TY - GEN

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:
This research has been supported in part by NSF Grants NeTS 1718203, CPS ECCS 1739189, ECCS 16-09370, CCF 1934986, NSF/USDA Grant AG 2018-67007-28379, ARO W911NF-19-1-0379, ECCS 2032321 and ONR Grant Navy N00014-19-1-2566.

PY - 2020/12/14

Y1 - 2020/12/14

N2 - We consider the problem of identifying parameters from data for systems with dynamics evolving according to a particular class of Markov chain processes, called Bernoulli Autoregressive (BAR) processes. The structure of any BAR model is encoded by a directed graph with p nodes. The edges of the graph indicate causal influences, or equivalently dynamic dependencies. More explicitly, the incoming edges to a node in the graph indicate that the state of the node at a particular time instant, which corresponds to a Bernoulli random variable, 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 variable; this convex combination corresponds to the associated parental edge weights and the contribution of the local noise variable. In this paper, we focus on the problem of structure and edge weight identification by relying on well-established statistical principles. We present two consistent estimators of the edge weights, a Maximum Likelihood (ML) estimator and a closed-form estimator, and numerically demonstrate that the derived estimators outperform existing algorithms in the literature in terms of sample complexity.

AB - We consider the problem of identifying parameters from data for systems with dynamics evolving according to a particular class of Markov chain processes, called Bernoulli Autoregressive (BAR) processes. The structure of any BAR model is encoded by a directed graph with p nodes. The edges of the graph indicate causal influences, or equivalently dynamic dependencies. More explicitly, the incoming edges to a node in the graph indicate that the state of the node at a particular time instant, which corresponds to a Bernoulli random variable, 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 variable; this convex combination corresponds to the associated parental edge weights and the contribution of the local noise variable. In this paper, we focus on the problem of structure and edge weight identification by relying on well-established statistical principles. We present two consistent estimators of the edge weights, a Maximum Likelihood (ML) estimator and a closed-form estimator, and numerically demonstrate that the derived estimators outperform existing algorithms in the literature in terms of sample complexity.

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U2 - 10.1109/CDC42340.2020.9304475

DO - 10.1109/CDC42340.2020.9304475

M3 - Conference contribution

AN - SCOPUS:85099885960

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 990

EP - 995

BT - 2020 59th IEEE Conference on Decision and Control, CDC 2020

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 59th IEEE Conference on Decision and Control, CDC 2020

Y2 - 14 December 2020 through 18 December 2020

ER -