Optimal network online change point localisation

• URL: http://arxiv.org/abs/2101.05477v1
• Date: Thu, 14 Jan 2021 07:24:39 GMT
• Title: Optimal network online change point localisation
• Authors: Yi Yu, Oscar Hernan Madrid Padilla, Daren Wang and Alessandro Rinaldo
• Abstract summary: We study the problem of online network change point detection. In this setting, a collection of independent Bernoulli networks is collected sequentially, and the underlying change point occurs. The goal is to detect the change point as quickly as possible, if it exists, subject to a constraint on the number or probability of false alarms.
• Score: 73.93301212629231
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the problem of online network change point detection. In this setting, a collection of independent Bernoulli networks is collected sequentially, and the underlying distributions change when a change point occurs. The goal is to detect the change point as quickly as possible, if it exists, subject to a constraint on the number or probability of false alarms. In this paper, on the detection delay, we establish a minimax lower bound and two upper bounds based on NP-hard algorithms and polynomial-time algorithms, i.e., \[ \mbox{detection delay} \begin{cases} \gtrsim \log(1/\alpha) \frac{\max\{r^2/n, \, 1\}}{\kappa_0^2 n \rho},\\ \lesssim \log(\Delta/\alpha) \frac{\max\{r^2/n, \, \log(r)\}}{\kappa_0^2 n \rho}, & \mbox{with NP-hard algorithms},\\ \lesssim \log(\Delta/\alpha) \frac{r}{\kappa_0^2 n \rho}, & \mbox{with polynomial-time algorithms}, \end{cases} \] where $\kappa_0, n, \rho, r$ and $\alpha$ are the normalised jump size, network size, entrywise sparsity, rank sparsity and the overall Type-I error upper bound. All the model parameters are allowed to vary as $\Delta$, the location of the change point, diverges. The polynomial-time algorithms are novel procedures that we propose in this paper, designed for quick detection under two different forms of Type-I error control. The first is based on controlling the overall probability of a false alarm when there are no change points, and the second is based on specifying a lower bound on the expected time of the first false alarm. Extensive experiments show that, under different scenarios and the aforementioned forms of Type-I error control, our proposed approaches outperform state-of-the-art methods.

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