Bayesian Kernel Mixtures for Counts

Canale, Antonio; Dunson, David B.

doi:10.1198/jasa.2011.tm10552

Cited by 74 publications

(88 citation statements)

References 39 publications

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“…Kernels are a widely used and flexible method to deal with complex data of various types: they can be obtained from β-diversity measures (Bray and Curtis, 1957;Lozupone et al, 2007) to explore microbiome datasets. They can also account for datasets obtained as read counts by the discrete Poisson kernel (Canale and Dunson, 2011) and are also commonly adopted to quantifies genetic similarities by the state kernel (Kwee et al, 2008;Wu et al, 2010). Our contribution is to propose three alternative approaches able to combine several kernels into one meta-kernel in an unsupervised framework.…”

Section: Introductionmentioning

confidence: 99%

Unsupervised multiple kernel learning for heterogeneous data integration

Mariette

Villa-Vialaneix

2017

Bioinformatics

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Motivation: Recent high-throughput sequencing advances have expanded the breadth of available omics datasets and the integrated analysis of multiple datasets obtained on the same samples has allowed to gain important insights in a wide range of applications. However, the integration of various sources of information remains a challenge for systems biology since produced datasets are often of heterogeneous types, with the need of developing generic methods to take their different specificities into account. Results: We propose a multiple kernel framework that allows to integrate multiple datasets of various types into a single exploratory analysis. Several solutions are provided to learn either a consensus metakernel or a meta-kernel that preserves the original topology of the datasets. We applied our framework to analyse two public multi-omics datasets. First, the multiple metagenomic datasets, collected during the TARA Oceans expedition, was explored to demonstrate that our method is able to retrieve previous findings in a single KPCA as well as to provide a new image of the sample structures when a larger number of datasets are included in the analysis. To perform this analysis, a generic procedure is also proposed to improve the interpretability of the kernel PCA in regards with the original data. Second, the multi-omics breast cancer datasets, provided by The Cancer Genome Atlas, is analysed using a kernel Self-Organizing Maps with both single and multi-omics strategies. The comparison of this two approaches demonstrates the benefit of our integration method to improve the representation of the studied biological system. Contact: jerome.mariette@inra.fr and nathalie.villa-vialaneix@inra.fr Availability and implementation: Proposed methods are available in the R package mixKernel, released on CRAN. It is fully compatible with the mixOmics package and a tutorial describing the approach can be found on mixOmics web site http://mixomics.org/mixkernel/.

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Section: Introductionmentioning

confidence: 99%

Unsupervised multiple kernel learning for heterogeneous data integration

Mariette

Villa-Vialaneix

2017

Bioinformatics

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“…It is common to incorporate latent variables in Poisson factor models (e.g Dunson and Herring, 2005). Including this generalization requires minor modifications of our current procedures, however, as noted in Canale and Dunson (2011), there is a pitfall in such models due to the dual role of the latent variable component in controlling the degree of dependence and the magnitude of over-dispersion in the marginal distributions. Canale and Dunson (2011) address these issues via a rounded kernel method which improves flexibility in modeling count variables.…”

Section: Discussionmentioning

confidence: 99%

“…Including this generalization requires minor modifications of our current procedures, however, as noted in Canale and Dunson (2011), there is a pitfall in such models due to the dual role of the latent variable component in controlling the degree of dependence and the magnitude of over-dispersion in the marginal distributions. Canale and Dunson (2011) address these issues via a rounded kernel method which improves flexibility in modeling count variables. Our current efforts are aimed at adapting these procedures to develop nonparametric approaches for inference on the distribution of weighted networks.…”

Section: Discussionmentioning

confidence: 99%

Bayesian Inference and Testing of Group Differences in Brain Networks

Durante¹,

Dunson²

2018

Bayesian Anal.

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Abstract. Network data are increasingly collected along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring brain connectivity networks for a sample of individuals along with their membership to a low or high creative reasoning group. It is of paramount importance to develop statistical methods for testing of global and local changes in the structural interconnections among brain regions across groups. We develop a general Bayesian procedure for inference and testing of group differences in the network structure, which relies on a nonparametric representation for the conditional probability mass function associated with a network-valued random variable. By leveraging a mixture of low-rank factorizations, we allow simple global and local hypothesis testing adjusting for multiplicity. An efficient Gibbs sampler is defined for posterior computation. We provide theoretical results on the flexibility of the model and assess testing performance in simulations. The approach is applied to provide novel insights on the relationships between human brain networks and creativity.

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“…The Gibbs sampler iterates through the following steps. Step 1 : the first step involves data augmentation in the spirit of Canale and Dunson () to simulate the latent variable

y_{i}^{*} false(s_{j} false)

from the corresponding truncated normal distribution, conditionally on the model parameters and the cluster indicators. Assuming that the random effects

u_{i} false(s_{j} false)

are drawn from

N ({italicθ}_{h}, 1)

, we have

y_{i}^{*} false(s_{j} false) \sim N false(x_{i} bold-italicβ + z_{j} bold-italicγ + θ_{h}, 1 false) 1 false{(a_{y_{i} false(s_{j} false)}, a_{y_{i} false(s_{j} false) + 1}) false},

where

N false(italicμ, σ^{2} false) 1 false{normalΔ false}

denotes the normal density with mean μ and variance

σ^{2}

, truncated to the set Δ. Step 2 : next, conditionally on the latent continuous variables, the cluster indicators

ξ = {({italicξ}_{i} false(s_{j} false))}^{'}

and the atoms θ , we sample the regression parameters.…”

Section: Bayesian Inferencementioning

confidence: 99%

Non-Parametric Spatial Models for Clustered Ordered Periodontal Data

Bandyopadhyay

Canale

2016

Journal of the Royal Statistical Society Series C: Applied Statistics

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Clinical attachment level (CAL) is regarded as the most popular measure to assess periodontal disease (PD). These probed tooth-site level measures are usually rounded and recorded as whole numbers (in mm) producing clustered (site measures within a mouth) error-prone ordinal responses representing some ordering of the underlying PD progression. In addition, it is hypothesized that PD progression can be spatially-referenced, i.e., proximal tooth-sites share similar PD status in comparison to sites that are distantly located. In this paper, we develop a Bayesian multivariate probit framework for these ordinal responses where the cut-point parameters linking the observed ordinal CAL levels to the latent underlying disease process can be fixed in advance. The latent spatial association characterizing conditional independence under Gaussian graphs is introduced via a nonparametric Bayesian approach motivated by the probit stick-breaking process, where the components of the stick-breaking weights follows a multivariate Gaussian density with the precision matrix distributed as G-Wishart. This yields a computationally simple, yet robust and flexible framework to capture the latent disease status leading to a natural clustering of tooth-sites and subjects with similar PD status (beyond spatial clustering), and improved parameter estimation through sharing of information. Both simulation studies and application to a motivating PD dataset reveal the advantages of considering this flexible nonparametric ordinal framework over other alternatives.

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Bayesian Kernel Mixtures for Counts

Cited by 74 publications

References 39 publications

Unsupervised multiple kernel learning for heterogeneous data integration

Unsupervised multiple kernel learning for heterogeneous data integration

Bayesian Inference and Testing of Group Differences in Brain Networks

Non-Parametric Spatial Models for Clustered Ordered Periodontal Data

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