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Normative Modeling of Neuroimaging Data Using Scalable Multi-task Gaussian Processes

  • Seyed Mostafa KiaEmail author
  • Andre Marquand
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11072)

Abstract

Normative modeling has recently been proposed as an alternative for the case-control approach in modeling heterogeneity within clinical cohorts. Normative modeling is based on single-output Gaussian process regression that provides coherent estimates of uncertainty required by the method but does not consider spatial covariance structure. Here, we introduce a scalable multi-task Gaussian process regression (S-MTGPR) approach to address this problem. To this end, we exploit a combination of a low-rank approximation of the spatial covariance matrix with algebraic properties of Kronecker product in order to reduce the computational complexity of Gaussian process regression in high-dimensional output spaces. On a public fMRI dataset, we show that S-MTGPR: (1) leads to substantial computational improvements that allow us to estimate normative models for high-dimensional fMRI data whilst accounting for spatial structure in data; (2) by modeling both spatial and across-sample variances, it provides higher sensitivity in novelty detection scenarios.

Keywords

Gaussian processes Multi-task learning Normative modeling Neuroimaging fMRI Clinical neuroscience Novelty detection 

Supplementary material

473976_1_En_15_MOESM1_ESM.pdf (82 kb)
Supplementary material 1 (pdf 82 KB)

References

  1. 1.
    Abraham, A., et al.: Machine learning for neuroimaging with scikit-learn. Front. Neuroinf. 8, 14 (2014)CrossRefGoogle Scholar
  2. 2.
    Alvarez, M., Lawrence, N.D.: Sparse convolved Gaussian processes for multi-output regression. In: Advances in Neural Information Processing Systems, pp. 57–64 (2009)Google Scholar
  3. 3.
    Álvarez, M.A., Lawrence, N.D.: Computationally efficient convolved multiple output Gaussian processes. J. Mach. Learn. Res. 12, 1459–1500 (2011)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Alvarez, M.A., Luengo, D., Titsias, M.K., Lawrence, N.D.: Efficient multioutput Gaussian processes through variational inducing kernels. In: International Conference on Artificial Intelligence and Statistics, pp. 25–32 (2010)Google Scholar
  5. 5.
    Bonilla, E.V., Chai, K.M., Williams, C.: Multi-task Gaussian process prediction. In: Advances in Neural Information Processing Systems, pp. 153–160 (2008)Google Scholar
  6. 6.
    Boyle, P., Frean, M.: Multiple output Gaussian process regression. Technical report (2005)Google Scholar
  7. 7.
    Huertas, I., et al.: A Bayesian spatial model for neuroimaging data based on biologically informed basis functions. NeuroImage 161, 134–148 (2017)CrossRefGoogle Scholar
  8. 8.
    Loan, C.F.: The ubiquitous Kronecker product. J. Comput. Appl. Math. 123(1), 85–100 (2000)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Marquand, A.F., Rezek, I., Buitelaar, J., Beckmann, C.F.: Understanding heterogeneity in clinical cohorts using normative models: beyond case-control studies. Biol. Psychiatry 80(7), 552–561 (2016)CrossRefGoogle Scholar
  10. 10.
    Marquand, A.F., Wolfers, T., Mennes, M., Buitelaar, J., Beckmann, C.F.: Beyond lumping and splitting: a review of computational approaches for stratifying psychiatric disorders. Biol. Psychiatry 1(5), 433–447 (2016)Google Scholar
  11. 11.
    Mirnezami, R., Nicholson, J., Darzi, A.: Preparing for precision medicine. New Engl. J. Med. 366(6), 489–491 (2012). pMID: 22256780CrossRefGoogle Scholar
  12. 12.
    Miyawaki, Y., et al.: Visual image reconstruction from human brain activity using a combination of multiscale local image decoders. Neuron 60(5), 915–929 (2008)CrossRefGoogle Scholar
  13. 13.
    Quinonero-Candela, J., Williams, C.K.: Approximation methods for Gaussian process regression. Large-Scale Kernel Mach. 203–224 (2007)Google Scholar
  14. 14.
    Rakitsch, B., Lippert, C., Borgwardt, K., Stegle, O.: It is all in the noise: efficient multi-task Gaussian process inference with structured residuals. In: Advances in Neural Information Processing Systems, pp. 1466–1474 (2013)Google Scholar
  15. 15.
    Stegle, O., Lippert, C., Mooij, J.M., Lawrence, N.D., Borgwardt, K.M.: Efficient inference in matrix-variate Gaussian models with iid observation noise. In: Advances in Neural Information Processing Systems, pp. 630–638 (2011)Google Scholar
  16. 16.
    Williams, C.K., Rasmussen, C.E.: Gaussian processes for regression. In: Advances in Neural Information Processing Systems, pp. 514–520 (1996)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Cognitive NeuroscienceRadboud University Medical CentreNijmegenThe Netherlands
  2. 2.Donders Centre for Cognitive Neuroimaging, Donders Institute for Brain, Cognition and BehaviourRadboud UniversityNijmegenThe Netherlands

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