Alexander G. Tartakovsky

Alexander G. Tartakovsky
University of Connecticut | UConn · Department of Statistics

PhD

About

151
Publications
17,513
Reads
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4,140
Citations
Additional affiliations
August 2013 - June 2016
University of Connecticut
Position
  • Professor (Full)
May 1997 - November 2013
University of Southern California, Los Angeles
Position
  • Managing Director

Publications

Publications (151)
Preprint
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 pointw...
Article
The paper addresses a sequential changepoint detection problem, assuming that the duration of change may be finite and unknown. This problem is of importance for many applications, e.g., for signal and image processing where signals appear and disappear at unknown points in time or space. In contrast to the conventional optimality criterion in quic...
Article
The paper addresses a joint sequential change-point detection and identification/isolation problem for a general stochastic model, assuming that the observed data may be dependent and non-identically distributed, the prior distribution of the change point is arbitrary, and the post-change hypotheses are composite. The developed detection–identifica...
Preprint
Full-text available
The paper addresses a joint sequential changepoint detection and identification/isolation problem for a general stochastic model, assuming that the observed data may be dependent and non-identically distributed, the prior distribution of the change point is arbitrary, and the post-change hypotheses are composite. The developed detection--identifica...
Preprint
Full-text available
The paper addresses a sequential changepoint detection problem, assuming that the duration of change may be finite and unknown. This problem is of importance for many applications, e.g., for signal and image processing where signals appear and disappear at unknown points in time or space. In contrast to the conventional optimality criterion in quic...
Article
Object detection in a cluttered environment, involving noisy measurements of signal over time, is a central problem in radar, sonar, optical, and communications applications. We consider the problem of detecting an object assuming that the distributions of the observed data are not exactly specified. As a result, the hypotheses to be tested are com...
Article
Full-text available
Assume that there are multiple data streams (channels, sensors) and in each stream the process of interest produces generally dependent and non-identically distributed observations. When the process is in a normal mode (in-control), the (pre-change) distribution is known, but when the process becomes abnormal there is a parametric uncertainty, i.e....
Article
A weighted Shiryaev–Roberts change detection procedure is shown to approximately minimize the expected delay to detection as well as higher moments of the detection delay among all change-point detection procedures with the given low maximal local probability of a false alarm within a window of a fixed length in pointwise and minimax settings for g...
Article
Typically, near-Earth space objects are observable for a small fraction of the orbit revolution. In this paper, we consider the problem of identification and fusion of two short optical tracks of near-Earth space objects, as well as the problem of estimation of the parameters of the corresponding orbits directly from these tracks in the absence of...
Article
The paper addresses a sequential changepoint detection problem for a general stochastic model, assuming that the observed data may be non-i.i.d. (i.e., dependent and non-identically distributed) and prior distribution of the change point is arbitrary. Tartakovsky and Veeravalli (2005), Baron and Tartakovsky (2006), and, more recently, Tartakovsky (...
Chapter
The term network surveillance is defined, and the statistical methodologies that can be used as tools for network surveillance are discussed. Three examples of network surveillance are used to illustrate the diversity of contexts where the term can apply. Common to all network surveillance applications is a desire to identify the anomalous patterns...
Preprint
Full-text available
The paper addresses a sequential changepoint detection problem for a general stochastic model, assuming that the observed data may be non-i.i.d. (i.e., dependent and non-identically distributed) and the prior distribution of the change point is arbitrary. Tartakovsky and Veeravalli (2005), Baron and Tartakovsky (2006), and, more recently, Tartakovs...
Preprint
Full-text available
Assume that there are multiple data streams (channels, sensors) and in each stream the process of interest produces generally dependent and non-identically distributed observations. When the process is in a normal mode (in-control), the (pre-change) distribution is known, but when the process becomes abnormal there is a parametric uncertainty, i.e....
Preprint
Full-text available
A weighted Shiryaev-Roberts change detection procedure is shown to approximately minimize the expected delay to detection as well as higher moments of the detection delay among all change-point detection procedures with the given low maximal local probability of a false alarm within a window of a fixed length in pointwise and minimax settings for g...
Article
Full-text available
The term network surveillance is defined in general terms and illustrated with many examples. Statistical methodologies that can be used as tools for network surveillance are discussed. Details for 3 illustrative examples that address network security, surveillance for data network failures, and surveillance of email traffic flows are presented. So...
Article
Full-text available
We consider the quickest change-point detection problem in pointwise and minimax settings for general dependent data models. Two new classes of sequential detection procedures associated with the maximal "local" probability of a false alarm within a period of some fixed length are introduced. For these classes of detection procedures, we consider t...
Article
Optimal stopping theory is a key part of sequential analysis and applied probability. Dr. Sören Christensen’s article is an important contribution to solving a class of optimal stopping problems for Markov processes mainly in continuous time, but a certain expansion to discrete time is also given. This discussion contains several issues that natura...
Article
Full-text available
In the 1960s, Shiryaev developed a Bayesian theory of change-point detection in the i.i.d. case, which was generalized in the beginning of the 2000s by Tartakovsky and Veeravalli for general stochastic models assuming a certain stability of the log-likelihood ratio process. Hidden Markov models represent a wide class of stochastic processes that ar...
Article
Full-text available
Simultaneous sequential changepoint detection and isolation is a challenging theoretical and practical direction of research. Professor Igor Nikiforov's article provides an excellent review of the state-of-the-art literature in this important field. This discussion addresses several issues and extensions important for modern applications of sequent...
Article
Full-text available
Activity profiles of terrorist groups show frequent spurts and downfalls corresponding to changes in the underlying organizational dynamics. In particular, it is of interest in understanding changes in attributes such as intentions/ideology, tactics/strategies, capabilities/resources, etc., that influence and impact the activity. The goal of this w...
Article
Full-text available
We consider the problem of sequential signal detection in a multichannel system where the number and location of signals is a priori unknown. We assume that the data in each channel are sequentially observed and follow a general non-i.i.d. stochastic model. Under the assumption that the local log-likelihood ratio processes in the channels converge...
Article
Full-text available
We revisit the problem of sequential testing composite hypotheses, considering multiple hypotheses and very general non-i.i.d. stochastic models. Two sequential tests are studied: the multihypothesis generalized sequential likelihood ratio test and the multihypothesis adaptive sequential likelihood ratio test with one-stage delayed estimators. Whil...
Article
Full-text available
We consider a sequential Bayesian changepoint detection problem for a general stochastic model, assuming that the observed data may be dependent and non-identically distributed and the prior distribution of the change point is arbitrary, not necessarily geometric. Tartakovsky and Veeravalli (2004) developed a general asymptotic theory of changepoin...
Article
Full-text available
We consider the issue of optimal design of the Exponentially Weighted Moving Average (EWMA) chart by properly selecting the smoothing factor and the initial value (headstart) of the decision statistic. The particular problem addressed is that of quickest detection of an abrupt change in the parameter of a discrete-time exponential model. Both pre-...
Book
The book reviews recent accomplishments in hypothesis testing and changepoint detection both in decision-theoretic (Bayesian) and non-decision-theoretic (non-Bayesian) contexts. The authors not only emphasize traditional binary hypotheses but also substantially more difficult multiple decision problems. They address scenarios with simple hypotheses...
Chapter
Full-text available
Changepoint problems deal with detecting changes in a process that occur at unknown points in time. The gist of the quickest changepoint problem is to design a detection procedure that minimizes the expected detection delay of a real change subject to a bound on the false alarm rate. In this chapter, we argue that network anomaly detection can be e...
Article
Full-text available
We consider the problem of quickly detecting a signal in a sensor network when the subset of sensors in which signal may be present is completely unknown. We formulate this problem as a sequential hypothesis testing problem with a simple null (signal is absent everywhere) and a composite alternative (signal is present somewhere). We introduce a nov...
Conference Paper
Full-text available
The problem of decentralized quickest change detection is studied with an additional constraint on the cost of observations used at each sensor. Minimax problem formulations are proposed for the problem. A distributed algorithm called the DE-All algorithm is proposed in which on-off observation control is employed locally at each sensor. It is show...
Conference Paper
Full-text available
We consider the problem of developing data-driven probabilistic models describing the activity profile of users in online social network settings. Previous models of user activities have discarded the potential influence of a user's network structure on his temporal activity patterns. Here we address this shortcoming and suggest an alternative appr...
Article
Full-text available
The focus of this work is on developing probabilistic models for user activity in social networks by incorporating the social network influence as perceived by the user. For this, we propose a coupled Hidden Markov Model, where each user's activity evolves according to a Markov chain with a hidden state that is influenced by the collective activity...
Article
Full-text available
We consider the problem of efficient on-line anomaly detection in computer network traffic. The problem is approached statistically, as that of sequential (quickest) changepoint detection. A multi-cyclic setting of quickest change detection is a natural fit for this problem. We propose a novel score-based multi-cyclic detection algorithm. The algor...
Article
Full-text available
Change-point detection is an important subarea of statistics that spans various branches of science and engineering. Professor David Siegmund is an internationally recognized expert and an eminent researcher in statistics in general and sequential analysis in particular, and his article [D. Siegmund, ibid. 32, No. 1, 2–14 (2013; Zbl 1271.62191)] is...
Article
Full-text available
The main focus of this work is on developing models for the activity profile of a terrorist group, detecting sudden spurts and downfalls in this profile, and in general, tracking it over a period of time. Toward this goal, a d-state hidden Markov model (HMM) that captures the latent states underlying the dynamics of the group and thus its activity...
Article
Full-text available
We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based likelihood ratio statistics and weighted generalized likelihood ratio statistics. It is shown that both sequential te...
Article
Full-text available
We address the sequential change-point detection problem for the Gaussian model where baseline distribution is Gaussian with variance \sigma^2 and mean \mu such that \sigma^2=a\mu, where a>0 is a known constant; the change is in \mu from one known value to another. First, we carry out a comparative performance analysis of four detection procedures:...
Article
Full-text available
We focus on one-sided, mixture-based stopping rules for the problem of sequential testing a simple null hypothesis against a composite alternative. For the latter, we consider two cases---either a discrete alternative or a continuous alternative that can be embedded into an exponential family. For each case, we find a mixture-based stopping rule th...
Article
Full-text available
We provide an overview of the state-of-the-art in the area of sequential change-point detection assuming discrete time and known pre- and post-change distributions. The overview spans over all major formulations of the underlying optimization problem, namely, Bayesian, generalized Bayesian, and minimax. We pay particular attention to the latest adv...
Conference Paper
Full-text available
We design a quickest change detection procedure that is almost minimax in the sense of minimizing the maximal (over change points) expected delay to detection for a given low false alarm rate. This procedure represents a variation of the Shiryaev-Roberts procedure that starts off at a fixed specially designed point.
Article
Full-text available
Let {Mn}n≥0 be a nonnegative time-homogeneous Markov process. The quasistationary distributions referred to in this note are of the form QA(x) = limn→∞P(Mn ≤ x | M0 ≤ A, M1 ≤ A, ..., Mn ≤ A). Suppose that M0 has distribution QA, and define TAQA = min{n | Mn > A, n ≥ 1}, the first time when Mn exceeds A. We provide sufficient conditions for QA(x) to...
Article
Full-text available
Let { M n } n ≥0 be a nonnegative time-homogeneous Markov process. The quasistationary distributions referred to in this note are of the form Q A ( x ) = lim n →∞ P( M n ≤ x | M 0 ≤ A , M 1 ≤ A , …, M n ≤ A ). Suppose that M 0 has distribution Q A , and define T A Q A = min{ n | M n > A , n ≥ 1}, the first time when M n exceeds A . We provide suffi...
Article
Full-text available
We study the behavior of mixture stopping rules in the one-sided sequential hypothesis testing problem with a simple null hypothesis and a composite alternative hypothesis. When the alternative hypothesis consists of a finite set of probability measures, we show how to select a particular mixing distribution in order to obtain a nearly minimax mixt...
Article
Full-text available
We analyze the article by Han and Tsung (20091. Han , D. and Tsung , F. ( 2009 ). The Optimal Stopping Time for Detecting Changes in Discrete Time Markov Processes , Sequential Analysis 28 : 115 – 135 . [Taylor & Francis Online]View all references) “The Optimal Stopping Time for Detecting Changes in Discrete Time Markov Processes,” and demonstrat...
Article
Full-text available
Quickest detection is a fascinating area of sequential analysis that spans across various branches of science and engineering. It is a pleasure to welcome Professor Albert Shiryaev's article, which provides a comprehensive overview (both scientific and historic) of this area. In this discussion, we expand on some of the issues raised in the article...
Article
Full-text available
We develop and evaluate the performance of advanced algorithms which provide significantly improved capabili-ties for automated detection and tracking of ballistic and flying dim objects in the presence of highly structured intense clutter. Applications include ballistic missile early warning, midcourse tracking, trajectory prediction, and resident...
Article
Full-text available
Let {M_n}_{n\ge 0}$ be a nonnegative Markov process with stationary transition probabilities. The quasistationary distributions referred to in this note are of the form Q_A(x) = lim_{n\to\infty} P(M_n \le x | M_0 \le A, M_1 \le A, ..., M_n \le A) . Suppose that $M_0$ has distribution $\Qb_A$ and define T_A^{Q_A} = \min\{n | M_n > A, n\ge 1\}, the f...
Article
Full-text available
Several variations of the Shiryaev-Roberts detection procedure in the context of the simple changepoint problem are considered: starting the procedure at $R_0=0$ (the original Shiryaev-Roberts procedure), at $R_0=r$ for fixed $r>0$, and at $R_0$ that has a quasi-stationary distribution. Comparisons of operating characteristics are made. The differe...
Article
Full-text available
We provide a brief overview of the state-of-the-art in quickest (sequential) changepoint detection and present some new results on asymptotic and numerical analysis of main competitors such as the CUSUM, Shiryaev–Roberts, and Shiryaev detection procedures in a Bayesian context.
Article
Full-text available
We begin with an overview of the quickest changepoint detection problem with an emphasis on Shiryaev's contributions to the field and show how the development in this area has led to optimal stopping theory. We then proceed to tackle application of optimal stopping and change detection in economics and finance, which has been a focus of Shiryaev's...
Article
Full-text available
We address a simple changepoint detection problem where observations are i.i.d. before and after the change with known pre-and post-change distributions. For this setting, the CUSUM test is known to be optimal in the minimax setting for Lorden's essential supremum metric, whereas the Shiryaev-Roberts procedure is optimal for detecting a change that...
Article
Full-text available
In 1985, for detecting a change in distribution Pollak introduced a minimax criterion and a randomized Shiryaev-Roberts procedure that starts off a random variable sampled from the quasi-stationary distribution of the Shiryaev-Roberts statistic. Pollak proved that this procedure is asymp-totically almost optimal as the mean time to false alarm beco...
Article
Full-text available
The CUSUM procedure is known to be optimal for detecting a change in distribution under a minimax scenario, whereas the Shiryaev-Roberts procedure is optimal for detecting a change that occurs at a distant time horizon. As a simpler alternative to the conventional Monte Carlo approach, we propose a numerical method for the systematic comparison of...
Article
Full-text available
Dr. Frisen gives an overview of the quickest change-point detection methods for on-line surveillance and a number of applications in economics, medicine, and environmental monitoring. In this discussion, we address optimality criteria in change-point detection problems as well as the issue of comparison of various change-point detection procedures.
Article
Full-text available
For the most popular sequential change detection rules such as CUSUM, EWMA, and the Shiryaev-Roberts test, we develop integral equations and a concise numerical method to compute a number of performance metrics, including average detection delay and average time to false alarm. We pay special attention to the Shiryaev-Roberts procedure and evaluate...
Article
Full-text available
This paper presents a combined geometric and statistical sampling algorithm for image segmentation inspired by a recently proposed algorithm for environmental sampling using autonomous robots
Article
Full-text available
In 1985, for detecting a change in distribution, Pollak introduced a specific minimax performance metric and a randomized version of the Shiryaev-Roberts procedure where the zero initial condition is replaced by a random variable sampled from the quasi-stationary distribution of the Shiryaev-Roberts statistic. Pollak proved that this procedure is t...
Conference Paper
Full-text available
We consider the simple changepoint problem setting, where observations are independent, iid pre-change and iid post-change, with known pre- and post-change distributions. The Shiryaev-Roberts detection procedure is known to be asymptotically minimax in the sense of minimizing maximal expected detection delay subject to a bound on the average run le...
Article
Full-text available
We develop and evaluate a suite of advanced algorithms which provide significantly-improved capabilities for finding, fixing, and tracking multiple ballistic and flying low observable objects in highly stressing cluttered environments. The algorithms have been developed for use in satellite-based staring and scanning optical surveillance suites for...
Article
Full-text available
In the 1960s Shiryaev developed the Bayesian theory of changepoint detection in independent and identically distributed (i.i.d.) sequences. In Shiryaev’s classical setting the goal is to minimize an average delay to detection under the constraint imposed on the average probability of false alarm. Recently, Tartakovsky and Veeravalli [Theory Probab....
Article
Full-text available
Dr. Mei points out an important issue of whether a conventional average run length to false alarm is a proper measure of the false alarm rate in change-point detection problems. In this discussion, we address this issue in detail and show that for non-i.i.d. observations this is indeed a big question.
Article
Full-text available
In the standard formulation of the quickest change-point detection problem, a sequence of observations, whose distribution changes at some unknown point in time, is available to a decision maker, and the goal is to detect this change as quickly as possible, subject to false alarm constraints. In this paper, we study the quickest change detection pr...
Article
Full-text available
In space-based infrared (IR) ballistic missile defense sensor systems, cluttered backgrounds are typically much more intense than the equivalent sensor noise or the targets being detected. Therefore, the development of efficient clutter removal and target preservation/enhancement algorithms is of crucial importance. To meet customer requirements, t...
Article
Full-text available
The following multidecision quickest detection problem, which is of importance for a variety of applications, is considered. There are N populations that are either statistically identical or where the change occurs in one of them at an unknown point in time. Alternatively, there may be N "isolated" points/hypotheses associated with a change. It is...
Article
Full-text available
We study asymptotic properties (as A → ∞) of the first exit time from the interval [0, A] of a non-negative Harris-recurrent Markov process. It is shown that under certain fairly general conditions the limiting distribution of the suit-ably normalized first exit time is exponential E(1) and that the moment generating function converges to that of E...
Conference Paper
Full-text available
The problem of decentralized changepoint detection in a distributed multisensor setting with binary quantization (BQ) is addressed. Attention is drawn to the case of composite post-change hypotheses when the post-change parameter is unknown. A multichart CUSUM detection procedure with binary quantization, called the M-BQ-CUSUM test, is proposed. Th...
Article
Full-text available
In 1961, for detecting a change in the drift of a Brownian motion, Shiryaev introduced what is now usually referred to as the Shiryaev-Roberts procedure. This procedure has a number of optimality and asymptotic optimality properties in various settings. Shiryaev (1961, 1963), and more recently Feinberg and Shiryaev (2006), established exact optimal...
Article
Full-text available
We consider the first exit time of a nonnegative Harris-recurrent Markov process from the interval $[0,A]$ as $A\to\infty$. We provide an alternative method of proof of asymptotic exponentiality of the first exit time (suitably standardized) that does not rely on embedding in a regeneration process. We show that under certain conditions the moment...
Article
Full-text available
In 1960s Shiryaev developed Bayesian theory of change detection in independent and identically distributed (i.i.d.) sequences. In Shiryaev's classical setting the goal is to minimize an average detection delay under the constraint imposed on the average probability of false alarm. Recently, Tartakovsky and Veeravalli (2005) developed a general Baye...
Article
Full-text available
In the early 1960s, Shiryaev obtained the structure of Bayesian stopping rules for detecting abrupt changes in independent and identically distributed sequences as well as in a constant drift of the Brownian motion. Since then, the methodology of optimal change-point detection has concentrated on the search for stopping rules that achieve the best...