Adaptive Markov chain Monte Carlo: theory and methods

Atchadé, Yves F.; Fort, Gersende; Moulines, Éric; Priouret, Pierre

doi:10.1017/cbo9780511984679.003

Cited by 57 publications

(66 citation statements)

References 43 publications

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“…Since direct sampling from π is difficult, we use an (adaptive) Metropolis-Hastings approach [22], [16]. That is, starting with the input graph, we use local transformations (i.e.…”

Section: Randomization Techniquementioning

confidence: 99%

Assessing the Significance of Data Mining Results on Graphs with Feature Vectors

Günnemann

Dao

Jamali

et al. 2012

2012 IEEE 12th International Conference on Data Mining

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Assessing the significance of data mining results is an important step in the knowledge discovery process. While results might appear interesting at a first glance, they can often be explained by already known characteristics of the data. Randomization is an established technique for significance testing, and methods to assess data mining results on vector data or network data have been proposed. In many applications, however, both sources are simultaneously given. Since these sources are rarely independent of each other but highly correlated, naively applying existing randomization methods on each source separately is questionable.In this work, we present a method to assess the significance of mining results on graphs with binary features vectors. We propose a novel null model that preserves correlation information between both sources. Our randomization exploits an adaptive Metropolis sampling and interweaves attribute randomization and graph randomization steps. In thorough experiments, we demonstrate the application of our technique. Our results indicate that while simultaneously using both sources is beneficial, often one source of information is dominant for determining the mining results.

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“…Since direct sampling from π is difficult, we use an (adaptive) Metropolis-Hastings approach [22], [16]. That is, starting with the input graph, we use local transformations (i.e.…”

Section: Randomization Techniquementioning

confidence: 99%

Assessing the Significance of Data Mining Results on Graphs with Feature Vectors

Günnemann

Dao

Jamali

et al. 2012

2012 IEEE 12th International Conference on Data Mining

View full text Add to dashboard Cite

show abstract

“…All the technical tools needed can be found in greater generality in Andrieu et al (2005) and Atchade et al (2009). We need two types of conditions.…”

Section: Convergencementioning

confidence: 99%

“…This type of conditions have been considered by many authors in the analysis of adaptive MCMC algorithms (see Atchade et al (2009) …”

Section: Convergencementioning

confidence: 99%

“…But this is not specific to the present algorithm: checking which MCMC kernels are geometrically ergodic and which are not is a well known difficult problem. Again we refer the reader to (Atchade et al (2009) for some pointers to the literature). We should mention that geometric ergodicity (that is A2(ii)) is not really essential to the convergence of Algorithm 2.2.…”

Section: And the References Therein) The Lipschitz Condition (A2(iii))mentioning

confidence: 99%

“…The proposed algorithm is based on stochastic approximation algorithms and builds on recent developments in adaptive Markov Chain Monte Carlo methodology (see e.g. Andrieu and Thoms (2008); Atchade et al (2009) and the references therein).…”

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confidence: 99%

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A computational framework for empirical Bayes inference

Atchadé

2010

Stat Comput

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In empirical Bayes inference one is typically interested in sampling from the posterior distribution of a parameter with a hyper-parameter set to its maximum likelihood estimate. This is often problematic particularly when the likelihood function of the hyper-parameter is not available in closed form and the posterior distribution is intractable.Previous works have dealt with this problem using a multi-step approach based on the EM algorithm and Markov Chain Monte Carlo (MCMC). We propose a framework based on recent developments in adaptive MCMC, where this problem is addressed more efficiently using a single Monte Carlo run. We discuss the convergence of the algorithm and its connection with the EM algorithm. We apply our algorithm to the Bayesian Lasso of Park and Casella (2008) and on the empirical Bayes variable selection of George and Foster (2000).

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References

2012

Computational Statistics

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Adaptive Markov chain Monte Carlo: theory and methods

Cited by 57 publications

References 43 publications

Assessing the Significance of Data Mining Results on Graphs with Feature Vectors

Assessing the Significance of Data Mining Results on Graphs with Feature Vectors

A computational framework for empirical Bayes inference

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