Diffusion basis spectrum imaging for identifying pathologies in MS subtypes

Diffusion basis spectrum imaging (DBSI) combines discrete anisotropic diffusion tensors and the spectrum of isotropic diffusion tensors to model the underlying multiple sclerosis (MS) pathologies. We used clinical MS subtypes as a surrogate of underlying pathologies to assess DBSI as a biomarker of pathology in 55 individuals with MS. Restricted isotropic fraction (reflecting cellularity) and fiber fraction (representing apparent axonal density) were the most important DBSI metrics to classify MS using brain white matter lesions. These DBSI metrics outperformed lesion volume. When analyzing the normal-appearing corpus callosum, the most significant DBSI metrics were fiber fraction, radial diffusivity (reflecting myelination), and nonrestricted isotropic fraction (representing edema). This study provides preliminary evidence supporting the ability of DBSI as a potential noninvasive biomarker of MS neuropathology

Average treatment effect estimation via random recursive partitioning

A new matching method is proposed for the estimation of the average treatment effect of social policy interventions (e.g., training programs or health care measures). Given an outcome variable, a treatment and a set of pre-treatment covariates, the method is based on the examination of random recursive partitions of the space of covariates using regression trees. A regression tree is grown either on the treated or on the untreated individuals {\it only} using as response variable a random permutation of the indexes 1...$n$ ($n$ being the number of units involved), while the indexes for the other group are predicted using this tree. The procedure is replicated in order to rule out the effect of specific permutations. The average treatment effect is estimated in each tree by matching treated and untreated in the same terminal nodes. The final estimator of the average treatment effect is obtained by averaging on all the trees grown. The method does not require any specific model assumption apart from the tree's complexity, which does not affect the estimator though. We show that this method is either an instrument to check whether two samples can be matched (by any method) and, when this is feasible, to obtain reliable estimates of the average treatment effect. We further propose a graphical tool to inspect the quality of the match. The method has been applied to the National Supported Work Demonstration data, previously analyzed by Lalonde (1986) and others

WARP: Wavelets with adaptive recursive partitioning for multi-dimensional data

Effective identification of asymmetric and local features in images and other data observed on multi-dimensional grids plays a critical role in a wide range of applications including biomedical and natural image processing. Moreover, the ever increasing amount of image data, in terms of both the resolution per image and the number of images processed per application, requires algorithms and methods for such applications to be computationally efficient. We develop a new probabilistic framework for multi-dimensional data to overcome these challenges through incorporating data adaptivity into discrete wavelet transforms, thereby allowing them to adapt to the geometric structure of the data while maintaining the linear computational scalability. By exploiting a connection between the local directionality of wavelet transforms and recursive dyadic partitioning on the grid points of the observation, we obtain the desired adaptivity through adding to the traditional Bayesian wavelet regression framework an additional layer of Bayesian modeling on the space of recursive partitions over the grid points. We derive the corresponding inference recipe in the form of a recursive representation of the exact posterior, and develop a class of efficient recursive message passing algorithms for achieving exact Bayesian inference with a computational complexity linear in the resolution and sample size of the images. While our framework is applicable to a range of problems including multi-dimensional signal processing, compression, and structural learning, we illustrate its work and evaluate its performance in the context of 2D and 3D image reconstruction using real images from the ImageNet database. We also apply the framework to analyze a data set from retinal optical coherence tomography