TY - GEN
T1 - Moments of parameter estimates for Chung-Lu random graph models
AU - Arcolano, Nicholas
AU - Ni, Karl
AU - Miller, Benjamin A.
AU - Bliss, Nadya T.
AU - Wolfe, Patrick J.
PY - 2012/10/23
Y1 - 2012/10/23
N2 - As abstract representations of relational data, graphs and networks find wide use in a variety of fields, particularly when working in non-Euclidean spaces. Yet for graphs to be truly useful in in the context of signal processing, one ultimately must have access to flexible and tractable statistical models. One model currently in use is the Chung-Lu random graph model, in which edge probabilities are expressed in terms of a given expected degree sequence. An advantage of this model is that its parameters can be obtained via a simple, standard estimator. Although this estimator is used frequently, its statistical properties have not been fully studied. In this paper, we develop a central limit theory for a simplified version of the Chung-Lu parameter estimator. We then derive approximations for moments of the general estimator using the delta method, and confirm the effectiveness of these approximations through empirical examples.
AB - As abstract representations of relational data, graphs and networks find wide use in a variety of fields, particularly when working in non-Euclidean spaces. Yet for graphs to be truly useful in in the context of signal processing, one ultimately must have access to flexible and tractable statistical models. One model currently in use is the Chung-Lu random graph model, in which edge probabilities are expressed in terms of a given expected degree sequence. An advantage of this model is that its parameters can be obtained via a simple, standard estimator. Although this estimator is used frequently, its statistical properties have not been fully studied. In this paper, we develop a central limit theory for a simplified version of the Chung-Lu parameter estimator. We then derive approximations for moments of the general estimator using the delta method, and confirm the effectiveness of these approximations through empirical examples.
KW - central limit theory
KW - delta method
KW - given expected degree models
KW - graphs and networks
KW - parameter estimation
UR - http://www.scopus.com/inward/record.url?scp=84867593239&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84867593239&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2012.6288785
DO - 10.1109/ICASSP.2012.6288785
M3 - Conference contribution
AN - SCOPUS:84867593239
SN - 9781467300469
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3961
EP - 3964
BT - 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings
T2 - 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012
Y2 - 25 March 2012 through 30 March 2012
ER -