Fast Estimation of L1-Regularized Linear Models in the Mass-Univariate Setting

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.