TY - GEN
T1 - Nonparametric detection of an anomalous disk over a two-dimensional lattice network
AU - Zou, Shaofeng
AU - Liang, Yingbin
AU - Poor, H. Vincent
N1 - Funding Information:
The work of S. Zou and Y. Liang was supported by an NSF CAREER Award under Grant CCF-10-26565. The work of H. V. Poor was supported by the ARO under MURI Grant W911NF-11-1-0036 and by the NSF under Grants CNS-14-56793 and EECS-13-43210.
Publisher Copyright:
© 2016 IEEE.
PY - 2016/5/18
Y1 - 2016/5/18
N2 - Nonparametric detection of existence of an anomalous disk over a lattice network is investigated. If an anomalous disk exists, then all nodes belonging to the disk observe samples generated by a distribution q, whereas all other nodes observe samples generated by a distribution p that is distinct from q. If there does not exist an anomalous disk, then all nodes receive samples generated by p. The distributions p and q are arbitrary and unknown. The goal is to design statistically consistent test as the network size becomes asymptotically large. A kernel-based test is proposed based on maximum mean discrepancy (MMD) which measures the distance between mean embeddings of distributions into a reproducing kernel Hilbert space (RKHS). A sufficient condition on the minimum size of candidate anomalous disks is characterized in order to guarantee the consistency of the proposed test. A necessary condition that any universally consistent test must satisfy is further derived. Comparison of sufficient and necessary conditions yields that the proposed test is order-level optimal.
AB - Nonparametric detection of existence of an anomalous disk over a lattice network is investigated. If an anomalous disk exists, then all nodes belonging to the disk observe samples generated by a distribution q, whereas all other nodes observe samples generated by a distribution p that is distinct from q. If there does not exist an anomalous disk, then all nodes receive samples generated by p. The distributions p and q are arbitrary and unknown. The goal is to design statistically consistent test as the network size becomes asymptotically large. A kernel-based test is proposed based on maximum mean discrepancy (MMD) which measures the distance between mean embeddings of distributions into a reproducing kernel Hilbert space (RKHS). A sufficient condition on the minimum size of candidate anomalous disks is characterized in order to guarantee the consistency of the proposed test. A necessary condition that any universally consistent test must satisfy is further derived. Comparison of sufficient and necessary conditions yields that the proposed test is order-level optimal.
KW - Consistency
KW - maximum mean discrepancy
KW - nonparametric detection
KW - reproducing kernel Hilbert space
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U2 - 10.1109/ICASSP.2016.7472106
DO - 10.1109/ICASSP.2016.7472106
M3 - Conference contribution
AN - SCOPUS:84973333433
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 2394
EP - 2398
BT - 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
Y2 - 20 March 2016 through 25 March 2016
ER -