autoregressive (VAR) processes from partial measurements. This model encompasses settings where there are limitations in the data acquisition of the underlying measurement systems so that data is lost or corrupted by noise. An estimator for the covariance matrix of the observations is first presented. More refined estimators, factoring in structural constraints on the covariance matrix such as sparsity, bandedness, sparsity of the inverse and low-rankness are then introduced that are particularly useful in the
high-dimensional regime. These estimates are then used to perform system identification by estimating the state transition matrix with or without further structural assumptions. Non-asymptotic guarantees are presented for all estimators.

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