17,858 research outputs found
Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction
There is often latent network structure in spatial and temporal data and the
tools of network analysis can yield fascinating insights into such data. In
this paper, we develop a nonparametric method for network reconstruction from
spatiotemporal data sets using multivariate Hawkes processes. In contrast to
prior work on network reconstruction with point-process models, which has often
focused on exclusively temporal information, our approach uses both temporal
and spatial information and does not assume a specific parametric form of
network dynamics. This leads to an effective way of recovering an underlying
network. We illustrate our approach using both synthetic networks and networks
constructed from real-world data sets (a location-based social media network, a
narrative of crime events, and violent gang crimes). Our results demonstrate
that, in comparison to using only temporal data, our spatiotemporal approach
yields improved network reconstruction, providing a basis for meaningful
subsequent analysis --- such as community structure and motif analysis --- of
the reconstructed networks
Unsupervised robust nonparametric learning of hidden community properties
We consider learning of fundamental properties of communities in large noisy
networks, in the prototypical situation where the nodes or users are split into
two classes according to a binary property, e.g., according to their opinions
or preferences on a topic. For learning these properties, we propose a
nonparametric, unsupervised, and scalable graph scan procedure that is, in
addition, robust against a class of powerful adversaries. In our setup, one of
the communities can fall under the influence of a knowledgeable adversarial
leader, who knows the full network structure, has unlimited computational
resources and can completely foresee our planned actions on the network. We
prove strong consistency of our results in this setup with minimal assumptions.
In particular, the learning procedure estimates the baseline activity of normal
users asymptotically correctly with probability 1; the only assumption being
the existence of a single implicit community of asymptotically negligible
logarithmic size. We provide experiments on real and synthetic data to
illustrate the performance of our method, including examples with adversaries.Comment: Experiments with new types of adversaries adde
Cluster detection in networks using percolation
We consider the task of detecting a salient cluster in a sensor network, that
is, an undirected graph with a random variable attached to each node. Motivated
by recent research in environmental statistics and the drive to compete with
the reigning scan statistic, we explore alternatives based on the percolative
properties of the network. The first method is based on the size of the largest
connected component after removing the nodes in the network with a value below
a given threshold. The second method is the upper level set scan test
introduced by Patil and Taillie [Statist. Sci. 18 (2003) 457-465]. We establish
the performance of these methods in an asymptotic decision- theoretic framework
in which the network size increases. These tests have two advantages over the
more conventional scan statistic: they do not require previous information
about cluster shape, and they are computationally more feasible. We make
abundant use of percolation theory to derive our theoretical results, and
complement our theory with some numerical experiments.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ412 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Low-frequency oscillatory correlates of auditory predictive processing in cortical-subcortical networks: a MEG-study
Emerging evidence supports the role of neural oscillations as a mechanism for predictive information processing across large-scale networks. However, the oscillatory signatures underlying auditory mismatch detection and information flow between brain regions remain unclear. To address this issue, we examined the contribution of oscillatory activity at theta/alpha-bands (4–8/8–13 Hz) and assessed directed connectivity in magnetoencephalographic data while 17 human participants were presented with sound sequences containing predictable repetitions and order manipulations that elicited prediction-error responses. We characterized the spectro-temporal properties of neural generators using a minimum-norm approach and assessed directed connectivity using Granger Causality analysis. Mismatching sequences elicited increased theta power and phase-locking in auditory, hippocampal and prefrontal cortices, suggesting that theta-band oscillations underlie prediction-error generation in cortical-subcortical networks. Furthermore, enhanced feedforward theta/alpha-band connectivity was observed in auditory-prefrontal networks during mismatching sequences, while increased feedback connectivity in the alpha-band was observed between hippocampus and auditory regions during predictable sounds. Our findings highlight the involvement of hippocampal theta/alpha-band oscillations towards auditory prediction-error generation and suggest a spectral dissociation between inter-areal feedforward vs. feedback signalling, thus providing novel insights into the oscillatory mechanisms underlying auditory predictive processing
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
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