Comparing variational Bayes with Markov chain Monte Carlo for Bayesian computation in neuroimaging

Nathoo, FS; Ml, Lesperance; Lawson, AB; Dean, CB

doi:10.1177/0962280212448973

Cited by 8 publications

(6 citation statements)

References 30 publications

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“…As such the posterior variance for VB and INLA are again listed relative to that obtained from HMC in order to determine the extent to which these approaches under-estimate or over-estimate posterior variability. For VB we see that the marginal posterior variance is under-estimated which is in line with expectations from the literature [34, 32]. INLA I and II provide measures of variability that are closer to that of HMC, while INLA III and IV tend to over-estimate the marginal posterior variance, with this over-estimation being substantial when the smaller mesh size is used.…”

Section: Simulation Studiessupporting

confidence: 88%

Bayesian computation for Log-Gaussian Cox processes: a comparative analysis of methods

Teng

Nathoo²,

Johnson

2017

Journal of Statistical Computation and Simulation

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The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data.

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Section: Simulation Studiessupporting

confidence: 88%

Bayesian computation for Log-Gaussian Cox processes: a comparative analysis of methods

Teng

Nathoo²,

Johnson

2017

Journal of Statistical Computation and Simulation

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“…The posterior variance statistics obtained from VB are also fairly close to those obtained from HMC, with slightly larger values for the former. Thus the over-confidence problem sometimes associated with VB ([21], [4]) does not seem to be an issue in this case. Both algorithms are performing well in terms of point estimation as they achieve a high level of correlation (around 0.99) with the true values.…”

Section: Resultsmentioning

confidence: 87%

“…While this approach often leads to computational efficiency, there are potential concerns with its accuracy. [4] have discussed this issue and demonstrated examples with neuroimaging data where the mean field variational Bayes approximation can severely underestimate posterior variability and produce biased estimates of model hyper-parameters. [5] study the performance of VB in a simulation study based on fMRI and raise concerns that while VB reduces computational cost it can suffer from lower specificity and smaller coverage of the credible intervals.…”

Section: Introductionmentioning

confidence: 99%

Time series analysis of fMRI data: Spatial modelling and Bayesian computation

Teng

Johnson

Nathoo

2018

Statistics in Medicine

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Time series analysis of fMRI data is an important area of medical statistics for neuroimaging data. Spatial models and Bayesian approaches for inference in such models have advantages over more traditional mass univariate approaches; however, a major challenge for such analyses is the required computation. As a result, the neuroimaging community has embraced approximate Bayesian inference based on mean-field variational Bayes (VB) approximations. These approximations are implemented in standard software packages such as the popular statistical parametric mapping software. While computationally efficient, the quality of VB approximations remains unclear even though they are commonly used in the analysis of neuroimaging data. For reliable statistical inference, it is important that these approximations be accurate and that users understand the scenarios under which they may not be accurate. We consider this issue for a particular model that includes spatially varying coefficients. To examine the accuracy of the VB approximation, we derive Hamiltonian Monte Carlo (HMC) for this model and conduct simulation studies to compare its performance with VB in terms of estimation accuracy, posterior variability, the spatial smoothness of estimated images, and computation time. As expected, we find that the computation time required for VB is considerably less than that for HMC. In settings involving a high or moderate signal-to-noise ratio (SNR), we find that the 2 approaches produce very similar results suggesting that the VB approximation is useful in this setting. On the other hand, when one considers a low SNR, substantial differences are found, suggesting that the approximation may not be accurate in such cases and we demonstrate that VB produces Bayes estimators with larger mean squared error. A comparison of the 2 computational approaches in an application examining the hemodynamic response to face perception in addition to a comparison with the traditional mass univariate approach in this application is also considered. Overall, our work clarifies the usefulness of VB for the spatiotemporal analysis of fMRI data, while also pointing out the limitation of VB when the SNR is low and the utility of HMC in this case.

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“…Our goal is to infer the posterior distributions over the factors U and V depending on the data X. To avoid using the heavy machinery of MCMC (Nathoo et al, 2013) to infer the intractable posterior of the latent variables in our model, we use the framework of variational inference (Hoffman et al, 2013). In particular, we extend the version of the variational EM algorithm (Beal and Ghahramani, 2003) proposed by Dikmen and Févotte (2012) in the context of the standard Gamma-Poisson factor model to our sparse and zero-inflated GaP model.…”

Section: Model Inference Using a Variational Em Algorithmmentioning

confidence: 99%

Probabilistic count matrix factorization for single cell expression data analysis

et al. 2019

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Motivation: The development of high throughput single-cell sequencing technologies now allows the investigation of the population diversity of cellular transcriptomes. The expression dynamics (gene-to-gene variability) can be quantified more accurately, thanks to the measurement of lowly-expressed genes. In addition, the cell-to-cell variability is high, with a low proportion of cells expressing the same genes at the same time/level. Those emerging patterns appear to be very challenging from the statistical point of view, especially to represent a summarized view of single-cell expression data. PCA is a most powerful tool for high dimensional data representation, by searching for latent directions catching the most variability in the data. Unfortunately, classical PCA is based on Euclidean distance and projections that poorly work in presence of over-dispersed count data with dropout events like single-cell expression data. Results: We propose a probabilistic Count Matrix Factorization (pCMF) approach for single-cell expression data analysis, that relies on a sparse Gamma-Poisson factor model. This hierarchical model is inferred using a variational EM algorithm. It is able to jointly build a low dimensional representation of cells and genes. We show how this probabilistic framework induces a geometry that is suitable for single-cell data visualization, and produces a compression of the data that is very powerful for clustering purposes. Our method is competed against other standard representation methods like t-SNE, and we illustrate its performance for the representation of single-cell expression (scRNA-seq) data. Availability: Our work is implemented in the pCMF R-package 1 .

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Comparing variational Bayes with Markov chain Monte Carlo for Bayesian computation in neuroimaging

Cited by 8 publications

References 30 publications

Bayesian computation for Log-Gaussian Cox processes: a comparative analysis of methods

Bayesian computation for Log-Gaussian Cox processes: a comparative analysis of methods

Time series analysis of fMRI data: Spatial modelling and Bayesian computation

Probabilistic count matrix factorization for single cell expression data analysis

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