Results 1 
9 of
9
Nearoptimal detection of geometric objects by fast multiscale methods
 IEEE Trans. Inform. Theory
, 2005
"... Abstract—We construct detectors for “geometric ” objects in noisy data. Examples include a detector for presence of a line segment of unknown length, position, and orientation in twodimensional image data with additive white Gaussian noise. We focus on the following two issues. i) The optimal detec ..."
Abstract

Cited by 24 (8 self)
 Add to MetaCart
Abstract—We construct detectors for “geometric ” objects in noisy data. Examples include a detector for presence of a line segment of unknown length, position, and orientation in twodimensional image data with additive white Gaussian noise. We focus on the following two issues. i) The optimal detection threshold—i.e., the signal strength below which no method of detection can be successful for large dataset size. ii) The optimal computational complexity of a nearoptimal detector, i.e., the complexity required to detect signals slightly exceeding the detection threshold. We describe a general approach to such problems which covers several classes of geometrically defined signals; for example, with onedimensional data, signals having elevated mean on an interval, and, indimensional data, signals with elevated mean on a rectangle, a ball, or an ellipsoid. In all these problems, we show that a naive or straightforward approach leads to detector thresholds and algorithms which are asymptotically far away from optimal. At the same time, a multiscale geometric analysis of these classes of objects allows us to derive asymptotically optimal detection thresholds and fast algorithms for nearoptimal detectors. Index Terms—Beamlets, detecting hot spots, detecting line segments, Hough transform, image processing, maxima of Gaussian processes, multiscale geometric analysis, Radon transform. I.
NONANTICIPATING ESTIMATION APPLIED TO SEQUENTIAL ANALYSIS AND CHANGEPOINT DETECTION
, 2005
"... Suppose a process yields independent observations whose distributions belong to a family parameterized by θ ∈ Θ. When the process is in control, the observations are i.i.d. with a known parameter value θ0. When the process is out of control, the parameter changes. We apply an idea of Robbins and Sie ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Suppose a process yields independent observations whose distributions belong to a family parameterized by θ ∈ Θ. When the process is in control, the observations are i.i.d. with a known parameter value θ0. When the process is out of control, the parameter changes. We apply an idea of Robbins and Siegmund [Proc. Sixth Berkeley Symp. Math. Statist. Probab. 4 (1972) 37–41] to construct a class of sequential tests and detection schemes whereby the unknown postchange parameters are estimated. This approach is especially useful in situations where the parametric space is intricate and mixturetype rules are operationally or conceptually difficult to formulate. We exemplify our approach by applying it to the problem of detecting a change in the shape parameter of a Gamma distribution, in both a univariate and a multivariate setting.
Sequential changepoint detection when unknown parameters are present in the prechange distribution
 Ann. Statist
"... In the sequential changepoint detection literature, most research specifies a required frequency of false alarms at a given prechange distribution fθ and tries to minimize the detection delay for every possible postchange distribution gλ. In this paper, motivated by a number of practical examples ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
In the sequential changepoint detection literature, most research specifies a required frequency of false alarms at a given prechange distribution fθ and tries to minimize the detection delay for every possible postchange distribution gλ. In this paper, motivated by a number of practical examples, we first consider the reverse question by specifying a required detection delay at a given postchange distribution and trying to minimize the frequency of false alarms for every possible prechange distribution fθ. We present asymptotically optimal procedures for oneparameter exponential families. Next, we develop a general theory for changepoint problems when both the prechange distribution fθ and the postchange distribution gλ involve unknown parameters. We also apply our approach to the special case of detecting shifts in the mean of independent normal observations. 1. Introduction. Suppose
Nonparametric Control Chart for Monitoring Profiles Using Change Point Formulation and Adaptive Smoothing
"... Abstract: In many applications, quality of a process is best characterized by a functional relationship between a response variable and one or more explanatory variables. Profile monitoring is used for checking the stability of this relationship over time. Control charts based on nonparametric regre ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract: In many applications, quality of a process is best characterized by a functional relationship between a response variable and one or more explanatory variables. Profile monitoring is used for checking the stability of this relationship over time. Control charts based on nonparametric regression are particularly useful when the incontrol (IC) or outofcontrol (OC) relationship is too complicated to be specified parametrically. This paper proposes a novel nonparametric control chart, using a sequential changepoint formulation with generalized likelihood ratio tests. Its control limits are determined by a bootstrap procedure. This chart can be implemented without any knowledge about the error distributions, as long as a few IC profiles are available beforehand. Moreover, benefiting from certain good properties of the dynamic changepoint approach and of the proposed charting statistic, the proposed control chart not only offers a balanced protection against shifts of different magnitudes, but also adapts to the smoothness of the difference between IC and OC regression functions. Consequently, it has a nearly optimal performance for various OC conditions.
Cooperative Robust Sequential Detection Algorithms for Spectrum Sensing in Cognitive Radio
"... a distributed algorithm for change detection and used it for cooperative spectrum sensing. The algorithm is based on sequential change detection techniques which optimally use the past observations. But DualCUSUM requires the knowledge of the channel gains for each of the secondary users. In this wo ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
a distributed algorithm for change detection and used it for cooperative spectrum sensing. The algorithm is based on sequential change detection techniques which optimally use the past observations. But DualCUSUM requires the knowledge of the channel gains for each of the secondary users. In this work we modify DualCUSUM to develop GLRCUSUM which can work with imprecise estimates of the channel gains. Next we extend the algorithm to the case where the receiver noise power is also not known exactly. We show that the SNR wall problem encountered in this scenario is not experienced by our algorithm. We also analyze these algorithms theoretically.
THE LIMIT DISTRIBUTION OF THE MAXIMUM INCREMENT OF A RANDOM WALK WITH REGULARLY VARYING JUMP SIZE DISTRIBUTION
, 2009
"... In this paper we deal with the asymptotic distribution of the maximum increment of a random walk with a regularly varying jump size distribution. This problem is motivated by a longstanding problem on change point detection for epidemic alternatives. It turns out that the limit distribution of the ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
In this paper we deal with the asymptotic distribution of the maximum increment of a random walk with a regularly varying jump size distribution. This problem is motivated by a longstanding problem on change point detection for epidemic alternatives. It turns out that the limit distribution of the maximum increment of the random walk is one of the classical extreme value distributions, the Fréchet distribution. We prove the results in the general framework of point processes and for jump sizes taking values in a separable Banach space.
eqr275 CHANGEPOINT METHODS
"... Changepoint methodologies applied to statistical process control are predicated on the possibility that a special cause induces a shift from an incontrol statistical model to an outofcontrol statistical model, and so are particularly attractive for persistent special causes. Along with indication ..."
Abstract
 Add to MetaCart
Changepoint methodologies applied to statistical process control are predicated on the possibility that a special cause induces a shift from an incontrol statistical model to an outofcontrol statistical model, and so are particularly attractive for persistent special causes. Along with indications of a loss of control, they provide estimates of when the shift occurred, and (if needed) of the before and aftershift process parameters. A less obvious advantage is that some changepoint proposals allow for the nearuniversal situation that the incontrol distribution of process readings is not known exactly. This feature largely removes the need for extensive Phase I calibration studies, and allows Phase II production use to start early. In addition to the standalone use of changepoint methodologies for both signalling and diagnosing the effects of special causes, they have been proposed as tools for following up signals given by other charting methods, when their likelihood properties lead to good estimators of the time of occurrence and effect of the special cause. Keywords: Changepoint, LRT, GLR, Phase I, Phase II, SPC. 1 1
Sequential Detection based Cooperative Spectrum Sensing Algorithms in Cognitive Radio
"... Abstract — This paper considers the problem of Spectrum Sensing in Cognitive Radio Networks. For this we use a recently developed distributed cooperative algorithm DualCUSUM. The algorithm is based on sequential change detection techniques which optimally use the past observations. But DualCUSUM req ..."
Abstract
 Add to MetaCart
Abstract — This paper considers the problem of Spectrum Sensing in Cognitive Radio Networks. For this we use a recently developed distributed cooperative algorithm DualCUSUM. The algorithm is based on sequential change detection techniques which optimally use the past observations. But DualCUSUM requires the knowledge of the channel gains for each of the secondary users. In this work we modify DualCUSUM to develop GLRCUSUM which can work with imprecise estimates of the channel gains. Next we extend the algorithm to the case where the receiver noise power is also not known exactly. We show that the SNR wall problem encountered in this scenario is not experienced by our algorithm.
An InformationGeometric Approach to RealTime Audio Segmentation
, 2013
"... Abstract—We present a generic approach to realtime audio segmentation in the framework of information geometry for exponential families. The proposed system detects changes by monitoring the information rate of the signals as they arrive in time. We also address shortcomings of traditional cumulati ..."
Abstract
 Add to MetaCart
Abstract—We present a generic approach to realtime audio segmentation in the framework of information geometry for exponential families. The proposed system detects changes by monitoring the information rate of the signals as they arrive in time. We also address shortcomings of traditional cumulative sum approaches to change detection, which assume known parameters before change. This is done by considering exact generalized likelihood ratio test statistics, with a complete estimation of the unknown parameters in the respective hypotheses. We derive an efficient sequential scheme to compute these statistics through convex duality. We finally provide results for speech segmentation in speakers, and polyphonic music segmentation in note slices. Index Terms—Audio segmentation, realtime system, information geometry, change detection.