Asymptotic delay times of sequential tests based on U-statistics for early and late change points

Spectrum Sensing using Distributed Sequential Detection via Noisy Reporting MAC

This paper considers cooperative spectrum sensing algorithms for Cognitive Radios which focus on reducing the number of samples to make a reliable detection. We develop an energy efficient detector with low detection delay using decentralized sequential hypothesis testing. Our algorithm at the Cognitive Radios employs an asynchronous transmission scheme which takes into account the noise at the fusion center. We start with a distributed algorithm, DualSPRT, in which Cognitive Radios sequentially collect the observations, make local decisions using SPRT (Sequential Probability Ratio Test) and s…

Cooperative Distributed Sequential Spectrum Sensing

We consider cooperative spectrum sensing for cognitive radios. We develop an energy efficient detector with low detection delay using sequential hypothesis testing. Sequential Probability Ratio Test (SPRT) is used at both the local nodes and the fusion center. We also analyse the performance of this algorithm and compare with the simulations. Modelling uncertainties in the distribution parameters are considered. Slow fading with and without perfect channel state information at the cognitive radios is taken into account.

Optimal sequential treatment allocation

In treatment allocation problems the individuals to be treated often arrive sequentially. We study a problem in which the policy maker is not only interested in the expected cumulative welfare but is also concerned about the uncertainty/risk of the treatment outcomes. At the outset, the total number of treatment assignments to be made may even be unknown. A sequential treatment policy which attains the minimax optimal regret is proposed. We also demonstrate that the expected number of suboptimal treatments only grows slowly in the number of treatments. Finally, we study a setting where outcome…

Sequential Multiple Structural Damage Detection and Localization: A Distributed Approach

As essential components of the modern urban system, the health conditions of civil structures are the foundation of urban system sustainability and need to be continuously monitored. In Structural Health Monitoring (SHM), many existing works will have limited performance in the sequential damage diagnosis process because 1) the damage events needs to be reported with short delay, 2) multiple damage locations have to be identified simultaneously, and 3) the computational complexity is intractable in large-scale wireless sensor networks (WSNs). To address these drawbacks, we propose a new damage…

状态依赖扩散模型中序贯检验与最快检测的延迟惩罚比较

Delay-Penalty Comparison for Sequential Testing and Quickest Detection in State-Dependent Diffusion Models

针对漂移在两种状态间切换且信噪比依赖当前观测的扩散过程，提出基于滤波框架的序贯检验与最快检测方法，建立延迟惩罚比较原理，证明点态更大的运行延迟惩罚会缩小停止区域并导致更早停止。

Optimal sequential detection in multi-stream data

Consider a large number of detectors each generating a data stream. The task is to detect online, distribution changes in a small fraction of the data streams. Previous approaches to this problem include the use of mixture likelihood ratios and sum of CUSUMs. We provide here extensions and modifications of these approaches that are optimal in detecting normal mean shifts. We show how the (optimal) detection delay depends on the fraction of data streams undergoing distribution changes as the number of detectors goes to infinity. There are three detection domains. In the first domain for moderat…

Optimal Sequential Kernel Detection for Dependent Processes

In many applications one is interested to detect certain (known) patterns in the mean of a process with smallest delay. Using an asymptotic framework which allows to capture that feature, we study a class of appropriate sequential nonparametric kernel procedures under local nonparametric alternatives. We prove a new theorem on the con- vergence of the normed delay of the associated sequential detection procedure which holds for dependent time series under a weak mixing condition. The result suggests a simple procedure to select a kernel from a finite set of candidate kernels, and therefore may…

Sequential Detection of an Abrupt Change in a Random Sequence with Unknown Initial State

The problem of sequentially detecting an abrupt change in a sequence of independent and identically distributed (IID) random variables is addressed. Whereas previous approaches assume a known probability density function (PDF) at the start of the sequence, the problem addressed is the detection of a single change in distribution among a finite number of known 'equal-energy' PDFs, but where the initial and final distributions are not known a priori. A Bayesian multiple hypothesis approach is proposed where (i) unlike previous threshold policies, the minimum cost hypothesis is tracked through ti…

Optimal Sequential Tests for Detection of Changes under Finite measure space for Finite Sequences of Networks

This paper considers the change-point problem for finite sequences of networks. To avoid the difficulty of computing the normalization coefficient, such as in Exponential random graphical models (ERGMs) and Markov networks, we construct a finite measure space with measure ratio statistics. A new performance measure of detection delay is proposed to detect the changes in distribution of the network. And an optimal sequential test is proposed under the performance measure. The good performance of the optimal sequential test is illustrated numerically on ERGMs and Erdos-Rényi network sequences.

具有差分隐私的序列变化检测

Sequential Change Detection with Differential Privacy

本文提出DP-CUSUM方法，在保证差分隐私的前提下，实现序列变化检测的最优性能。

Sequential detection of multiple change points in networks: a graphical model approach

We propose a probabilistic formulation that enables sequential detection of multiple change points in a network setting. We present a class of sequential detection rules for certain functionals of change points (minimum among a subset), and prove their asymptotic optimality properties in terms of expected detection delay time. Drawing from graphical model formalism, the sequential detection rules can be implemented by a computationally efficient message-passing protocol which may scale up linearly in network size and in waiting time. The effectiveness of our inference algorithm is demonstrated…

Estimation of common change point and isolation of changed panels after sequential detection

Quick detection of common changes is critical in sequential monitoring of multi-stream data where a common change is referred as a change that only occurs in a portion of panels. After a common change is detected by using a combined CUSUM-SR procedure, we first study the joint distribution for values of the CUSUM process and the estimated delay detection time for the unchanged panels. The BH method by using the asymptotic exponential property for the CUSUM process is developed to isolate the changed panels with the control on FDR. The common change point is then estimated based on the isolated…

Minimax and pointwise sequential changepoint detection and identification for general stochastic models

This paper considers the problem of joint change detection and identification assuming multiple composite postchange hypotheses. We propose a multihypothesis changepoint detection-identification procedure that controls the probabilities of false alarm and wrong identification. We show that the proposed procedure is asymptotically minimax and pointwise optimal, minimizing moments of the detection delay as probabilities of false alarm and wrong identification approach zero. The asymptotic optimality properties hold for general stochastic models with dependent observations. We illustrate general …

Optimal Sequential Tests for Monitoring Changes in the Distribution of Finite Observation Sequences

This article develops a method to construct the optimal sequential test for monitoring the changes in the distribution of finite observation sequences with a general dependence structure. This method allows us to prove that different optimal sequential tests can be constructed for different performance measures of detection delay times. We also provide a formula to calculate the value of the generalized out-of-control average run length for every optimal sequential test. Moreover, we show that there is an equivalent optimal control limit which does not depend on the test statistic directly whe…

未知有限时域上的高概率延迟序贯变化检测

High Probability Latency Sequential Change Detection over an Unknown Finite Horizon

针对未知有限时域上的快速变化检测问题，提出一种阈值随时间对数增长的CuSum检验变体，并推导信息论下界以证明其渐近最优性，实验验证了性能。