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41
An Optimal Algorithm for Monte Carlo Estimation
, 1995
"... A typical approach to estimate an unknown quantity is to design an experiment that produces a random variable Z distributed in [0; 1] with E[Z] = , run this experiment independently a number of times and use the average of the outcomes as the estimate. In this paper, we consider the case when no a ..."
Abstract

Cited by 53 (4 self)
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A typical approach to estimate an unknown quantity is to design an experiment that produces a random variable Z distributed in [0; 1] with E[Z] = , run this experiment independently a number of times and use the average of the outcomes as the estimate. In this paper, we consider the case when no a priori information about Z is known except that is distributed in [0; 1]. We describe an approximation algorithm AA which, given ffl and ffi, when running independent experiments with respect to any Z, produces an estimate that is within a factor 1 + ffl of with probability at least 1 \Gamma ffi. We prove that the expected number of experiments run by AA (which depends on Z) is optimal to within a constant factor for every Z. An announcement of these results appears in P. Dagum, D. Karp, M. Luby, S. Ross, "An optimal algorithm for MonteCarlo Estimation (extended abstract)", Proceedings of the Thirtysixth IEEE Symposium on Foundations of Computer Science, 1995, pp. 142149 [3]. Section ...
Heavy Traffic Limits for Queues with Many Deterministic Servers
"... Consider a sequence of stationary GI/D/N queues indexed by N with servers' utilization 1 #/ # N , # > 0. For such queues we show that the scaled waiting times NWN converge to the (finite) supremum of a Gaussian random walk with drift #. ..."
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Cited by 24 (3 self)
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Consider a sequence of stationary GI/D/N queues indexed by N with servers' utilization 1 #/ # N , # > 0. For such queues we show that the scaled waiting times NWN converge to the (finite) supremum of a Gaussian random walk with drift #.
Asymptotically efficient adaptive allocation rules for the multiarmed bandit problem with switching cost
 IEEE Trans. Automat. Control
, 1988
"... AbstractWe consider multiarmed bandit problems with switching cost, define uniformly good allocation rules, and restrict attention to such rules. We present a lower bound on the asymptotic performance of uniformly good allocation rules and construct an allocation scheme that achieves the bound. We ..."
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Cited by 21 (6 self)
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AbstractWe consider multiarmed bandit problems with switching cost, define uniformly good allocation rules, and restrict attention to such rules. We present a lower bound on the asymptotic performance of uniformly good allocation rules and construct an allocation scheme that achieves the bound. We discover that despite the inclusion of a switching cost the proposed allocation scheme achieves the same asymptotic performance as the optimal rule for the bandit problem without switching cost. This is made possible by grouping together the samples in a certain fashion. Finally, we illustrate an optimal allocation scheme for a large class of distributions which includes members of the exponential family. I.
Asymptotic Operating Characteristics of an Optimal Change Point Detection in Hidden Markov Models
 The Annals of Statistics
"... Let ξ0,ξ1,...,ξω−1 be observations from the hidden Markov model with probability distribution P θ0, and let ξω,ξω+1,... be observations from the hidden Markov model with probability distribution P θ1. The parameters θ0 and θ1 are given, while the change point ω is unknown. The problem is to raise an ..."
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Cited by 10 (1 self)
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Let ξ0,ξ1,...,ξω−1 be observations from the hidden Markov model with probability distribution P θ0, and let ξω,ξω+1,... be observations from the hidden Markov model with probability distribution P θ1. The parameters θ0 and θ1 are given, while the change point ω is unknown. The problem is to raise an alarm as soon as possible after the distribution changes from P θ0 to P θ1, but to avoid false alarms. Specifically, we seek a stopping rule N which allows us to observe the ξ ′ s sequentially, such that E∞N is large, and subject to this constraint, sup k Ek(N − kN ≥ k) is as small as possible. Here Ek denotes expectation under the change point k, and E ∞ denotes expectation under the hypothesis of no change whatever. In this paper we investigate the performance of the Shiryayev– Roberts–Pollak (SRP) rule for change point detection in the dynamic system of hidden Markov models. By making use of Markov chain representation for the likelihood function, the structure of asymptotically minimax policy and of the Bayes rule, and sequential hypothesis testing theory for Markov random walks, we show that the SRP procedure is asymptotically minimax in the sense of Pollak [Ann. Statist. 13 (1985) 206–227]. Next, we present a secondorder asymptotic approximation for the expected stopping time of such a stopping scheme when ω = 1. Motivated by the sequential analysis in hidden Markov models, a nonlinear renewal theory for Markov random walks is also given.
Detection Algorithms And Track Before Detect Architecture Based On Nonlinear Filtering For Infrared Search And Track Systems
, 1998
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Sequential Classification in Point Clouds of Urban Scenes
"... Laser range scanners have now the ability to acquire millions of 3D points of highly detailed and geometrically complex urban sites, opening new avenues of exploration in modeling urban environments. In the traditional modeling pipeline, range scans are processed offline after acquisition. The slow ..."
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Cited by 9 (2 self)
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Laser range scanners have now the ability to acquire millions of 3D points of highly detailed and geometrically complex urban sites, opening new avenues of exploration in modeling urban environments. In the traditional modeling pipeline, range scans are processed offline after acquisition. The slow sequential acquisition though is a bottleneck. The goal of our work is to alleviate this bottleneck, by exploiting the sequential nature of the data acquisition process. We have developed novel online algorithms, never before used in laser range scanning, that perform data classification onthefly as data is being acquired. These algorithms are extremely efficient, and can be potentially integrated with the scanner’s hardware, rendering a sensor that not only acquires but also intelligently processes and classifies the scene points. This sensor, armed with the proposed algorithms, can classify 3D points in realtime as being in vegetation vs. nonvegetation regions, or in horizontal vs. vertical regions. The former classification is possible by the implementation of sequential algorithms through a hidden Markov model (HMM) formulation, and the latter through the use of a combination of cleverly designed sequential detection algorithms. We envision an arsenal of algorithms of this type to be developed in the future. 1.
Calculation Of The Gi/g/1 WaitingTime Distribution And Its Cumulants From Pollaczek's Formulas
"... The steadystate waiting time in a stable GI/G/1 queue is equivalent to the maximum of a general random walk with negative drift. Thus, the distribution of the steadystate waiting time in the GI/G/1 queue is characterized by Spitzer's (1956) formula. However, earlier, Pollaczek (1952) derived an eq ..."
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Cited by 9 (5 self)
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The steadystate waiting time in a stable GI/G/1 queue is equivalent to the maximum of a general random walk with negative drift. Thus, the distribution of the steadystate waiting time in the GI/G/1 queue is characterized by Spitzer's (1956) formula. However, earlier, Pollaczek (1952) derived an equivalent contourintegral expression for the Laplace transform of the GI/G/1 steadystate waiting time. Since Spitzer's formula is easier to understand probabilistically, it is better known today, but it is not so easy to apply directly except in special cases. In contrast, we show that it is easy to compute the GI/G/1 waitingtime distribution and its cumulants (and thus its moments) from Pollaczek's formulas. For the waitingtime tail probabilities, we use numerical transform inversion, numerically integrating the Pollaczek contour integral to obtain the transform values. For the cumulants and the probability of having to wait, we directly integrate the Pollazcek contour integrals numerically. The resulting algorithm is evidently the first for a GI/G/1 queue in which neither the transform of the interarrivaltime distribution nor the transform of the servicetime transform distribution need be rational. The algorithm can even be applied to longtail distributions, i.e., distributions with some infinite moments. To treat these distributions, we approximate them by suitable exponentiallydamped versions of these distributions. Overall, the algorithm is remarkably simple compared to alternative algorithms requiring more structure.
Threshold learning from samples drawn from the null hypothesis for the GLR CUSUM test
 In Proc. IEEE MLSP
, 2005
"... Although optimality of sequential tests for the detection of a change in the parameter of a model has been widely discussed, the test parameter tuning is still an issue. In this communication, we propose a learning strategy to set the threshold of the GLR CUSUM statistics to take a decision with a d ..."
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Cited by 7 (4 self)
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Although optimality of sequential tests for the detection of a change in the parameter of a model has been widely discussed, the test parameter tuning is still an issue. In this communication, we propose a learning strategy to set the threshold of the GLR CUSUM statistics to take a decision with a desired false alarm probability. Only data before the change point are required to perform the learning process. Extensive simulations are performed to assess the validity of the proposed method. The paper is concluded by opening the path to a new approach to multimodal feature based event detection for video parsing. 1.
Mining distribution change in stock order streams
 In Prof. of ICDE
, 2010
"... Abstract — Detecting changes in stock prices is a well known problem in finance with important implications for monitoring and business intelligence. Forewarning of changes in stock price, can be made by the early detection of changes in the distributions of stock order numbers. In this paper, we ad ..."
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Cited by 7 (6 self)
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Abstract — Detecting changes in stock prices is a well known problem in finance with important implications for monitoring and business intelligence. Forewarning of changes in stock price, can be made by the early detection of changes in the distributions of stock order numbers. In this paper, we address the change detection problem for streams of stock order numbers and propose a novel incremental detection algorithm. Our algorithm gains high accuracy and low delay by employing a natural Poisson distribution assumption about the nature of stock order streams. We establish that our algorithm is highly scalable and has linear complexity. We also experimentally demonstrate its effectiveness for detecting change points, via experiments using both synthetic and realworld datasets. I.
On the universality of Burnashev’s error exponent
 the IEEE Trans. on Info. Th
"... Abstract — We consider communication over a time invariant discrete memoryless channel with noiseless and instantaneous feedback. We assume that the communicating parties are not aware of the underlying channel, however they know that it belongs to some specific family of discrete memoryless channel ..."
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Cited by 7 (0 self)
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Abstract — We consider communication over a time invariant discrete memoryless channel with noiseless and instantaneous feedback. We assume that the communicating parties are not aware of the underlying channel, however they know that it belongs to some specific family of discrete memoryless channels. Recent results [4] show that for certain families (e.g., binary symmetric channels and Z channels) there exists coding schemes that universally achieve any rate below capacity while attaining Burnashev’s error exponent. We show that this is not the case in general by deriving an upper bound to the universally achievable error exponent. I.