Testing for Differences in Gaussian Graphical Models: Applications to Brain Connectivity

Functional brain networks are well described and estimated from data with Gaussian Graphical Models (GGMs), e.g. using sparse inverse covariance estimators. Comparing functional connectivity of subjects in two populations calls for comparing these estimated GGMs. Our goal is to identify differences in GGMs known to have similar structure. We characterize the uncertainty of differences with confidence intervals obtained using a parametric distribution on parameters of a sparse estimator. Sparse penalties enable statistical guarantees and interpretable models even in high-dimensional and low-sample settings. Characterizing the distributions of sparse models is inherently challenging as the penalties produce a biased estimator. Recent work invokes the sparsity assumptions to effectively remove the bias from a sparse estimator such as the lasso. These distributions can be used to give confidence intervals on edges in GGMs, and by extension their differences. However, in the case of comparing GGMs, these estimators do not make use of any assumed joint structure among the GGMs. Inspired by priors from brain functional connectivity we derive the distribution of parameter differences under a joint penalty when parameters are known to be sparse in the difference. This leads us to introduce the debiased multi-task fused lasso, whose distribution can be characterized in an efficient manner. We then show how the debiased lasso and multi-task fused lasso can be used to obtain confidence intervals on edge differences in GGMs. We validate the techniques proposed on a set of synthetic examples as well as neuro-imaging dataset created for the study of autism

Voxel selection in fMRI data analysis based on sparse representation

Multivariate pattern analysis approaches toward detection of brain regions from fMRI data have been gaining attention recently. In this study, we introduce an iterative sparse-representation-based algorithm for detection of voxels in functional MRI (fMRI) data with task relevant information. In each iteration of the algorithm, a linear programming problem is solved and a sparse weight vector is subsequently obtained. The final weight vector is the mean of those obtained in all iterations. The characteristics of our algorithm are as follows: 1) the weight vector (output) is sparse; 2) the magnitude of each entry of the weight vector represents the significance of its corresponding variable or feature in a classification or regression problem; and 3) due to the convergence of this algorithm, a stable weight vector is obtained. To demonstrate the validity of our algorithm and illustrate its application, we apply the algorithm to the Pittsburgh Brain Activity Interpretation Competition 2007 functional fMRI dataset for selecting the voxels, which are the most relevant to the tasks of the subjects. Based on this dataset, the aforementioned characteristics of our algorithm are analyzed, and a comparison between our method with the univariate general-linear-model-based statistical parametric mapping is performed. Using our method, a combination of voxels are selected based on the principle of effective/sparse representation of a task. Data analysis results in this paper show that this combination of voxels is suitable for decoding tasks and demonstrate the effectiveness of our method

Improving accuracy and power with transfer learning using a meta-analytic database

Typical cohorts in brain imaging studies are not large enough for systematic testing of all the information contained in the images. To build testable working hypotheses, investigators thus rely on analysis of previous work, sometimes formalized in a so-called meta-analysis. In brain imaging, this approach underlies the specification of regions of interest (ROIs) that are usually selected on the basis of the coordinates of previously detected effects. In this paper, we propose to use a database of images, rather than coordinates, and frame the problem as transfer learning: learning a discriminant model on a reference task to apply it to a different but related new task. To facilitate statistical analysis of small cohorts, we use a sparse discriminant model that selects predictive voxels on the reference task and thus provides a principled procedure to define ROIs. The benefits of our approach are twofold. First it uses the reference database for prediction, i.e. to provide potential biomarkers in a clinical setting. Second it increases statistical power on the new task. We demonstrate on a set of 18 pairs of functional MRI experimental conditions that our approach gives good prediction. In addition, on a specific transfer situation involving different scanners at different locations, we show that voxel selection based on transfer learning leads to higher detection power on small cohorts.Comment: MICCAI, Nice : France (2012

A Sparse Graph-Structured Lasso Mixed Model for Genetic Association with Confounding Correction

While linear mixed model (LMM) has shown a competitive performance in correcting spurious associations raised by population stratification, family structures, and cryptic relatedness, more challenges are still to be addressed regarding the complex structure of genotypic and phenotypic data. For example, geneticists have discovered that some clusters of phenotypes are more co-expressed than others. Hence, a joint analysis that can utilize such relatedness information in a heterogeneous data set is crucial for genetic modeling. We proposed the sparse graph-structured linear mixed model (sGLMM) that can incorporate the relatedness information from traits in a dataset with confounding correction. Our method is capable of uncovering the genetic associations of a large number of phenotypes together while considering the relatedness of these phenotypes. Through extensive simulation experiments, we show that the proposed model outperforms other existing approaches and can model correlation from both population structure and shared signals. Further, we validate the effectiveness of sGLMM in the real-world genomic dataset on two different species from plants and humans. In Arabidopsis thaliana data, sGLMM behaves better than all other baseline models for 63.4% traits. We also discuss the potential causal genetic variation of Human Alzheimer's disease discovered by our model and justify some of the most important genetic loci.Comment: Code available at https://github.com/YeWenting/sGLM

Identifying progressive imaging genetic patterns via multi-task sparse canonical correlation analysis: a longitudinal study of the ADNI cohort

Motivation Identifying the genetic basis of the brain structure, function and disorder by using the imaging quantitative traits (QTs) as endophenotypes is an important task in brain science. Brain QTs often change over time while the disorder progresses and thus understanding how the genetic factors play roles on the progressive brain QT changes is of great importance and meaning. Most existing imaging genetics methods only analyze the baseline neuroimaging data, and thus those longitudinal imaging data across multiple time points containing important disease progression information are omitted. Results We propose a novel temporal imaging genetic model which performs the multi-task sparse canonical correlation analysis (T-MTSCCA). Our model uses longitudinal neuroimaging data to uncover that how single nucleotide polymorphisms (SNPs) play roles on affecting brain QTs over the time. Incorporating the relationship of the longitudinal imaging data and that within SNPs, T-MTSCCA could identify a trajectory of progressive imaging genetic patterns over the time. We propose an efficient algorithm to solve the problem and show its convergence. We evaluate T-MTSCCA on 408 subjects from the Alzheimer’s Disease Neuroimaging Initiative database with longitudinal magnetic resonance imaging data and genetic data available. The experimental results show that T-MTSCCA performs either better than or equally to the state-of-the-art methods. In particular, T-MTSCCA could identify higher canonical correlation coefficients and capture clearer canonical weight patterns. This suggests that T-MTSCCA identifies time-consistent and time-dependent SNPs and imaging QTs, which further help understand the genetic basis of the brain QT changes over the time during the disease progression. Availability and implementation The software and simulation data are publicly available at https://github.com/dulei323/TMTSCCA. Supplementary information Supplementary data are available at Bioinformatics online