Robust outlier detection for heterogeneous distributions applicable to censoring in functional MRI

Functional magnetic resonance imaging (fMRI) data are prone to intense "burst" noise artifacts due to head movements and other sources. Such volumes can be considered as high-dimensional outliers that can be identified using statistical outlier detection techniques, which allows for controlling the false positive rate. Previous work has used dimension reduction and multivariate outlier detection techniques, including the use of robust minimum covariance determinant (MCD) distances. Under Gaussianity, the distribution of these robust distances can be approximated, and an upper quantile of that distribution can be used to identify outlying volumes. Unfortunately, the Gaussian assumption is unrealistic for fMRI data in this context. One way to address this is to transform the data to Normality. A limitation of existing robust methods for this purpose, such as robust Box-Cox and Yeo-Johnson transformations, is that they can deal with skew but not heavy or light tails. Here, we develop a novel robust method for transformation to central Normality based on the highly flexible sinh-arcsinh (SHASH) family of distributions. To avoid the influence of outliers, it is crucial to initialize the outlier labels with a high degree of sensitivity. For this purpose, we consider a commonplace robust z-score approach, and a modified isolation forest (iForest) approach, a popular technique for anomaly detection in machine learning. Through extensive simulation studies, we find that our proposed SHASH transformation initialized using iForest clearly outperforms benchmark methods in a variety of settings, including skewed and heavy tailed distributions, and light to heavy outlier contamination. We also apply the proposed techniques to several example datasets and find this combination to have consistently strong performance.