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

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.

SUBMITTER: Mohr H

PROVIDER: S-EPMC8233242 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BackgroundGraphical Gaussian models are popular tools for the estimation of (undirected) gene association networks from microarray data. A key issue when the number of variables greatly exceeds the number of samples is the estimation of the matrix of partial correlations. Since the (Moore-Penrose) inverse of the sample covariance matrix leads to poor estimates in this scenario, standard methods are inappropriate and adequate regularization techniques are needed. Popular approaches include biased estimates of the covariance matrix and high-dimensional regression schemes, such as the Lasso and Partial Least Squares.ResultsIn this article, we investigate a general framework for combining regularized regression methods with the estimation of Graphical Gaussian models. This framework includes various existing methods as well as two new approaches based on ridge regression and adaptive lasso, respectively. These methods are extensively compared both qualitatively and quantitatively within a simulation study and through an application to six diverse real data sets. In addition, all proposed algorithms are implemented in the R package "parcor", available from the R repository CRAN.ConclusionIn our simulation studies, the investigated non-sparse regression methods, i.e. Ridge Regression and Partial Least Squares, exhibit rather conservative behavior when combined with (local) false discovery rate multiple testing in order to decide whether or not an edge is present in the network. For networks with higher densities, the difference in performance of the methods decreases. For sparse networks, we confirm the Lasso's well known tendency towards selecting too many edges, whereas the two-stage adaptive Lasso is an interesting alternative that provides sparser solutions. In our simulations, both sparse and non-sparse methods are able to reconstruct networks with cluster structures. On six real data sets, we also clearly distinguish the results obtained using the non-sparse methods and those obtained using the sparse methods where specification of the regularization parameter automatically means model selection. In five out of six data sets, Partial Least Squares selects very dense networks. Furthermore, for data that violate the assumption of uncorrelated observations (due to replications), the Lasso and the adaptive Lasso yield very complex structures, indicating that they might not be suited under these conditions. The shrinkage approach is more stable than the regression based approaches when using subsampling.

Project description:A variety of statistical methods, such as admixture models, have been used to estimate genomic breed composition (GBC). These methods, however, tend to produce non-zero components to reference breeds that shared some genomic similarity with a test animal. These non-essential GBC components, in turn, offset the estimated GBC for the breed to which it belongs. As a result, not all purebred animals have 100% GBC of their respective breeds, which statistically indicates an elevated false-negative rate in the identification of purebred animals with 100% GBC as the cutoff. Otherwise, a lower cutoff of estimated GBC will have to be used, which is arbitrary, and the results are less interpretable. In the present study, three admixture models with regularization were proposed, which produced sparse solutions through suppressing the noise in the estimated GBC due to genomic similarities. The regularization or penalty forms included the L1 norm penalty, minimax concave penalty (MCP), and smooth clipped absolute deviation (SCAD). The performances of these regularized admixture models on the estimation of GBC were examined in purebred and composite animals, respectively, and compared to that of the non-regularized admixture model as the baseline model. The results showed that, given optimal values for ?, the three sparsely regularized admixture models had higher power and thus reduced the false-negative rate for the breed identification of purebred animals than the non-regularized admixture model. Of the three regularized admixture models, the two with a non-convex penalty outperformed the one with L1 norm penalty. In the Brangus, a composite cattle breed, estimated GBC were roughly comparable among the four admixture models, but all the four models underestimated the GBC for these composite animals when non-ancestral breeds were included as the reference. In conclusion, the admixture models with sparse regularization gave more parsimonious, consistent and interpretable results of estimated GBC for purebred animals than the non-regularized admixture model. Nevertheless, the utility of regularized admixture models for estimating GBC in crossbred or composite animals needs to be taken with caution.

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

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