Bayesian estimation of hidden Markov chains: a stochastic implementation

Robert, Christian P.; Celeux, Gilles; Diebolt, Jean

doi:10.1016/0167-7152(93)90127-5

Cited by 147 publications

(91 citation statements)

References 18 publications

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“…The most likely trace is computed by keeping track, at each time 2 ≤ t ≤ T , of the argument (region ρ) that maximizes (18) and, for t = T , the one that maximizes (20). Then, we can backtrack from time T back to time 1 and reconstruct the trace.…”

Section: (16)mentioning

confidence: 99%

“…Convergence properties of the Gibbs sampling for this problem are studied in [20]. We are interested in the sequence of the P {l} ij values; it is not a Markov chain, but it is ergodic and converges at geometric rate to a stationary distribution, which is the desired Pr(P |T T, T C).…”

Section: B Knowledge Of the Adversarymentioning

confidence: 99%

“…To sample an ET {l} from (8), we follow the simplification proposed in [20] and iteratively construct ET {l} by performing T successive samplings, for t = 1, . .…”

Section: B Knowledge Of the Adversarymentioning

confidence: 99%

“…The objective of the adversary is to construct P u starting with the prior mobility information (traces and T C u ). The construction is done with Gibbs sampling [20] to find the conditional probability distribution of the entries of the MC matrix, given the prior information. Then, one MC matrix is created out of the distribution, for instance by averaging.…”

Section: B Knowledge Of the Adversarymentioning

confidence: 99%

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Quantifying Location Privacy

Shokri

Theodorakopoulos

Boudec

et al. 2011

2011 IEEE Symposium on Security and Privacy

606

607

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Abstract-It is a well-known fact that the progress of personal communication devices leads to serious concerns about privacy in general, and location privacy in particular. As a response to these issues, a number of Location-Privacy Protection Mechanisms (LPPMs) have been proposed during the last decade. However, their assessment and comparison remains problematic because of the absence of a systematic method to quantify them. In particular, the assumptions about the attacker's model tend to be incomplete, with the risk of a possibly wrong estimation of the users' location privacy.In this paper, we address these issues by providing a formal framework for the analysis of LPPMs; it captures, in particular, the prior information that might be available to the attacker, and various attacks that he can perform. The privacy of users and the success of the adversary in his location-inference attacks are two sides of the same coin. We revise location privacy by giving a simple, yet comprehensive, model to formulate all types of location-information disclosure attacks. Thus, by formalizing the adversary's performance, we propose and justify the right metric to quantify location privacy. We clarify the difference between three aspects of the adversary's inference attacks, namely their accuracy, certainty, and correctness. We show that correctness determines the privacy of users. In other words, the expected estimation error of the adversary is the metric of users' location privacy. We rely on well-established statistical methods to formalize and implement the attacks in a tool: the Location-Privacy Meter that measures the location privacy of mobile users, given various LPPMs. In addition to evaluating some example LPPMs, by using our tool, we assess the appropriateness of some popular metrics for location privacy: entropy and k-anonymity. The results show a lack of satisfactory correlation between these two metrics and the success of the adversary in inferring the users' actual locations.

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Section: (16)mentioning

confidence: 99%

Section: B Knowledge Of the Adversarymentioning

confidence: 99%

“…To sample an ET {l} from (8), we follow the simplification proposed in [20] and iteratively construct ET {l} by performing T successive samplings, for t = 1, . .…”

Section: B Knowledge Of the Adversarymentioning

confidence: 99%

Section: B Knowledge Of the Adversarymentioning

confidence: 99%

See 2 more Smart Citations

Quantifying Location Privacy

Shokri

Theodorakopoulos

Boudec

et al. 2011

2011 IEEE Symposium on Security and Privacy

606

607

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show abstract

“…Two alternatives are possible to sample the hidden variables with a Markov chain prior model (equation 9): an exact method based on the Baum & Walsh procedure [6] and an approximate one based on Gibbs sampling procedure [7]. In this work, we adopt the second one being simpler and faster to implement, it is detail hereafter:…”

Section: Monte Carlo Samplingmentioning

confidence: 99%

Bayesian Blind Source Separation of Positive Non Stationary Sources

Ichir¹

2004

AIP Conference Proceedings

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Abstract. In this contribution, we address the problem of blind non negative source separation. This problem finds its application in many fields of data analysis. We propose herein a novel approach based on Gamma mixture probability priors: Gamma densities to constraint the unobserved sources to lie on the positive half plane; a mixture density with a first order Markov model on the associated hidden variables to account for eventual non stationarity on the sources. Posterior mean estimates are obtained via appropriate Monte Carlo Markov Chain sampling.

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Hidden M arkov Models

Churchill¹

2005

Encyclopedia of Biostatistics

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Hidden Markov models are a generalization of the finite mixture model that allow for dependence in a sequence of observations via Markovian dependence of an unobserved (hidden) sequence of states. Inference problems associated with hidden Markov models include parameter estimation and restoration of the hidden state sequence. The recursive algorithms employed to solve these problems are related to the Kalman filter and have spawned a wide variety of applications. Areas of application range from speech recognition and signal processing through analysis of molecular sequence data.

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Bayesian estimation of hidden Markov chains: a stochastic implementation

Cited by 147 publications

References 18 publications

Quantifying Location Privacy

Quantifying Location Privacy

Bayesian Blind Source Separation of Positive Non Stationary Sources

Hidden M arkov Models

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