Discovering and deciphering relationships across disparate data modalities

Kernel-based joint independence tests for multivariate stationary and non-stationary time series

Multivariate time-series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the accurate statistical modelling and analysis of such systems. Here, we introduce kernel-based statistical tests of joint independence in multivariate time series by extending the d-variable Hilbert-Schmidt independence criterion to encompass both stationary and non-stationary processes, thus allowing broader real-world applications. By leveraging resampling techniques tailored for both single- and multiple-realization time series, we show how the method robustly uncovers significant higher-order dependencies in synthetic examples, including frequency mixing data and logic gates, as well as real-world climate, neuroscience and socio-economic data. Our method adds to the mathematical toolbox for the analysis of multivariate time series and can aid in uncovering high-order interactions in data.

Wavelet coherence phase analysis decodes the universal switching mechanism of Ras GTPase superfamily

The Ras superfamily of GTPases regulate critical cellular processes by shuttling between GTP-bound ON and GDP-bound OFF states. This switching mechanism is attributed to the conformational changes in two loops, SWI and SWII, upon GTP binding and hydrolysis. Since these conformational changes vary across the Ras superfamily, there is no generic parameter to define their functional states. A unique wavelet coherence (WC) analysis-based approach developed here shows that the structural changes in switch regions could be mapped onto the wavelet coherence phase couplings (WPCs). Thus, WPCs could serve as unique parameters to define their functional states. Disentanglement of WPCs in oncogenic GTPases shows how breakdown of structural allostery leads to their aberrant function. These observations stand out even for simulated ensemble of switch region conformers. Overall, for the first time, we show that WPCs could unravel the latent structural deviations in Ras proteins to decode their universal switching mechanism.

The Chi-Square Test of Distance Correlation

Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any type of dependency structure given sufficient sample size. One major bottleneck is the testing process: because the null distribution of distance correlation depends on the underlying random variables and metric choice, it typically requires a permutation test to estimate the null and compute the p-value, which is very costly for large amount of data. To overcome the difficulty, in this paper we propose a chi-square test for distance correlation. Method-wise, the chi-square test is non-parametric, extremely fast, and applicable to bias-corrected distance correlation using any strong negative type metric or characteristic kernel. The test exhibits a similar testing power as the standard permutation test, and can be utilized for K-sample and partial testing. Theory-wise, we show that the underlying chi-square distribution well approximates and dominates the limiting null distribution in upper tail, prove the chi-square test can be valid and universally consistent for testing independence, and establish a testing power inequality with respect to the permutation test.

Evaluation of a personalized functional near infra-red optical tomography workflow using maximum entropy on the mean

In the present study, we proposed and evaluated a workflow of personalized near infra-red optical tomography (NIROT) using functional near-infrared spectroscopy (fNIRS) for spatiotemporal imaging of cortical hemodynamic fluctuations. The proposed workflow from fNIRS data acquisition to local 3D reconstruction consists of: (a) the personalized optimal montage maximizing fNIRS channel sensitivity to a predefined targeted brain region; (b) the optimized fNIRS data acquisition involving installation of optodes and digitalization of their positions using a neuronavigation system; and (c) the 3D local reconstruction using maximum entropy on the mean (MEM) to accurately estimate the location and spatial extent of fNIRS hemodynamic fluctuations along the cortical surface. The workflow was evaluated on finger-tapping fNIRS data acquired from 10 healthy subjects for whom we estimated the reconstructed NIROT spatiotemporal images and compared with functional magnetic resonance imaging (fMRI) results from the same individuals. Using the fMRI activation maps as our reference, we quantitatively compared the performance of two NIROT approaches, the MEM framework and the conventional minimum norm estimation (MNE) method. Quantitative comparisons were performed at both single subject and group-level. Overall, our results suggested that MEM provided better spatial accuracy than MNE, while both methods offered similar temporal accuracy when reconstructing oxygenated (HbO) and deoxygenated hemoglobin (HbR) concentration changes evoked by finger-tapping. Our proposed complete workflow was made available in the brainstorm fNIRS processing plugin-NIRSTORM, thus providing the opportunity for other researchers to further apply it to other tasks and on larger populations.

Eliminating accidental deviations to minimize generalization error and maximize replicability: Applications in connectomics and genomics

Replicability, the ability to replicate scientific findings, is a prerequisite for scientific discovery and clinical utility. Troublingly, we are in the midst of a replicability crisis. A key to replicability is that multiple measurements of the same item (e.g., experimental sample or clinical participant) under fixed experimental constraints are relatively similar to one another. Thus, statistics that quantify the relative contributions of accidental deviations-such as measurement error-as compared to systematic deviations-such as individual differences-are critical. We demonstrate that existing replicability statistics, such as intra-class correlation coefficient and fingerprinting, fail to adequately differentiate between accidental and systematic deviations in very simple settings. We therefore propose a novel statistic, discriminability, which quantifies the degree to which an individual's samples are relatively similar to one another, without restricting the data to be univariate, Gaussian, or even Euclidean. Using this statistic, we introduce the possibility of optimizing experimental design via increasing discriminability and prove that optimizing discriminability improves performance bounds in subsequent inference tasks. In extensive simulated and real datasets (focusing on brain imaging and demonstrating on genomics), only optimizing data discriminability improves performance on all subsequent inference tasks for each dataset. We therefore suggest that designing experiments and analyses to optimize discriminability may be a crucial step in solving the replicability crisis, and more generally, mitigating accidental measurement error.

Functional connectivity of EEG is subject-specific, associated with phenotype, and different from fMRI

A variety of psychiatric, behavioral and cognitive phenotypes have been linked to brain ''functional connectivity'' -- the pattern of correlation observed between different brain regions. Most commonly assessed using functional magnetic resonance imaging (fMRI), here, we investigate the connectivity-phenotype associations with functional connectivity measured with electroencephalography (EEG), using phase-coupling. We analyzed data from the publicly available Healthy Brain Network Biobank. This database compiles a growing sample of children and adolescents, currently encompassing 1657 individuals. Among a variety of assessment instruments we focus on ten phenotypic and additional demographic measures that capture most of the variance in this sample. The largest effect sizes are found for age and sex for both fMRI and EEG. We replicate previous findings of an association of Intelligence Quotient (IQ) and Attention Deficit Hyperactivity Disorder (ADHD) with the pattern of fMRI functional connectivity. We also find an association with socioeconomic status, anxiety and the Child Behavior Checklist Score. For EEG we find a significant connectivity-phenotype relationship with IQ. The actual spatial patterns of functional connectivity are quite different between fMRI and source-space EEG. However, within EEG we observe clusters of functional connectivity that are consistent across frequency bands. Additionally we analyzed reproducibility of functional connectivity. We compare connectivity obtained with different tasks, including resting state, a video and a visual flicker task. For both EEG and fMRI the variation between tasks was smaller than the variability observed between subjects. We also found an increase of reliability with increasing frequency of the EEG, and increased sampling duration. We conclude that, while the patterns of functional connectivity are distinct between fMRI and phase-coupling of EEG, they are nonetheless similar in their robustness to the task, and similar in that idiosyncratic patterns of connectivity predict individual phenotypes.

Toward Community-Driven Big Open Brain Science: Open Big Data and Tools for Structure, Function, and Genetics

As acquiring bigger data becomes easier in experimental brain science, computational and statistical brain science must achieve similar advances to fully capitalize on these data. Tackling these problems will benefit from a more explicit and concerted effort to work together. Specifically, brain science can be further democratized by harnessing the power of community-driven tools, which both are built by and benefit from many different people with different backgrounds and expertise. This perspective can be applied across modalities and scales and enables collaborations across previously siloed communities.

Analysis of brain subnetworks within the context of their whole-brain networks

Analyzing the structure and function of the brain from a network perspective has increased considerably over the past two decades, with regional subnetwork analyses becoming prominent in the recent literature. However, despite the fact that the brain, as a complex system of interacting subsystems (i.e., subnetworks), cannot be fully understood by analyzing its constituent parts as independent elements, most studies extract subnetworks from the whole and treat them as independent networks. This approach entails neglecting their interactions with other brain regions and precludes identifying potential compensatory mechanisms outside the analyzed subnetwork. In this study, using simulated and empirical data, we show that the analysis of brain subnetworks within the context of their whole-brain networks, that is, including their interactions with other brain regions, can yield different outcomes when compared to analyzing them as independent networks. We also provide a multivariate mixed-effects modeling framework that allows analyzing subnetworks within the context of their whole-brain networks, and show that it can better disentangle global (whole-brain) and local (subnetwork) differences when compared to standard t-test analyses. T-test analyses may produce misleading results in identifying complex global and local level differences. The provided multivariate model is an extension of a previously developed model for global, system-level hypotheses about the brain. The modified version detailed here provides the same utilities as the original model-quantifying the relationship between phenotypes and brain connectivity, comparing brain networks among groups, predicting brain connectivity from phenotypes, and simulating brain networks-but for local, subnetwork-level hypotheses.

Network dependence testing via diffusion maps and distance-based correlations

Deciphering the associations between network connectivity and nodal attributes is one of the core problems in network science. The dependency structure and high dimensionality of networks pose unique challenges to traditional dependency tests in terms of theoretical guarantees and empirical performance. We propose an approach to test network dependence via diffusion maps and distance-based correlations. We prove that the new method yields a consistent test statistic under mild distributional assumptions on the graph structure, and demonstrate that it is able to efficiently identify the most informative graph embedding with respect to the diffusion time. The methodology is illustrated on both simulated and real data.