Aleksey Polunchenko | Binghamton University (original) (raw)

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Papers by Aleksey Polunchenko

Abstract We address the sequential change-point detection problem for the Gaussian model where ba... more Abstract We address the sequential change-point detection problem for the Gaussian model where baseline distribution is Gaussian with variance σ2 and mean μ such that σ2= a μ, where a> 0 is a known constant; the change is in μ from one known value to another. First, we carry out a comparative performance analysis of four detection procedures: the Cumulative Sum (CUSUM) procedure, the Shiryaev–Roberts (SR) procedure, and two its modifications—the Shiryaev–Roberts–Pollak and Shiryaev–Roberts–r procedures.

Abstract We consider the problem of efficient on-line anomaly detection in computer network traff... more Abstract 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 scorebased multi-cyclic detection algorithm. The algorithm is based on the so-called ShiryaevRoberts procedure.

Abstract. We study asymptotic properties (as A→∞) of the first exit time from the interval [0, A]... more Abstract. 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 suitably normalized first exit time is exponential E (1) and that the moment generating function converges to that of E (1). The method of proof is based on considering the quasi-stationary distribution and its relation to the normalizing factor.

Methodology and Computing in …, Jan 1, 2011

We provide an overview of the state-of-the-art in the area of sequential changepoint detection as... more We provide an overview of the state-of-the-art in the area of sequential changepoint 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 advances in each. Also, we link together the generalized Bayesian problem with multi-cyclic disorder detection in a stationary regime when the change occurs at a distant time horizon. We conclude with two case studies to illustrate the cutting edge of the field at work.

Proceedings of the …, Jan 1, 2009

We address a simple changepoint detection problem where observations are i.i.d. before and after ... more 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 occurs at a distant time horizon. At the same time, a randomized extension of the Shiryaev-Roberts test proposed by Pollak, enjoys a very strong asymptotic minimax property with respect to Pollak's supremum metric. We conjecture that a deterministically initialized version of the Shiryaev-Roberts test can compete with the latter procedure very efficiently. We propose a numerical scheme for the systematic comparison of these detection procedures in both settings, i.e., minimax and for detecting changes that occur in the distant future. Our goal is accomplished by deriving a set of integral equations for the performance metrics of interest, which are solved numerically. We present numerical results for the problem of detecting a change in the mean of an exponential sequence which justify our conjecture and allow for a precise comparison of a number of changepoint detection procedures.

Proceedings of the 5th …, Jan 1, 2010

In 1985, for detecting a change in distribution Pollak introduced a minimax criterion and a rando... more 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 quasistationary distribution of the Shiryaev-Roberts statistic. Pollak proved that this procedure is asymptotically almost optimal as the mean time to false alarm becomes large. The question whether Pollak's procedure is strictly minimax has been open for more than two decades. We provide a counterexample which shows that Pollak's procedure is not optimal and that there is a strictly minimax procedure which is nothing but the Shiryaev-Roberts procedure that starts with a specially designed deterministic point.

Arxiv preprint arXiv: …, Jan 1, 2009

The CUSUM procedure is known to be optimal for detecting a change in distribution under a minimax... more 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 the two detection schemes in both settings, i.e., minimax and for detecting changes that occur in the distant future. Our goal is accomplished by deriving a set of exact integral equations for the performance metrics, which are then solved numerically. We present detailed numerical results for the problem of detecting a change in the mean of a Gaussian sequence, which show that the difference between the two procedures is significant only when detecting small 1 changes.

Arxiv preprint arXiv: …, Jan 1, 2010

Several variations of the Shiryaev-Roberts detection procedure in the context of the simple chang... more 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 the quasi-stationary distribution. Comparisons of operating characteristics are made. The differences fade as the average run length to false alarm tends to infinity. It is shown that the Shiryaev-Roberts procedures that start either from a specially designed point r or from the random "quasi-stationary" point are third-order asymptotically optimal.

Arxiv preprint arXiv: …, Jan 1, 2009

For the most popular sequential change detection rules such as CUSUM, EWMA, and the Shiryaev-Robe... more 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 its performance for various initialization strategies. Regarding the randomized initialization variant proposed by Pollak, known to be asymptotically optimal of order-3, we offer a means for numerically computing the quasi-stationary distribution of the Shiryaev-Roberts statistic that is the distribution of the initializing random variable, thus making this test applicable in practice. A significant side-product of our computational technique is the observation that deterministic initializations of the Shiryaev-Roberts procedure can also enjoy the same order-3 optimality property as Pollak's randomized test and, after careful selection, even uniformly outperform it.

Information Fusion, 2008 …, Jan 1, 2008

The problem of decentralized changepoint detection in a distributed multisensor setting with bina... more 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 postchange hypotheses when the post-change parameter is unknown. A multichart CUSUM detection procedure with binary quantization, called the M-BQ-CUSUM test, is proposed. The methodology is based on using M 2 putative values of the parameter as "reference" points. The data are optimally quantized at these points and then sent to the fusion center for making a final decision by running M BQ-CUSUM statistics in parallel. The M-BQ-CUSUM procedure is shown to be asymptotically optimal at the reference points and rather efficient elsewhere.

The Annals of Statistics, Jan 1, 2010

In 1985, for detecting a change in distribution Pollak introduced a specific minimax performance ... more 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 third-order asymptotically optimal as the mean time to false alarm becomes large. The question whether Pollak's procedure is strictly minimax for any false alarm rate has been open for more than two decades, and there were several attempts to prove this strict optimality. In this paper, we provide a counterexample which shows that Pollak's procedure is not optimal and that there is a strictly optimal procedure which is nothing but the Shiryaev-Roberts procedure that starts with a specially designed deterministic point.

Abstract We address the sequential change-point detection problem for the Gaussian model where ba... more Abstract We address the sequential change-point detection problem for the Gaussian model where baseline distribution is Gaussian with variance σ2 and mean μ such that σ2= a μ, where a> 0 is a known constant; the change is in μ from one known value to another. First, we carry out a comparative performance analysis of four detection procedures: the Cumulative Sum (CUSUM) procedure, the Shiryaev–Roberts (SR) procedure, and two its modifications—the Shiryaev–Roberts–Pollak and Shiryaev–Roberts–r procedures.

Abstract We consider the problem of efficient on-line anomaly detection in computer network traff... more Abstract 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 scorebased multi-cyclic detection algorithm. The algorithm is based on the so-called ShiryaevRoberts procedure.

Abstract. We study asymptotic properties (as A→∞) of the first exit time from the interval [0, A]... more Abstract. 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 suitably normalized first exit time is exponential E (1) and that the moment generating function converges to that of E (1). The method of proof is based on considering the quasi-stationary distribution and its relation to the normalizing factor.

Methodology and Computing in …, Jan 1, 2011

We provide an overview of the state-of-the-art in the area of sequential changepoint detection as... more We provide an overview of the state-of-the-art in the area of sequential changepoint 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 advances in each. Also, we link together the generalized Bayesian problem with multi-cyclic disorder detection in a stationary regime when the change occurs at a distant time horizon. We conclude with two case studies to illustrate the cutting edge of the field at work.

Proceedings of the …, Jan 1, 2009

We address a simple changepoint detection problem where observations are i.i.d. before and after ... more 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 occurs at a distant time horizon. At the same time, a randomized extension of the Shiryaev-Roberts test proposed by Pollak, enjoys a very strong asymptotic minimax property with respect to Pollak's supremum metric. We conjecture that a deterministically initialized version of the Shiryaev-Roberts test can compete with the latter procedure very efficiently. We propose a numerical scheme for the systematic comparison of these detection procedures in both settings, i.e., minimax and for detecting changes that occur in the distant future. Our goal is accomplished by deriving a set of integral equations for the performance metrics of interest, which are solved numerically. We present numerical results for the problem of detecting a change in the mean of an exponential sequence which justify our conjecture and allow for a precise comparison of a number of changepoint detection procedures.

Proceedings of the 5th …, Jan 1, 2010

In 1985, for detecting a change in distribution Pollak introduced a minimax criterion and a rando... more 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 quasistationary distribution of the Shiryaev-Roberts statistic. Pollak proved that this procedure is asymptotically almost optimal as the mean time to false alarm becomes large. The question whether Pollak's procedure is strictly minimax has been open for more than two decades. We provide a counterexample which shows that Pollak's procedure is not optimal and that there is a strictly minimax procedure which is nothing but the Shiryaev-Roberts procedure that starts with a specially designed deterministic point.

Arxiv preprint arXiv: …, Jan 1, 2009

The CUSUM procedure is known to be optimal for detecting a change in distribution under a minimax... more 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 the two detection schemes in both settings, i.e., minimax and for detecting changes that occur in the distant future. Our goal is accomplished by deriving a set of exact integral equations for the performance metrics, which are then solved numerically. We present detailed numerical results for the problem of detecting a change in the mean of a Gaussian sequence, which show that the difference between the two procedures is significant only when detecting small 1 changes.

Arxiv preprint arXiv: …, Jan 1, 2010

Several variations of the Shiryaev-Roberts detection procedure in the context of the simple chang... more 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 the quasi-stationary distribution. Comparisons of operating characteristics are made. The differences fade as the average run length to false alarm tends to infinity. It is shown that the Shiryaev-Roberts procedures that start either from a specially designed point r or from the random "quasi-stationary" point are third-order asymptotically optimal.

Arxiv preprint arXiv: …, Jan 1, 2009

For the most popular sequential change detection rules such as CUSUM, EWMA, and the Shiryaev-Robe... more 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 its performance for various initialization strategies. Regarding the randomized initialization variant proposed by Pollak, known to be asymptotically optimal of order-3, we offer a means for numerically computing the quasi-stationary distribution of the Shiryaev-Roberts statistic that is the distribution of the initializing random variable, thus making this test applicable in practice. A significant side-product of our computational technique is the observation that deterministic initializations of the Shiryaev-Roberts procedure can also enjoy the same order-3 optimality property as Pollak's randomized test and, after careful selection, even uniformly outperform it.

Information Fusion, 2008 …, Jan 1, 2008

The problem of decentralized changepoint detection in a distributed multisensor setting with bina... more 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 postchange hypotheses when the post-change parameter is unknown. A multichart CUSUM detection procedure with binary quantization, called the M-BQ-CUSUM test, is proposed. The methodology is based on using M 2 putative values of the parameter as "reference" points. The data are optimally quantized at these points and then sent to the fusion center for making a final decision by running M BQ-CUSUM statistics in parallel. The M-BQ-CUSUM procedure is shown to be asymptotically optimal at the reference points and rather efficient elsewhere.

The Annals of Statistics, Jan 1, 2010

In 1985, for detecting a change in distribution Pollak introduced a specific minimax performance ... more 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 third-order asymptotically optimal as the mean time to false alarm becomes large. The question whether Pollak's procedure is strictly minimax for any false alarm rate has been open for more than two decades, and there were several attempts to prove this strict optimality. In this paper, we provide a counterexample which shows that Pollak's procedure is not optimal and that there is a strictly optimal procedure which is nothing but the Shiryaev-Roberts procedure that starts with a specially designed deterministic point.