Decoding fingerprints using the Markov Chain Monte Carlo method

Furon, Teddy; Guyader, Arnaud; Cérou, Frédéric

doi:10.1109/wifs.2012.6412647

Cited by 12 publications

(6 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Section 3 we present results from simulations suggesting that our approach for solving the SSS problems, besides theoretically optimally in terms of recovery, is efficient and furthermore is able to outperform the other known popular algorithms for approximate inference of the set of defective items (including DD, COMP among others) when n ≥ (1 + )k log 2 ( p k ) for any > 0. As a final remark, our results are in agreement with earlier experimental findings on Markov Chain Monte Carlo algorithms for noisy group testing settings in applied contexts, such as computational biology [35,49] and security [26], but we note that our work is the first one to provide a concrete theoretical explanation for their strong performance in simulations, and a principled way to exploit local algorithms for implementing the SSS estimator.…”

supporting

confidence: 91%

Group testing and local search: is there a computational-statistical gap?

Iliopoulos,

Zadik

2020

Preprint

View full text Add to dashboard Cite

Group testing is a fundamental problem in statistical inference with many real-world applications, including the need for massive group testing during the ongoing COVID-19 pandemic. The goal is to detect a set of k defective items out of a population of size p using n p tests. Towards that end, one is allowed to utilize a procedure that can test groups of items, in which each test is returned positive if and only if at least one item in the group is defective. In this paper we study the task of approximate recovery, in which we tolerate having a small number of incorrectly classified items.One of the most well-known, optimal, and easy to implement testing procedures is the non-adaptive Bernoulli group testing problem, where all tests are conducted in parallel, and each item is chosen to be part of any certain test independently with some fixed probability. In this setting, there is an observed gap between the number of tests above which recovery is information theoretically possible, and the number of tests required by the currently best known efficient algorithms to succeed. Often times such gaps are explained by a phase transition in the landscape of the solution space of the problem (an Overlap Gap Property (OGP) phase transition). In this paper we seek to understand whether such a phenomenon takes place for Bernoulli group testing as well. Our main contributions are the following:

show abstract

supporting

confidence: 91%

Group testing and local search: is there a computational-statistical gap?

Iliopoulos,

Zadik

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…A distinct but related approach to belief propagation is based on generating samples from P(K | y) via Markov Chain Monte Carlo (MCMC). To our knowledge, the MCMC approach to group testing was initiated by Knill et al [123]; see also [169] and [84] for related follow-up works. Each of these papers uses the notion of Gibbs sampling: A randomly-initialized set K 0 ⊆ {1, .…”

Section: Related Monte Carlo Decoding Algorithmsmentioning

confidence: 99%

Group Testing: An Information Theory Perspective

Aldridge¹,

Johnson²,

Scarlett³

2019

View full text Add to dashboard Cite

The group testing problem concerns discovering a small number of defective items within a large population by performing tests on pools of items. A test is positive if the pool contains at least one defective, and negative if it contains no defectives. This is a sparse inference problem with a combinatorial flavour, with applications in medical testing, biology, telecommunications, information technology, data science, and more.In this monograph, we survey recent developments in the group testing problem from an information-theoretic perspective. We cover several related developments: efficient algorithms with practical storage and computation requirements, achievability bounds for optimal decoding methods, and algorithmindependent converse bounds. We assess the theoretical guarantees not only in terms of scaling laws, but also in terms of the constant factors, leading to the notion of the rate of group testing, indicating the amount of information learned per test. Considering both noiseless and noisy settings, we identify several regimes where existing algorithms are provably optimal or near-optimal, as well as regimes where there remains greater potential for improvement.In addition, we survey results concerning a number of variations on the standard group testing problem, including partial recovery criteria, adaptive algorithms with a limited number of stages, constrained test designs, and sublineartime algorithms.S 0 , S 1 partition of the defective set (Equation (4.4)) ı information density (Equation (4.6)) X 0,τ , X 1,τ sub-matrices of X corresponding to (S 0 , S 1 ) with |S 0 | = τ (Equation (4.14))τ ) (Equation (4.16)) 2. If the preceding test is negative, A contains no defective items, and we halt. If the test is positive, continue. 3. If A consists of a single item, then that item is defective, and we halt. Otherwise, pick half of the items in A, and call this set B. Perform a single test of the pool B. 4. If the test is positive, set A := B. If the test is negative, set A := A \ B. Return to Step 3. A BRIEF REVIEW OF ZERO-ERROR GROUP TESTINGObserve that S(i) is the set of tests containing item i, while S(K) is the set of positive tests when the defective set is K.Definition 1.10. A matrix X is called k-separable if the support unions S(L) are distinct over all subsets L ⊆ {1, 2, . . . , n} of size |L| = k.A matrix X is calledk-separable if the support unions S(L) are distinct over all subsets L ⊆ {1, 2, . . . , n} of size |L| ≤ k.Clearly, using a k-separable matrix as a test design ensures that group testing will provide different outcomes for each possible defective set of size k; thus,

show abstract

“…This score is computed by taking into account L symbols but the complexity of a joint decoder is proportional to |P| (i.e., O(N c )), which is computationally expensive. Yet, there exists at least three possible approaches that approximate joint decoding with a reasonable complexity: 1) Monte Carlo Markov Chain (MCMC) [19,20], 2) Belief Propagation Decoder [21] and 3) Joint Iterative Decoder [22].…”

Section: Joint Decodermentioning

confidence: 99%

Challenging Differential Privacy:The Case of Non-interactive Mechanisms

Balu

Furon

Gambs

2014

Computer Security - ESORICS 2014

Self Cite

View full text Add to dashboard Cite

To cite this version:Raghavendran Balu, Teddy Furon, Sébastien Gambs. Abstract. In this paper, we consider personalized recommendation systems in which before publication, the profile of a user is sanitized by a non-interactive mechanism compliant with the concept of differential privacy. We consider two existing schemes offering a differentially private representation of profiles: BLIP (BLoom-and-flIP) and JLT (JohnsonLindenstrauss Transform). For assessing their security levels, we play the role of an adversary aiming at reconstructing a user profile. We compare two inference attacks, namely single and joint decoding. The first one decides of the presence of a single item in the profile, and sequentially explores all the item set. The latter strategy decides whether a subset of items is likely to be the user profile, and considers all the possible subsets. Our contributions are a theoretical analysis as well as a practical implementation of both attacks, which were evaluated on datasets of real user profiles. The results obtained clearly demonstrates that joint decoding is the most powerful attack, while also giving useful insights on how to set the differential privacy parameter ǫ.

show abstract

Decoding fingerprints using the Markov Chain Monte Carlo method

Cited by 12 publications

References 9 publications

Group testing and local search: is there a computational-statistical gap?

Group testing and local search: is there a computational-statistical gap?

Group Testing: An Information Theory Perspective

Challenging Differential Privacy:The Case of Non-interactive Mechanisms

Contact Info

Product

Resources

About