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Fast Bayesian whole-brain fMRI analysis with spatial 3D priors
Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences.
Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Faculty of Science & Engineering. Linköping University, Faculty of Arts and Sciences.
Division of Mathematical Statistics, Department of Mathematical Sciences, Chalmers, Göteborg, Sweden; University of Gothenburg, Göteborg, Sweden.
Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences.
2017 (English)In: NeuroImage, ISSN 1053-8119, E-ISSN 1095-9572, Vol. 146, p. 211-225Article in journal (Refereed) Published
Abstract [en]

Spatial whole-brain Bayesian modeling of task-related functional magnetic resonance imaging (fMRI) is a great computational challenge. Most of the currently proposed methods therefore do inference in subregions of the brain separately or do approximate inference without comparison to the true posterior distribution. A popular such method, which is now the standard method for Bayesian single subject analysis in the SPM software, is introduced in Penny et al. (2005b). The method processes the data slice-by-slice and uses an approximate variational Bayes (VB) estimation algorithm that enforces posterior independence between activity coefficients in different voxels. We introduce a fast and practical Markov chain Monte Carlo (MCMC) scheme for exact inference in the same model, both slice-wise and for the whole brain using a 3D prior on activity coefficients. The algorithm exploits sparsity and uses modern techniques for efficient sampling from high-dimensional Gaussian distributions, leading to speed-ups without which MCMC would not be a practical option. Using MCMC, we are for the first time able to evaluate the approximate VB posterior against the exact MCMC posterior, and show that VB can lead to spurious activation. In addition, we develop an improved VB method that drops the assumption of independent voxels a posteriori. This algorithm is shown to be much faster than both MCMC and the original VB for large datasets, with negligible error compared to the MCMC posterior.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 146, p. 211-225
Keywords [en]
fMRI, Spatial priors, Variational Bayes, Markov chain Monte Carlo, Gaussian Markov random fields, General linear model
National Category
Medical Engineering
Identifiers
URN: urn:nbn:se:liu:diva-132945DOI: 10.1016/j.neuroimage.2016.11.040ISI: 000394560700019PubMedID: 27876654Scopus ID: 2-s2.0-84999622353OAI: oai:DiVA.org:liu-132945DiVA, id: diva2:1051973
Note

Funding agencies: Swedish Research Council (Vetenskapsradet) [20135229]; Knut and Alice Wallenberg Foundation [KAW 20012.0067]

Available from: 2016-12-05 Created: 2016-12-05 Last updated: 2020-06-29Bibliographically approved
In thesis
1. Scalable Bayesian spatial analysis with Gaussian Markov random fields
Open this publication in new window or tab >>Scalable Bayesian spatial analysis with Gaussian Markov random fields
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Skalbar Bayesiansk spatial analys med Gaussiska Markov-fält
Abstract [en]

Accurate statistical analysis of spatial data is important in many applications. Failing to properly account for spatial autocorrelation may often lead to false conclusions. At the same time, the ever-increasing sizes of spatial datasets pose a great computational challenge, as many standard methods for spatial analysis are limited to a few thousand data points.

In this thesis, we explore how Gaussian Markov random fields (GMRFs) can be used for scalable analysis of spatial data. GMRFs are closely connected to the commonly used Gaussian processes, but have sparsity properties that make them computationally cheap both in time and memory. The Bayesian framework enables a GMRF to be used as a spatial prior, comprising the assumption of smooth variation over space, and gives a principled way to estimate the parameters and propagate uncertainty.

We develop new algorithms that enable applying GMRF priors in 3D to the brain activity inherent in functional magnetic resonance imaging (fMRI) data, with millions of observations. We show that our methods are both faster and more accurate than previous work. A method for approximating selected elements of the inverse precision matrix (i.e. the covariance matrix) is also proposed, which is important for evaluating the posterior uncertainty. In addition, we establish a link between GMRFs and deep convolutional neural networks, which have been successfully used in countless machine learning tasks for images, resulting in a deep GMRF model. Finally, we show how GMRFs can be used in real-time robotic search and rescue operations, for modeling the spatial distribution of injured persons.

Abstract [sv]

Tillförlitlig statistisk analys av spatiala data är viktigt inom många tillämpningar. Om inte korrekt hänsyn tas till spatial autokorrelation kan det ofta leda till felaktiga slutsatser. Samtidigt ökar ständigt storleken på de spatiala datamaterialen vilket utgör en stor beräkningsmässig utmaning, eftersom många standardmetoder för spatial analys är begränsade till några tusental datapunkter.

I denna avhandling utforskar vi hur Gaussiska Markov-fält (eng: Gaussian Markov random fields, GMRF) kan användas för mer skalbara analyser av spatiala data. GMRF-modeller är nära besläktade med de ofta använda Gaussiska processerna, men har gleshetsegenskaper som gör dem beräkningsmässigt effektiva både vad gäller tids- och minnesåtgång. Det Bayesianska synsättet gör det möjligt att använda GMRF som en spatial prior som innefattar antagandet om långsam spatial variation och ger ett principiellt tillvägagångssätt för att skatta parametrar och propagera osäkerhet.

Vi utvecklar nya algoritmer som gör det möjligt att använda GMRF-priors i 3D för den hjärnaktivitet som indirekt kan observeras i hjärnbilder framtagna med tekniken fMRI, som innehåller milliontals datapunkter. Vi visar att våra metoder är både snabbare och mer korrekta än tidigare forskning. En metod för att approximera utvalda element i den inversa precisionsmatrisen (dvs. kovariansmatrisen) framförs också, vilket är viktigt för att kunna evaluera osäkerheten i posteriorn. Vidare gör vi en koppling mellan GMRF och djupa neurala faltningsnätverk, som har använts framgångsrikt för mängder av bildrelaterade problem inom maskininlärning, vilket mynnar ut i en djup GMRF-modell. Slutligen visar vi hur GMRF kan användas i realtid av autonoma drönare för räddningsinsatser i katastrofområden för att modellera den spatiala fördelningen av skadade personer.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2020. p. 53
Series
Linköping Studies in Arts and Sciences, ISSN 0282-9800 ; 790Linköping Studies in Statistics, ISSN 1651-1700 ; 15
Keywords
Spatial statistics, Bayesian statistics, Gaussian Markov random fields, fMRI, Machine learning, Spatial statistik, Bayesiansk statistik, Gaussiska Markov-fält, fMRI, Maskininlärning
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-165872 (URN)10.3384/diss.diva-165872 (DOI)9789179298180 (ISBN)
Public defence
2020-09-18, Ada Lovelace, B Building, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2020-08-17 Created: 2020-06-01 Last updated: 2020-11-24Bibliographically approved

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