Sparse linear regression methods including the well-known LASSO and the Dantzig selector have become ubiquitous in the engineering practice, including in medical imaging. Among other tasks, they have been successfully applied for the estimation of neuronal activity from functional magnetic resonance data without prior knowledge of the stimulus or activation timing, utilizing an approximate knowledge of the hemodynamic response to local neuronal activity. These methods work by generating a parametric family of solutions with different sparsity, among which an ultimate choice is made using an information criteria. We propose a novel approach, that instead of selecting a single option from the family of regularized solutions, utilizes the whole family of such sparse regression solutions. Namely, their ensemble provides a first approximation of probability of activation at each time-point, and together with the conditional neuronal activity distributions estimated with the theory of mixtures with varying concentrations, they serve as the inputs to a Bayes classifier eventually deciding on the verity of activation at each time-point. We show in extensive numerical simulations that this new method performs favourably in comparison with standard approaches in a range of realistic scenarios. This is mainly due to the avoidance of overfitting and underfitting that commonly plague the solutions based on sparse regression combined with model selection methods, including the corrected Akaike Information Criterion. This advantage is finally documented in selected fMRI task datasets.
翻译:包括著名的LASSO 和 Dantzig 选择器在内的松散线性回归方法,包括众所周知的LASSO 和 Dantzig 选择器等,在工程实践,包括医学成像中已变得无处不在。除其他任务外,这些方法成功地用于从功能磁共振数据中估计神经活动,而没有事先知道刺激或激活时间,同时利用对当地神经活动热动反应的大致知识。这些方法通过产生一个具有不同广度的参数式解决方案组合发挥作用,其中采用信息标准标准标准标准标准方法。我们提出了一个新办法,即不从常规解决方案中选择单一选项,而是利用这种稀薄的回归解决方案的全组。也就是说,它们的集束提供了每个时间点启动概率的第一近似近似值,同时利用不同浓度混合物理论估计的有条件的神经性活动分布。这些方法为最终决定每个时间点激活的概率的巴耶斯分解器提供了投入。我们用大量数字模拟来显示,这种新方法与标准方法相比,在一系列现实的情景中,使用这种稀有的回归解决方案。 它们的集提供了最接近性选择方法,这主要是为了避免在模型下选择。