Sequential change detection based on universal compression algorithms

Jacob, Tony; Bansal, Rakesh Kumar

doi:10.1109/isit.2008.4595159

Cited by 13 publications

(11 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consider the test of versus . If we denote , the sample expectation of the data observed, , can be expressed as (17) where . Here the stopping time defined by sequential universal test is: (18) By defining two sample size parameters , where is the initial sample size, and is the truncation sample size, one can construct a stopping time associated with the threshold parameter : (19) Stop sampling at and reject the null hypothesis if and only if .…”

Section: Numeric Simulationsmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotical Optimality of Sequential Universal Hypothesis Testing Based on the Method of Types

Wang

2014

IEEE Signal Process. Lett.

View full text Add to dashboard Cite

In this letter, we introduce a sequential version of universal hypothesis testing, where the goal of the test is not only to decide between the known null hypothesis and some other unknown alternative hypothesis, but also to use a stopping time to stop the test as soon as rejecting the null hypothesis. Motivated by the method of types in information theory, we establish the sequential test by Hö-effding's universal test associated with a curved stopping boundary. It is proved that this sequential test uniformly asymptotically minimizes average sample size for any other sequential test.Index Terms-Asymptotical optimality, error exponents, generalized likelihood ratio, method of types, sequential hypothesis testing, universal hypothesis testing.

show abstract

Section: Numeric Simulationsmentioning

confidence: 99%

“…Recently, several works investigate the universal source coding framework for sequential analysis [17], [18], which provide an alternative approach to study the asymptotical optimality for the sequential composite hypothesis testing problem. The approximation of the distribution of crossing boundary is established directly on the types.…”

Section: Introductionmentioning

confidence: 99%

Asymptotical Optimality of Sequential Universal Hypothesis Testing Based on the Method of Types

Wang

2014

IEEE Signal Process. Lett.

View full text Add to dashboard Cite

show abstract

“…Also for Gaussian f 0 and f 1 , θ ∈ [a 1 , a 2 ] , S n = n k=1 X k,l ,θ n = max{a 1 , min[S n /n, a 2 ]}. At time N decide upon H 0 or H 1 according asθ N ≤ θ * orθ N ≥ θ * , where θ * is obtained by solving I(θ * , θ 0 ) = I(θ * , θ 1 ), and I(θ, λ) is the Kullback-Leibler information number, which is the K-L Divergence I(f θ , f λ ) in (9). Here, as the threshold g(cn) is a time varying and decreasing function, the quantisation (7) is changed in the following way:…”

Section: E Unknown Parametersmentioning

confidence: 99%

“…[25] studies classification of finite alphabet sources using universal coding. [9] considers universal hypothesis testing problem in sequential framework using universal source coding. It derives asymptotically optimal one sided sequential hypothesis tests and sequential change detection algorithms for finite and countable alphabets.…”

Section: Introductionmentioning

confidence: 99%

Novel algorithms for distributed sequential hypothesis testing

Jithin

Sharma

2011

2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

View full text Add to dashboard Cite

This paper considers sequential hypothesis testing in a decentralized framework. We start with two simple decentralized sequential hypothesis testing algorithms. One of which is later proved to be asymptotically Bayes optimal. We also consider composite versions of decentralized sequential hypothesis testing. A novel nonparametric version for decentralized sequential hypothesis testing using universal source coding theory is developed. Finally we design a simple decentralized multihypothesis sequential detection algorithm.

show abstract

“…Statistical inference with universal source codes, started in [27] where classification of finite alphabet sources is studied in the fixed sample size setup. [17] considers the universal hypothesis testing problem in the sequential framework using universal source coding. It derives asymptotically optimal one sided sequential hypothesis tests and sequential change detection algorithms for countable alphabet.…”

mentioning

confidence: 99%

Nonparametric distributed sequential detection via universal source coding

Sreedharan

Sharma

2013

2013 Information Theory and Applications Workshop (ITA)

View full text Add to dashboard Cite

Abstract-We consider nonparametric or universal sequential hypothesis testing when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution. These algorithms are primarily motivated from spectrum sensing in Cognitive Radios and intruder detection in wireless sensor networks. We use easily implementable universal lossless source codes to propose simple algorithms for such a setup. The algorithms are first proposed for discrete alphabet. Their performance and asymptotic properties are studied theoretically. Later these are extended to continuous alphabets. Their performance with two well known universal source codes, Lempel-Ziv code and KT-estimator with Arithmetic Encoder are compared. These algorithms are also compared with the tests using various other nonparametric estimators. Finally a decentralized version utilizing spatial diversity is also proposed and analysed.

show abstract

Sequential change detection based on universal compression algorithms

Cited by 13 publications

References 13 publications

Asymptotical Optimality of Sequential Universal Hypothesis Testing Based on the Method of Types

Asymptotical Optimality of Sequential Universal Hypothesis Testing Based on the Method of Types

Novel algorithms for distributed sequential hypothesis testing

Nonparametric distributed sequential detection via universal source coding

Contact Info

Product

Resources

About