3,926 research outputs found
Change Point Methods on a Sequence of Graphs
Given a finite sequence of graphs, e.g., coming from technological,
biological, and social networks, the paper proposes a methodology to identify
possible changes in stationarity in the stochastic process generating the
graphs. In order to cover a large class of applications, we consider the
general family of attributed graphs where both topology (number of vertexes and
edge configuration) and related attributes are allowed to change also in the
stationary case. Novel Change Point Methods (CPMs) are proposed, that (i) map
graphs into a vector domain; (ii) apply a suitable statistical test in the
vector space; (iii) detect the change --if any-- according to a confidence
level and provide an estimate for its time occurrence. Two specific
multivariate CPMs have been designed: one that detects shifts in the
distribution mean, the other addressing generic changes affecting the
distribution. We ground our proposal with theoretical results showing how to
relate the inference attained in the numerical vector space to the graph
domain, and vice versa. We also show how to extend the methodology for handling
multiple change points in the same sequence. Finally, the proposed CPMs have
been validated on real data sets coming from epileptic-seizure detection
problems and on labeled data sets for graph classification. Results show the
effectiveness of what proposed in relevant application scenarios
Brain Activity Mapping from MEG Data via a Hierarchical Bayesian Algorithm with Automatic Depth Weighting
A recently proposed iterated alternating sequential (IAS) MEG inverse solver algorithm, based on the coupling of a hierarchical Bayesian model with computationally efficient Krylov subspace linear solver, has been shown to perform well for both superficial and deep brain sources. However, a systematic study of its ability to correctly identify active brain regions is still missing. We propose novel statistical protocols to quantify the performance of MEG inverse solvers, focusing in particular on how their accuracy and precision at identifying active brain regions. We use these protocols for a systematic study of the performance of the IAS MEG inverse solver, comparing it with three standard inversion methods, wMNE, dSPM, and sLORETA. To avoid the bias of anecdotal tests towards a particular algorithm, the proposed protocols are Monte Carlo sampling based, generating an ensemble of activity patches in each brain region identified in a given atlas. The performance in correctly identifying the active areas is measured by how much, on average, the reconstructed activity is concentrated in the brain region of the simulated active patch. The analysis is based on Bayes factors, interpreting the estimated current activity as data for testing the hypothesis that the active brain region is correctly identified, versus the hypothesis of any erroneous attribution. The methodology allows the presence of a single or several simultaneous activity regions, without assuming that the number of active regions is known. The testing protocols suggest that the IAS solver performs well with both with cortical and subcortical activity estimation
Degree-based goodness-of-fit tests for heterogeneous random graph models : independent and exchangeable cases
The degrees are a classical and relevant way to study the topology of a
network. They can be used to assess the goodness-of-fit for a given random
graph model. In this paper we introduce goodness-of-fit tests for two classes
of models. First, we consider the case of independent graph models such as the
heterogeneous Erd\"os-R\'enyi model in which the edges have different
connection probabilities. Second, we consider a generic model for exchangeable
random graphs called the W-graph. The stochastic block model and the expected
degree distribution model fall within this framework. We prove the asymptotic
normality of the degree mean square under these independent and exchangeable
models and derive formal tests. We study the power of the proposed tests and we
prove the asymptotic normality under specific sparsity regimes. The tests are
illustrated on real networks from social sciences and ecology, and their
performances are assessed via a simulation study
Temporal Evolution of Multiday, Epileptic Functional Networks Prior to Seizure Occurrence
Epilepsy is one of the most common neurological disorders, characterized by the occurrence of repeated seizures. Given that epilepsy is considered a network disorder, tools derived from network neuroscience may confer the valuable ability to quantify the properties of epileptic brain networks. In this study, we use well-established brain network metrics (i.e., mean strength, variance of strength, eigenvector centrality, betweenness centrality) to characterize the temporal evolution of epileptic functional networks over several days prior to seizure occurrence. We infer the networks using long-term electroencephalographic recordings from 12 people with epilepsy. We found that brain network metrics are variable across days and show a circadian periodicity. In addition, we found that in 9 out of 12 patients the distribution of the variance of strength in the day (or even two last days) prior to seizure occurrence is significantly different compared to the corresponding distributions on all previous days. Our results suggest that brain network metrics computed fromelectroencephalographic recordings could potentially be used to characterize brain network changes that occur prior to seizures, and ultimately contribute to seizure warning systems
Direct Estimation of Differences in Causal Graphs
We consider the problem of estimating the differences between two causal
directed acyclic graph (DAG) models with a shared topological order given
i.i.d. samples from each model. This is of interest for example in genomics,
where changes in the structure or edge weights of the underlying causal graphs
reflect alterations in the gene regulatory networks. We here provide the first
provably consistent method for directly estimating the differences in a pair of
causal DAGs without separately learning two possibly large and dense DAG models
and computing their difference. Our two-step algorithm first uses invariance
tests between regression coefficients of the two data sets to estimate the
skeleton of the difference graph and then orients some of the edges using
invariance tests between regression residual variances. We demonstrate the
properties of our method through a simulation study and apply it to the
analysis of gene expression data from ovarian cancer and during T-cell
activation
Clustering time series data by analysing graphical models of connectivity and the application to diagnosis of brain disorders
In this thesis we investigate clustering and classification techniques applied to time series data from multivariate stochastic processes. In particular we focus on extracting features in the form of graphical models of conditional
dependence between the process components. The motivation is to use the techniques on brain EEG data measured from multiple patients and investigate whether it can be used in areas such as medical diagnosis. We look at both the case where the graphical model is estimated based on time series recorded on the scalp and also where the graphical model is estimated based on source signals within the brain. In the first case we use a multiple hypothesis testing approach to build the graphical models and a learning algorithm based on random forests to find patterns within multiple graphical models. In the second case we use independent component analysis (ICA) to extract the source time series and estimate the conditional dependence graphs using partial mutual information. It is of particular note that in this case due to the indeterminacy issues associated with ICA we only know the conditional
dependence graphs up to some unknown permutation of the nodes. To solve this issue we use novel methods based on an extension of graph matching to multiple inputs in order to develop a new clustering algorithm. Finally, we
show how this algorithm can be combined with further information obtained during the ICA phase contained in columns of the unmixing matrix, to create a more powerful method.Open Acces
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