Institute for Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands.
Neuroimage. 2010 Mar;50(1):150-61. doi: 10.1016/j.neuroimage.2009.11.064. Epub 2009 Dec 1.
Bayesian logistic regression with a multivariate Laplace prior is introduced as a multivariate approach to the analysis of neuroimaging data. It is shown that, by rewriting the multivariate Laplace distribution as a scale mixture, we can incorporate spatio-temporal constraints which lead to smooth importance maps that facilitate subsequent interpretation. The posterior of interest is computed using an approximate inference method called expectation propagation and becomes feasible due to fast inversion of a sparse precision matrix. We illustrate the performance of the method on an fMRI dataset acquired while subjects were shown handwritten digits. The obtained models perform competitively in terms of predictive performance and give rise to interpretable importance maps. Estimation of the posterior of interest is shown to be feasible even for very large models with thousands of variables.
贝叶斯逻辑回归与多元拉普拉斯先验被引入到神经影像学数据的分析中，作为一种多元方法。通过将多元拉普拉斯分布重写为尺度混合，我们可以引入时空约束，从而得到平滑的重要图，便于后续解释。感兴趣的后验使用一种称为期望传播的近似推理方法进行计算，并且由于稀疏精度矩阵的快速反转而变得可行。我们在手写数字展示给受试者时获取的 fMRI 数据集上说明了该方法的性能。所获得的模型在预测性能方面表现出色，并产生了可解释的重要图。即使对于具有数千个变量的非常大的模型，也可以证明对感兴趣的后验的估计是可行的。
