Fast Estimation of L1-Regularized Linear Models in the Mass-Univariate Setting
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SOFTWARE ORIGINAL ARTICLE
Fast Estimation of L1-Regularized Linear Models in the Mass-Univariate Setting Holger Mohr 1 & Hannes Ruge 1
# The Author(s) 2020
Abstract In certain modeling approaches, activation analyses of task-based fMRI data can involve a relatively large number of predictors. For example, in the encoding model approach, complex stimuli are represented in a high-dimensional feature space, resulting in design matrices with many predictors. Similarly, single-trial models and finite impulse response models may also encompass a large number of predictors. In settings where only few of those predictors are expected to be informative, a sparse model fit can be obtained via L1-regularization. However, estimating L1-regularized models requires an iterative fitting procedure, which considerably increases computation time compared to estimating unregularized or L2-regularized models, and complicates the application of L1-regularization on whole-brain data and large sample sizes. Here we provide several functions for estimating L1-regularized models that are optimized for the mass-univariate analysis approach. The package includes a parallel implementation of the coordinate descent algorithm for CPU-only systems and two implementations of the alternating direction method of multipliers algorithm requiring a GPU device. While the core algorithms are implemented in C++/CUDA, data input/output and parameter settings can be conveniently handled via Matlab. The CPU-based implementation is highly memory-efficient and provides considerable speed-up compared to the standard implementation not optimized for the mass-univariate approach. Further acceleration can be achieved on systems equipped with a CUDA-enabled GPU. Using the fastest GPU-based implementation, computation time for whole-brain estimates can be reduced from 9 h to 5 min in an exemplary data setting. Overall, the provided package facilitates the use of L1-regularization for fMRI activation analyses and enables an efficient employment of L1-regularization on whole-brain data and large sample sizes. Keywords fMRI . L1-regularization . Lasso . Sparsity . Encoding model . GPU
Introduction Over the last two decades, various fMRI activation analysis approaches have been established that involve a relatively large number of predictors. For example, single-trial models can be employed to obtain activation estimates for individual experimental trials (Mumford et al. 2012). The single-trial estimates can be subsequently used as input for further Electronic supplementary material The online version of this article (https://doi.org/10.1007/s12021-020-09489-1) contains supplementary material, which is available to authorized users. * Holger Mohr [email protected] 1
Department of Psychology, Technische Universität Dresden, 01062 Dresden, Germany
analyses such as multivariate pattern analyses or connectivity analyses (Mumford et al. 2014; Rissman et al. 2004). As single-trial models require a separate predictor for each experimental trial, the resulting de
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