Sampling Methods for Wallenius' and Fisher's Noncentral Hypergeometric Distributions

Fog, Agner

doi:10.1080/03610910701790236

Cited by 66 publications

(59 citation statements)

References 25 publications

(30 reference statements)

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“…For instance, overlap counts with different pathways are statistically dependent whose impact on the multiple hypothesis testing problem is nearly impossible to estimate; in particular it is unclear to what extent Benjamini and Yekutieli's notion of positive regression dependency is applicable [39]. However, the problem has already been recognized and discussed in the literature [24]. …”

Section: Discussionmentioning

confidence: 99%

Integration of gene expression data with prior knowledge for network analysis and validation

2011

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BackgroundReconstruction of protein-protein interaction or metabolic networks based on expression data often involves in silico predictions, while on the other hand, there are unspecific networks of in vivo interactions derived from knowledge bases.We analyze networks designed to come as close as possible to data measured in vivo, both with respect to the set of nodes which were taken to be expressed in experiment as well as with respect to the interactions between them which were taken from manually curated databasesResultsA signaling network derived from the TRANSPATH database and a metabolic network derived from KEGG LIGAND are each filtered onto expression data from breast cancer (SAGE) considering different levels of restrictiveness in edge and vertex selection.We perform several validation steps, in particular we define pathway over-representation tests based on refined null models to recover functional modules. The prominent role of the spindle checkpoint-related pathways in breast cancer is exhibited. High-ranking key nodes cluster in functional groups retrieved from literature. Results are consistent between several functional and topological analyses and between signaling and metabolic aspects.ConclusionsThis construction involved as a crucial step the passage to a mammalian protein identifier format as well as to a reaction-based semantics of metabolism. This yielded good connectivity but also led to the need to perform benchmark tests to exclude loss of essential information. Such validation, albeit tedious due to limitations of existing methods, turned out to be informative, and in particular provided biological insights as well as information on the degrees of coherence of the networks despite fragmentation of experimental data.Key node analysis exploited the networks for potentially interesting proteins in view of drug target prediction.

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Section: Discussionmentioning

confidence: 99%

Integration of gene expression data with prior knowledge for network analysis and validation

2011

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“…The problem of selecting L atoms out of the possible K can be formalized similarly to the classical experiment of taking colored balls at random from an urn without replacement [54], [55]. If the balls have a different weight, the result follows the Wallenius’ noncentral hypergeometric distribution [56].…”

Section: Problem Formulationmentioning

confidence: 99%

“…For sampling without replacement, re-adjusting the atom weights requires 𝒪 (( K − 1) + … + ( K − L + 1)) ~ 𝒪( LK ). Since each of the L iterations takes into account the previously selected atoms [55], the cost of the Wallenius distribution is 𝒪 ( K + ( K − 1) + … + ( K − L + 1)) ~ 𝒪( LK ). Each of the L coefficients is generated from the normal distribution, whose mean requires 𝒪( P ), therefore the entire complexity is 𝒪( LP ). Regarding the dictionary atom parameters, their posterior (7) requires 𝒪 ( L ( P + Q 2 )), while the typical cost of the Nelder Mead’s simplex is 𝒪 ( Q 2 ) [80].…”

Section: Mcmc Ergodicity Proofsmentioning

confidence: 99%

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Markov Chain Monte Carlo Inference of Parametric Dictionaries for Sparse Bayesian Approximations

Chaspari

Tsiartas

Tsilifis

et al. 2016

IEEE Trans. Signal Process.

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Parametric dictionaries can increase the ability of sparse representations to meaningfully capture and interpret the underlying signal information, such as encountered in biomedical problems. Given a mapping function from the atom parameter space to the actual atoms, we propose a sparse Bayesian framework for learning the atom parameters, because of its ability to provide full posterior estimates, take uncertainty into account and generalize on unseen data. Inference is performed with Markov Chain Monte Carlo, that uses block sampling to generate the variables of the Bayesian problem. Since the parameterization of dictionary atoms results in posteriors that cannot be analytically computed, we use a Metropolis-Hastings-within-Gibbs framework, according to which variables with closed-form posteriors are generated with the Gibbs sampler, while the remaining ones with the Metropolis Hastings from appropriate candidate-generating densities. We further show that the corresponding Markov Chain is uniformly ergodic ensuring its convergence to a stationary distribution independently of the initial state. Results on synthetic data and real biomedical signals indicate that our approach offers advantages in terms of signal reconstruction compared to previously proposed Steepest Descent and Equiangular Tight Frame methods. This paper demonstrates the ability of Bayesian learning to generate parametric dictionaries that can reliably represent the exemplar data and provides the foundation towards inferring the entire variable set of the sparse approximation problem for signal denoising, adaptation and other applications.

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“…[54][55][56][57][58] Both the Wallenius and Fisher distributions generalize the standard central hypergeometric distribution to allow for unequal weighting of different types of species in a given population. The difference between the two distributions is that with the Wallenius distribution the total number of draws is a known quantity, and with the Fisher distribution the draws occur independently such that the total number of draws is known only after completion of the experiment.…”

Section: B Noncentral Hypergeometric Distributionmentioning

confidence: 99%

Statistics of modifier distributions in mixed network glasses

Mauro

2013

The Journal of Chemical Physics

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The constituents of any network glass can be broadly classified as either network formers or network modifiers. Network formers, such as SiO2, Al2O3, B2O3, P2O5, etc., provide the backbone of the glass network and are the primary source of its rigid constraints. Network modifiers play a supporting role, such as charge stabilization of the network formers or alteration of the network topology through rupture of bridging bonds and introduction of floppy modes. The specific role of the modifiers depends on which network formers are present in the glass and the relative free energies of modifier interactions with each type of network former site. This variation of free energy with modifier speciation is responsible for the so-called mixed network former effect, i.e., the nonlinear scaling of property values in glasses having fixed modifier concentration but a varying ratio of network formers. In this paper, a general theoretical framework is presented describing the statistical mechanics of modifier speciation in mixed network glasses. The model provides a natural explanation for the mixed network former effect and also accounts for the impact of thermal history and relaxation on glass network topology.

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Sampling Methods for Wallenius' and Fisher's Noncentral Hypergeometric Distributions

Cited by 66 publications

References 25 publications

Integration of gene expression data with prior knowledge for network analysis and validation

Integration of gene expression data with prior knowledge for network analysis and validation

Markov Chain Monte Carlo Inference of Parametric Dictionaries for Sparse Bayesian Approximations

Statistics of modifier distributions in mixed network glasses

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