Surveillance systems [HC11] are equipped with a suite of sensors that can be switched and steered to focus attention on any target or location over a physical landscape (see Figure 1) to detect abrupt changes at any location. On the other hand, sensor suites are resource limited, and only a limited subset, among all the locations, can be probed at any time.

Surveillance systems [HC11] are equipped with a suite of sensors that can be switched and steered to focus attention on any target or location over a physical landscape (see Figure 1) to detect abrupt changes at any location. On the other hand, sensor suites are resource limited, and only a limited subset, among all the locations, can be probed at any time.

Online changepoint detection algorithms that are based on likelihood-ratio tests have been shown to have excellent statistical properties. However, a simple online implementation is computationally infeasible as, at time $T$, it involves considering $O(T)$ possible locations for the change. Recently, the FOCuS algorithm has been introduced for detecting changes in mean in Gaussian data that decreases the per-iteration cost to $O(\log T)$. This is possible by using pruning ideas, which reduce the set of changepoint locations that need to be considered at time $T$ to approximately $\log T$. We show that if one wishes to perform the likelihood ratio test for a different one-parameter exponential family model, then exactly the same pruning rule can be used, and again one need only consider approximately $\log T$ locations at iteration $T$. Furthermore, we show how we can adaptively perform the maximisation step of the algorithm so that we need only maximise the test statistic over a small subset of these possible locations. Empirical results show that the resulting online algorithm, which can detect changes under a wide range of models, has a constant-per-iteration cost on average.

In this paper, we attempt to detect an inflection or change-point resulting from the Covid-19 pandemic on supply chain data received from a large furniture company. To accomplish this, we utilize a modified CUSUM (Cumulative Sum) procedure on the company's spatial-temporal order data as well as a GLR (Generalized Likelihood Ratio) based method. We model the order data using the Hawkes Process Network, a multi-dimensional self and mutually exciting point process, by discretizing the spatial data and treating each order as an event that has a corresponding node and time. We apply the methodologies on the company's most ordered item on a national scale and perform a deep dive into a single state. Because the item was ordered infrequently in the state compared to the nation, this approach allows us to show efficacy upon different degrees of data sparsity. Furthermore, it showcases use potential across differing levels of spatial detail.

Detecting abrupt changes in temporal behavior patterns is of interest in many industrial and security applications. Abrupt changes are often local and observable primarily through a well-aligned sensing action (e.g., a camera with a narrow field-of-view). Due to resource constraints, continuous monitoring of all of the sensors is impractical. We propose the bandit quickest changepoint detection framework as a means of balancing sensing cost with detection delay. In this framework, sensing actions (or sensors) are sequentially chosen, and only measurements corresponding to chosen actions are observed. We derive an information-theoretic lower bound on the detection delay for a general class of finitely parameterized probability distributions. We then propose a computationally efficient online sensing scheme, which seamlessly balances the need for exploration of different sensing options with exploitation of querying informative actions. We derive expected delay bounds for the proposed scheme and show that these bounds match our information-theoretic lower bounds at low false alarm rates, establishing optimality of the proposed method. We then perform a number of experiments on synthetic and real datasets demonstrating the efficacy of our proposed method.

We present a new CUSUM procedure for sequentially detecting change-point in the self and mutual exciting processes, a.k.a. Hawkes networks using discrete events data. Hawkes networks have become a popular model for statistics and machine learning due to their capability in modeling irregularly observed data where the timing between events carries a lot of information. The problem of detecting abrupt changes in Hawkes networks arises from various applications, including neuronal imaging, sensor network, and social network monitoring. Despite this, there has not been a computationally and memory-efficient online algorithm for detecting such changes from sequential data. We present an efficient online recursive implementation of the CUSUM statistic for Hawkes processes, both decentralized and memory-efficient, and establish the theoretical properties of this new CUSUM procedure. We then show that the proposed CUSUM method achieves better performance than existing methods, including the Shewhart procedure based on count data, the generalized likelihood ratio (GLR) in the existing literature, and the standard score statistic. We demonstrate this via a simulated example and an application to population code change-detection in neuronal networks.