Search

Data produced by resting-state functional Magnetic Resonance Imaging are widely used to infer brain functional connectivity networks. Such networks correlate neural signals to connect brain regions, which consist in groups of dependent voxels. Previous work has focused on aggregating data across voxels within predefined regions. However, the presence of within-region correlations has noticeable impacts on inter-regional correlation detection, and thus edge identification. To alleviate them, we propose to leverage techniques from the large-scale correlation screening literature, and derive simple and practical characterizations of the mean number of correlation discoveries that flexibly incorporate intra-regional dependence structures. A connectivity network inference framework is then presented. First, inter-regional correlation distributions are estimated. Then, correlation thresholds that can be tailored to one's application are constructed for each edge. Finally, the proposed framework is implemented on synthetic and real-world datasets. This novel approach for handling arbitrary intra-regional correlation is shown to limit false positives while improving true positive rates.

Artificial neural networks are prone to being fooled by carefully perturbed inputs which cause an egregious misclassification. These \textit{adversarial} attacks have been the focus of extensive research. Likewise, there has been an abundance of research in ways to detect and defend against them. We introduce a novel approach of detection and interpretation of adversarial attacks from a graph perspective. For an input image, we compute an associated sparse graph using the layer-wise relevance propagation algorithm \cite{bach15}. Specifically, we only keep edges of the neural network with the highest relevance values. Three quantities are then computed from the graph which are then compared against those computed from the training set. The result of the comparison is a classification of the image as benign or adversarial. To make the comparison, two classification methods are introduced: 1) an explicit formula based on Wasserstein distance applied to the degree of node and 2) a logistic regression. Both classification methods produce strong results which lead us to believe that a graph-based interpretation of adversarial attacks is valuable., Comment: published in Neural Networks

A novel non-parametric estimator of the correlation between grouped measurements of a quantity is proposed in the presence of noise. This work is primarily motivated by functional brain network construction from fMRI data, where brain regions correspond to groups of spatial units, and correlation between region pairs defines the network. The challenge resides in the fact that both noise and intra-regional correlation lead to inconsistent inter-regional correlation estimation using classical approaches. While some existing methods handle either one of these issues, no non-parametric approaches tackle both simultaneously. To address this problem, we propose a trade-off between two procedures: correlating regional averages, which is not robust to intra-regional correlation; and averaging pairwise inter-regional correlations, which is not robust to noise. To that end, we project the data onto a space where Euclidean distance is used as a proxy for sample correlation. We then propose to leverage hierarchical clustering to gather together highly correlated variables within each region prior to inter-regional correlation estimation. We provide consistency results, and empirically show our approach surpasses several other popular methods in terms of quality. We also provide illustrations on real-world datasets that further demonstrate its effectiveness.

Resting state brain functional connectivity quantifies the similarity between brain regions, each of which consists of voxels at which dynamic signals are acquired via neuroimaging techniques such as blood-oxygen-level-dependent signals in functional magnetic resonance imaging. Pearson correlation and similar metrics have been adopted by neuroscientists to estimate inter-regional connectivity, usually after averaging of signals within regions. However, dependencies between signals within each region and the presence of noise could contaminate such inter-regional correlation estimates. We propose a mixed-effects model with a novel covariance structure that explicitly isolates the different sources of variability in the observed BOLD signals, including correlated regional signals, local spatiotemporal variability, and measurement error. Methods for tackling the computational challenges associated with restricted maximum likelihood estimation will be discussed. Large sample properties are discussed and used for uncertainty quantification. Simulation results demonstrate that the parameters of the proposed model parameters can be accurately estimated and is superior to the Pearson correlation of averages in the presence of spatiotemporal noise. The proposed model is also applied to a real data set of BOLD signals collected from rats to construct individual brain networks., Comment: 25 pages, 6 figures

Node role explainability in complex networks is very difficult, yet is crucial in different application domains such as social science, neurosciences or computer science. Many efforts have been made on the quantification of hubs revealing particular nodes in a network using a given structural property. Yet, in several applications, when multiple instances of networks are available and several structural properties appear to be relevant, the identification of node roles remains largely unexplored. Inspired by the node automorphically equivalence relation, we define an equivalence relation on graph nodes associated with any collection of nodal statistics (i.e. any functions on the node-set). This allows us to define new graph global measures: the power coefficient, and the orthogonality score to evaluate the parsimony and heterogeneity of a given nodal statistics collection. In addition, we introduce a new method based on structural patterns to compare graphs that have the same vertices set. This method assigns a value to a node to determine its role distinctiveness in a graph family. Extensive numerical results of our method are conducted on both generative graph models and real data concerning human brain functional connectivity. The differences in nodal statistics are shown to be dependent on the underlying graph structure. Comparisons between generative models and real networks combining two different nodal statistics reveal the complexity of human brain functional connectivity with differences at both global and nodal levels. Using a group of 200 healthy controls connectivity networks, our method computes high correspondence scores among the whole population, to detect homotopy, and finally quantify differences between comatose patients and healthy controls., Comment: 15 pages, 16 figures

In the general setting of long-memory multivariate time series, the long-memory characteristics are defined by two components. The long-memory parameters describe the autocorrelation of each time series. And the long-run covariance measures the coupling between time series, with general phase parameters. It is of interest to estimate the long-memory, long-run covariance and general phase parameters of time series generated by this wide class of models although they are not necessarily Gaussian nor stationary. This estimation is thus not directly possible using real wavelets decomposition or Fourier analysis. Our purpose is to define an inference approach based on a representation using quasi-analytic wavelets. We first show that the covariance of the wavelet coefficients provides an adequate estimator of the covariance structure including the phase term. Consistent estimators based on a local Whittle approximation are then proposed. Simulations highlight a satisfactory behavior of the estimation on finite samples on linear time series and on multivariate fractional Brownian motions. An application on a real neuroscience dataset is presented, where long-memory and brain connectivity are inferred.

Functional magnetic resonance imaging (fMRI) functional connectivity between brain regions is often computed using parcellations defined by functional or structural atlases. Typically, some kind of voxel averaging is performed to obtain a single temporal correlation estimate per region pair. However, several estimators can be defined for this task, with various assumptions and degrees of robustness to local noise, global noise, and region size. In this paper, we systematically present and study the properties of 9 different functional connectivity estimators taking into account the spatial structure of fMRI data, based on a simple fMRI data spatial model. These include 3 existing estimators and 6 novel estimators. We demonstrate the empirical properties of the estimators using synthetic, animal, and human data, in terms of graph structure, repeatability and reproducibility, discriminability, dependence on region size, as well as local and global noise robustness. We prove analytically the link between regional intra-correlation and inter-region correlation, and show that the choice of estimator has a strong influence on inter-correlation values.

In many applications, hypothesis testing is based on an asymptotic distribution of statistics. The aim of this paper is to clarify and extend multiple correction procedures when the statistics are asymptotically Gaussian. We propose a unified framework to prove their asymptotic behavior which is valid in the case of highly correlated tests. We focus on correlation tests where several test statistics are proposed. All these multiple testing procedures on correlations are shown to control FWER. An extensive simulation study on correlation-based graph estimation highlights finite sample behavior, independence on the sparsity of graphs and dependence on the values of correlations. Empirical evaluation of power provides comparisons of the proposed methods. Finally validation of our procedures is proposed on real dataset of rats brain connectivity measured by fMRI. We confirm our theoretical findings by applying our procedures on a full null hypotheses with data from dead rats. Data on alive rats show the performance of the proposed procedures to correctly identify brain connectivity graphs with controlled errors.

Human brain connectome studies aim at extracting and analyzing relevant features associated to pathologies of interest. Usually this consists in modeling the brain connectome as a graph and in using graph metrics as features. A fine brain description requires graph metrics computation at the node level. Given the relatively reduced number of patients in standard cohorts, such data analysis problems fall in the high-dimension low sample size framework. In this context, our goal is to provide a machine learning technique that exhibits flexibility, gives the investigator grip on the features and covariates, allows visualization and exploration, and yields insight into the data and the biological phenomena at stake. The retained approach is dimension reduction in a manifold learning methodology, the originality lying in that one (or several) reduced variables be chosen by the investigator. The proposed method is illustrated on two studies, the first one addressing comatose patients, the second one addressing young versus elderly population comparison. The method sheds light on the graph metrics and underlying neurobiological phenomena., Comment: submitted

Multivariate time series with long-dependence are observed in many applications such as finance , geophysics or neuroscience. Many packages provide estimation tools for univariate settings but few are addressing the problem of long-dependence estimation for multivariate settings. The package multiwave is providing efficient estimation procedures for multivariate time series. Two semi-parametric estimation methods of the long-memory exponents and long-run covariance matrix of time series are implemented. The first one is the Fourier-based estimation proposed by [18] and the second one is a wavelet-based estimation described in [4]. The objective of this paper is to provide an overview of the R package multiwave with its practical application perspectives.

In this paper, we consider the design of wavelet filters based on the Thiran common-factor approach proposed in Selesnick [2001]. This approach aims at building finite impulseresponse filters of a Hilbert-pair of wavelets serving as real and imaginary part of a complexwavelet. Unfortunately it is not possible to construct wavelets which are both finitelysupported and analytic. The wavelet filters constructed using the common-factor approachare then approximately analytic. Thus, it is of interest to control their analyticity. Thepurpose of this paper is to first provide precise and explicit expressions as well as easilyexploitable bounds for quantifying the analytic approximation of this complex wavelet.Then, we prove the existence of such filters enjoying the classical perfect reconstructionconditions, with arbitrarily many vanishing moments.

Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual estimations of correlation can be highly biased due to phase-shifts caused by the differences in the properties of autocorrelation in the processes. To address this issue, we introduce a semiparametric estimation of multivariate long-range dependent processes. The parameters of interest in the model are the vector of the long-range dependence parameters and the long-run covariance matrix, also called functional connectivity in neuroscience. This matrix characterizes coupling between time series. The proposed multivariate wavelet-based Whittle estimation is shown to be consistent for the estimation of both the long-range dependence and the covariance matrix and to encompass both stationary and nonstationary processes. A simulation study and a real data example are presented to illustrate the finite sample behaviour.

This paper addresses the issue of detecting change-points in multivariate time series. The proposed approach differs from existing counterparts by making only weak assumptions on both the change-points structure across series, and the statistical signal distributions. Specifically change-points are not assumed to occur at simultaneous time instants across series, and no specific distribution is assumed on the individual signals. It relies on the combination of a local robust statistical test acting on individual time segments, with a global Bayesian framework able to optimize configurations from multiple local statistics (from segments of a unique time series or multiple time series). Using an extensive experimental set-up, our algorithm is shown to perform well on Gaussian data, with the same results in term of recall and precision as classical approaches, such as the fused lasso and the Bernoulli Gaussian model. Furthermore, it outperforms the reference models in the case of non normal data with outliers. The control of the False Discovery Rate by an acceptance level is confirmed. In the case of multivariate data, the probabilities that simultaneous change-points are shared by some specific time series are learned. We finally illustrate our algorithm with real datasets from energy monitoring and genomic. Segmentations are compared to state-of-the-art approaches based on fused lasso and group fused lasso., Comment: 29 pages, 27 figures

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires a know-how of all the methodological steps of the processing pipeline that manipulates the input brain signals and extract the functional network properties. On the other hand, a knowledge of the neural phenomenon under study is required to perform physiological-relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes.

The work developed in the paper concerns the multivariate fractional Brownian motion (mfBm) viewed through the lens of the wavelet transform. After recalling some basic properties on the mfBm, we calculate the correlation structure of its wavelet transform. We particularly study the asymptotic behavior of the correlation, showing that if the analyzing wavelet has a sufficient number of null first order moments, the decomposition eliminates any possible long-range (inter)dependence. The cross-spectral density is also considered in a second part. Its existence is proved and its evaluation is performed using a von Bahr-Essen like representation of the function $\sign(t) |t|^\alpha$. The behavior of the cross-spectral density of the wavelet field at the zero frequency is also developed and confirms the results provided by the asymptotic analysis of the correlation.

Asymptotic properties of a dimension-robust dependence measure are investigated. It is related to those used in independence tests, but is derivable, thus suitable for independent component analysis. An adjustable kernel allows to accelerate the convergence of the estimator without affecting the bias., Comment: 18 pages, 3 figures, uses natbib.sty