Random forests on distance matrices for imaging genetics studies

Abstract

We propose a non-parametric regression methodology, Random Forests on Distance Matrices (RFDM), for detecting genetic variants associated to quantitative phenotypes, obtained using neuroimaging techniques, representing the human brain's structure or function. RFDM, which is an extension of decision forests, requires a distance matrix as the response that encodes all pair-wise phenotypic distances in the random sample. We discuss ways to learn such distances directly from the data using manifold learning techniques, and how to define such distances when the phenotypes are non-vectorial objects such as brain connectivity networks. We also describe an extension of RFDM to detect espistatic effects while keeping the computational complexity low. Extensive simulation results and an application to an imaging genetics study of Alzheimer's Disease are presented and discussed.

Random forest regression for manifold-valued responses

“…In this work we presented a predictive modeling approach for response objects occupying non-linear manifold spaces. The regression methodology is based on a distance modification of the RF algorithm that we previously published [16], which decouples the model's training from the problem of response representation. For prediction purposes, we constructed a framework in which point estimates are first predicted on a Euclidean embedding of the response manifold, learned from the training dataset, and then projected back on the original space.…”

“…See [2] for a detailed description of RF. In [16], we presented a modified distance Random Forest (dRF) algorithm, where the split criterion was formulated to depend only on pairwise distances between responses:…”

“…As such, it enables the RF algorithm to be applied in general metric spaces. Previously, we used dRF for regression applications with graph and covariance-based response objects [16]. dRF lends itself naturally to manifold-valued data, whether the manifold in question is analytically defined or implied by the use of a specific distance metric.…”

“…Our objective was to propose a unified framework for regression and prediction of complex objects that is accurate, computationally efficient and can be readily deployed in a variety of applications. In the training phase, we employ our modified Random Forest (RF) regression algorithm that can be trained using only pairwise distances between response observations [16]. The non-parametric RF methodology is efficient and can handle high dimensional input spaces.…”

A review of multivariate analyses in imaging genetics

“…One of strengths of this approach is that genetic markers and imaging biomarkers relevant for both diagnosis and cognitive function are identified. Another new application of learning algorithms in imaging genetics is random forest on distance matrices, where by employing distance measures between input variables, various interactions (away from original space) are modeled and random forest search is used for selection of best sets of features (Sim et al, 2013). While it provides promising results, the requirement for intensive computation and sophisticated modeling may hinder further applications, which is true for other methods too.…”