Nonparametric Detection of An Anomalous Disk Over A Two-Dimensional Lattice Network

H. Vincent Poor1, Shaofeng Zou2, Yingbin Liang2

  • 1Princeton University
  • 2Syracuse University

Details

13:30 - 15:30 | Tue 22 Mar | Poster Area E | MLSP-P1.6

Session: Classification and Pattern Recognition I

Abstract

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.