arXiv subjects

Georgios Fellouris

Publications and source records attributed to Georgios Fellouris.

29 records · Page 2Linked to original sources

arXiv2016

Multichannel Sequential Detection- Part I: Non-i.i.d. Data

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 r-completely to positive and finite numbers, we establish the asymptotic optimality of a generalized sequential likelihood ratio test and a mixture-based sequential likelihood ratio test. Specifically, we show that both tests minimize the first r moments of the stopping time distribution asymptotically as the probabilities of false alarm and missed detection approach zero. Moreover, we show that both tests asymptotically minimize all moments of the stopping time distribution when the local log-likelihood ratio processes have independent increments and simply obey the Strong Law of Large Numbers. This extends a result previously known in the case of i.i.d. observations when only one channel is affected. We illustrate the general detection theory using several practical examples, including the detection of signals in Gaussian hidden Markov models, white Gaussian noises with unknown intensity, and testing of the first-order autoregression's correlation coefficient. Finally, we illustrate the feasibility of both sequential tests when assuming an upper and a lower bound on the number of signals and compare their non-asymptotic performance using a simulation study.

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arXiv2016

Second-Order Asymptotic Optimality in Multisensor Sequential Change Detection

A generalized multisensor sequential change detection problem is considered, in which a number of (possibly correlated) sensors monitor an environment in real time, the joint distribution of their observations is determined by a global parameter vector, and at some unknown time there is a change in an unknown subset of components of this parameter vector. In this setup, we consider the problem of detecting the time of the change as soon as possible, while controlling the rate of false alarms. We establish the second-order asymptotic optimality (with respect to Lorden's criterion) of various generalizations of the CUSUM rule; that is, we show that their additional expected worst-case detection delay (relative to the one that could be achieved if the affected subset was known) remains bounded as the rate of false alarm goes to 0, for any possible subset of affected components. This general framework incorporates the traditional multisensor setup in which only an unknown subset of sensors is affected by the change. The latter problem has a special structure which we exploit in order to obtain feasible representations of the proposed schemes. We present the results of a simulation study where we compare the proposed schemes with scalable detection rules that are only first-order asymptotically optimal. Finally, in the special case that the change affects exactly one sensor, we consider the scheme that runs in parallel the local CUSUM rules and study the problem of specifying the local thresholds.

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arXiv2015

Sequential Design for Computerized Adaptive Testing that Allows for Response Revision

In computerized adaptive testing (CAT), items (questions) are selected in real time based on the already observed responses, so that the ability of the examinee can be estimated as accurately as possible. This is typically formulated as a non-linear, sequential, experimental design problem with binary observations that correspond to the true or false responses. However, most items in practice are multiple-choice and dichotomous models do not make full use of the available data. Moreover, CAT has been heavily criticized for not allowing test-takers to review and revise their answers. In this work, we propose a novel CAT design that is based on the polytomous nominal response model and in which test-takers are allowed to revise their responses at any time during the test. We show that as the number of administered items goes to infinity, the proposed estimator is (i) strongly consistent for any item selection and revision strategy and (ii) asymptotically normal when the items are selected to maximize the Fisher information at the current ability estimate and the number of revisions is smaller than the number of items. We also present the findings of a simulation study that supports our asymptotic results.

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arXiv2013

Bandwidth and Energy Efficient Decentralized Sequential Change Detection

The problem of decentralized sequential change detection is considered, where an abrupt change occurs in an area monitored by a number of sensors; the sensors transmit their data to a fusion center, subject to bandwidth and energy constraints, and the fusion center is responsible for detecting the change as soon as possible. A novel sequential detection rule is proposed that requires communication from the sensors at random times and transmission of only low-bit messages, on which the fusion center runs in parallel a CUSUM test. The second-order asymptotic optimality of the proposed scheme is established both in discrete and in continuous time. Specifically, it is shown that the inflicted performance loss (with respect to the optimal detection rule that uses the complete sensor observations) is asymptotically bounded as the rate of false alarms goes to 0, for any fixed rate of communication. When the rate of communication from the sensors is asymptotically low, the proposed scheme remains first-order asymptotically optimal. Finally, simulation experiments illustrate its efficiency and its superiority over a decentralized detection rule that relies on communication at deterministic times.

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arXiv2013

Low-rate renewal theory and estimation

Certain renewal theorems are extended to the case that the rate of the renewal process goes to 0 and, more generally, to the case that the drift of the random walk goes to infinity. These extensions are motivated by and applied to the problem of decentralized parameter estimation under severe communication constraints.

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arXiv2013

Unstructured sequential testing in sensor networks

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 novel class of scalable sequential tests which, for any subset of affected sensors, minimize the expected sample size for a decision asymptotically, that is as the error probabilities go to 0. Moreover, we propose sequential tests that require minimal transmission activity from the sensors to the fusion center, while preserving this asymptotic optimality property.

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arXiv2013

Asymptotically optimal parameter estimation under communication constraints

A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear with respect to a common parameter. A novel estimating scheme is suggested, according to which each sensor transmits only one-bit messages at stopping times of its local filtration. The proposed estimator is shown to be consistent and, for a large class of processes, asymptotically optimal, in the sense that its asymptotic distribution is the same as the exact distribution of the optimal estimator that has full access to the sensor observations. These properties are established under an asymptotically low rate of communication between the sensors and the statistician. Thus, despite being asymptotically efficient, the proposed estimator requires minimal transmission activity, which is a desirable property in many applications. Finally, the case of discrete sampling at the sensors is studied when their underlying processes are independent Brownian motions.

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arXiv2013

Almost optimal sequential tests of discrete composite hypotheses

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 tests have several asymptotic optimality properties as error probabilities go to zero. First, for any weights, they minimize the expected sample size within a constant term under every scenario in the alternative hypothesis and at least to first order under the null hypothesis. Second, for appropriate weights that are specified up to a prior distribution, they minimize within an asymptotically negligible term a weighted expected sample size in the alternative hypothesis. Third, for a particular prior distribution, they are almost minimax with respect to the expected Kullback-Leibler divergence until stopping. Furthermore, based on high-order asymptotic expansions for the operating characteristics, we propose prior distributions that lead to a robust behavior. Finally, based on asymptotic analysis as well as on simulation experiments, we argue that both tests have the same performance when they are designed with the same weights.

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arXiv2012

Optimal sequential change-detection for fractional diffusion-type processes

We consider the problem of detecting an abrupt change in the distribution of a sequentially observed stochastic process. We establish the optimality of the CUSUM test with respect to a modified version of Lorden's criterion for arbitrary processes with continuous paths and apply this general result to the special case of fractional diffusion-type processes. As a by-product, we show that the CUSUM test optimizes Lorden's original criterion when a fractional Brownian motion with Hurst index H adopts a polynomial drift term with exponent H + 1/2 after the change.

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arXiv2012

Nearly Minimax One-Sided Mixture-Based Sequential Tests

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 that is nearly minimax in the sense of minimizing the maximal Kullback-Leibler information. The proof of this result is based on finding an almost Bayes rule for an appropriate sequential decision problem and on high-order asymptotic approximations for the performance characteristics of arbitrary mixture-based stopping times. We also evaluate the asymptotic performance loss of certain intuitive mixture rules and verify the accuracy of our asymptotic approximations with simulation experiments.

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arXiv2009

Decentralized Sequential Hypothesis Testing using Asynchronous Communication

We present a test for the problem of decentralized sequential hypothesis testing, which is asymptotically optimum. By selecting a suitable sampling mechanism at each sensor, communication between sensors and fusion center is asynchronous and limited to 1-bit data. The proposed SPRT-like test turns out to be order-2 asymptotically optimum in the case of continuous time and continuous path signals, while in discrete time this strong asymptotic optimality property is preserved under proper conditions. If these conditions do not hold, then we can show optimality of order-1. Simulations corroborate the excellent performance characteristics of the test of interest.

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