TY - JOUR
T1 - On the Consistency of Maximum Likelihood Estimators for Causal Network Identification
AU - Xie, Xiaotian
AU - Katselis, Dimitrios
AU - Beck, Carolyn L.
AU - Srikant, R.
N1 - Funding Information:
Manuscript received October 29, 2020; revised December 28, 2020; accepted January 14, 2021. Date of publication January 22, 2021; date of current version June 24, 2021. This work was supported in part by NSF under Grant NeTS 1718203, Grant CPS ECCS 1739189, Grant ECCS 16-09370, Grant ECCS 2032321, and Grant CCF 1934986; in part by NSF/USDA under Grant AG 2018-67007-28379; in part by ARO under Grant W911NF-19-1-0379; and in part by ONR under Grant N00014-19-1-2566. Recommended by Senior Editor R. S. Smith. (Corresponding author: Xiaotian Xie.) Xiaotian Xie, Carolyn L. Beck, and R. Srikant are with the Coordinated Science Laboratory, University of Illinois at Urbana–Champaign, Urbana, IL 61801 USA (e-mail: [email protected]; [email protected]; [email protected]).
Publisher Copyright:
© 2017 IEEE.
PY - 2022
Y1 - 2022
N2 - We consider the problem of identifying parameters of a particular class of Markov chains, called Bernoulli Autoregressive (BAR) processes. The structure of any BAR model is encoded by a directed graph. Incoming edges to a node in the graph indicate that the state of the node at a particular time instant is influenced by the states of the corresponding parental nodes in the previous time instant. The associated edge weights determine the corresponding level of influence from each parental node. In the simplest setup, the Bernoulli parameter of a particular node's state variable is a convex combination of the parental node states in the previous time instant and an additional Bernoulli noise random variable. This letter focuses on the problem of edge weight identification using Maximum Likelihood (ML) estimation and proves that the ML estimator is strongly consistent for two variants of the BAR model. We additionally derive closed-form estimators for the aforementioned two variants and prove their strong consistency.
AB - We consider the problem of identifying parameters of a particular class of Markov chains, called Bernoulli Autoregressive (BAR) processes. The structure of any BAR model is encoded by a directed graph. Incoming edges to a node in the graph indicate that the state of the node at a particular time instant is influenced by the states of the corresponding parental nodes in the previous time instant. The associated edge weights determine the corresponding level of influence from each parental node. In the simplest setup, the Bernoulli parameter of a particular node's state variable is a convex combination of the parental node states in the previous time instant and an additional Bernoulli noise random variable. This letter focuses on the problem of edge weight identification using Maximum Likelihood (ML) estimation and proves that the ML estimator is strongly consistent for two variants of the BAR model. We additionally derive closed-form estimators for the aforementioned two variants and prove their strong consistency.
KW - Identification
KW - Markov chains
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U2 - 10.1109/LCSYS.2021.3053610
DO - 10.1109/LCSYS.2021.3053610
M3 - Article
AN - SCOPUS:85100511474
SN - 2475-1456
VL - 6
SP - 175
EP - 180
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
M1 - 9333685
ER -