Sequential change-point detection seeks to rapidly identify distributional changes in streaming data while controlling false alarms. Existing multi-stream detection methods typically rely on non-private access to raw observations or intermediate statistics, limiting their usage in privacy-sensitive settings. We study sequential change-point detection for multiple data streams under differential privacy constraints. We consider multiple independent streams undergoing a synchronized change at an unknown time and in an unknown subset of streams, and propose DP-SUM-CUSUM, a differentially private detection procedure based on the summation of per-stream CUSUM statistics with calibrated Laplace noise injection. We show that DP-SUM-CUSUM satisfies sequential $\varepsilon$-differential privacy and derive bounds on the average run length to false alarm and the worst-case average detection delay, explicitly characterizing the privacy--efficiency tradeoff. A truncation-based extension is also presented to handle distributional shifts with unbounded log-likelihood ratios. Simulations and experiments on an Internet of Things (IoT) botnet dataset validate the proposed approach.

Sequential change detection is a fundamental problem in statistics and signal processing, with the CUSUM procedure widely used to achieve minimax detection delay under a prescribed false-alarm rate when pre- and post-change distributions are fully known. However, releasing CUSUM statistics and the corresponding stopping time directly can compromise individual data privacy. We therefore introduce a differentially private (DP) variant, called DP-CUSUM, that injects calibrated Laplace noise into both the vanilla CUSUM statistics and the detection threshold, preserving the recursive simplicity of the classical CUSUM statistics while ensuring per-sample differential privacy. We derive closed-form bounds on the average run length to false alarm and on the worst-case average detection delay, explicitly characterizing the trade-off among privacy level, false-alarm rate, and detection efficiency. Our theoretical results imply that under a weak privacy constraint, our proposed DP-CUSUM procedure achieves the same first-order asymptotic optimality as the classical, non-private CUSUM procedure. Numerical simulations are conducted to demonstrate the detection efficiency of our proposed DP-CUSUM under different privacy constraints, and the results are consistent with our theoretical findings.

Sequential change-point detection has many important applications in industrial quality control, signal detection, and clinical trials. However, many classical procedures may fail when the observed data are contaminated by outliers, even if the percentage of outliers is very small. In this paper, we focus on the problem of robust sequential change-point detection in the presence of a small proportion of random outliers. We first study the statistical detection properties of a general family of detection procedures under Huber’s gross error model. Moreover, we incorporate ideas of the breakdown point and the influence function from the classical offline robust statistics literature and propose their new definitions to quantify the robustness of general sequential change-point detection procedures. Then, we derive the breakdown points and influence functions of our proposed family of detection procedures, which provide a quantitative analysis of the robustness of these procedures. Moreover, we find the optimal robust bounded-influence procedure in that general family that has the smallest detection delay subject to the constraints on the false alarm rate influence function. It turns out the optimal procedure is based on truncation of the scaled likelihood ratio statistic and has a simple form. Finally, we demonstrate the robustness and the detection efficiency of the optimal robust bounded-influence procedure through extensive simulations and compute numerical approximations of breakdown points and influence functions of some procedures to have a quantitative understanding of the robustness of different procedures.

Community detection is a fundamental problem in network analysis and has important applications in sensor networks and social networks. In many cases, the community structure of the network may change at some unknown time and thus it is desirable to come up with efficient monitoring procedures that can detect the change as quickly as possible. In this work, we use the Erdős-Rényi model and the bisection stochastic block model (SBM) to model the pre-change and post-change distributions of the network, respectively. That is, initially, we assume there is no community in the network. However, at some unknown time, a change occurs, and two communities are formed in the network. We then propose an efficient monitoring procedure by using the number of k-cycles in the graph. The asymptotic detection properties of our proposed procedure are derived when all parameters are known. A generalized likelihood ratio (GLR) type detection procedure and an adaptive CUSUM type detection procedure are constructed to address the problem when parameters are unknown.

The problem of quickest change detection in anonymous heterogeneous sensor networks is studied. The sensors are clustered into$K$groups, and different groups follow different data generating distributions. At some unknown time, an event occurs in the network and changes the data generating distribution of the sensors. The goal is to detect the change as quickly as possible, subject to false alarm constraints. The anonymous setting is studied, where at each time step, the fusion center receives unordered samples without knowing which sensor each sample comes from, and thus does not know its exact distribution. In [1], an optimal algorithm was provided, which however is not computational efficient for large networks. In this paper, a computationally efficient test is proposed and a novel theoretical characterization of its false alarm rate is further developed.

The problem of sequential binary hypothesis testing in an adversarial environment is investigated. Specifically, if there is no adversary, the samples are generated independently by a distribution p; and if the adversary is present, the samples are generated independently by another distribution q. The adversary picks a distribution q ∈ Q with cost c(q). The goal of the defender is to decide whether there is an adversary using samples as few as possible; and the goal of the adversary is to fool the defender. The problem is formulated as a non-zero-sum game between the adversary and the defender. A pair of strategies (attack strategy from the adversary and the sequential hypothesis testing scheme from the detector) is proposed and proved to be a Nash equilibrium pair for the non-zero-sum game asymptotically. Numerical experiments are provided to validate our results.