7,893 research outputs found
Causal conditioning and instantaneous coupling in causality graphs
The paper investigates the link between Granger causality graphs recently
formalized by Eichler and directed information theory developed by Massey and
Kramer. We particularly insist on the implication of two notions of causality
that may occur in physical systems. It is well accepted that dynamical
causality is assessed by the conditional transfer entropy, a measure appearing
naturally as a part of directed information. Surprisingly the notion of
instantaneous causality is often overlooked, even if it was clearly understood
in early works. In the bivariate case, instantaneous coupling is measured
adequately by the instantaneous information exchange, a measure that
supplements the transfer entropy in the decomposition of directed information.
In this paper, the focus is put on the multivariate case and conditional graph
modeling issues. In this framework, we show that the decomposition of directed
information into the sum of transfer entropy and information exchange does not
hold anymore. Nevertheless, the discussion allows to put forward the two
measures as pillars for the inference of causality graphs. We illustrate this
on two synthetic examples which allow us to discuss not only the theoretical
concepts, but also the practical estimation issues.Comment: submitte
Tensor Analysis and Fusion of Multimodal Brain Images
Current high-throughput data acquisition technologies probe dynamical systems
with different imaging modalities, generating massive data sets at different
spatial and temporal resolutions posing challenging problems in multimodal data
fusion. A case in point is the attempt to parse out the brain structures and
networks that underpin human cognitive processes by analysis of different
neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the
multimodal, multi-scale nature of neuroimaging data is well reflected by a
multi-way (tensor) structure where the underlying processes can be summarized
by a relatively small number of components or "atoms". We introduce
Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network
notation in order to analyze these models. These diagrams not only clarify
matrix and tensor EEG and fMRI time/frequency analysis and inverse problems,
but also help understand multimodal fusion via Multiway Partial Least Squares
and Coupled Matrix-Tensor Factorization. We show here, for the first time, that
Granger causal analysis of brain networks is a tensor regression problem, thus
allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI
recordings shows the potential of the methods and suggests their use in other
scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE
An Approach to Relate Viewpoints and Modeling Languages
The architectural design of distributed enterprise applications from the viewpoints of different stakeholders has been proposed for some time, for example, as part of RM-ODP and IEEE 1471, and seems now-a-days to gain acceptance in practice. However, much work remains to be done on the relationships between different viewpoints. Failing to relate viewpoints may lead to a collection of viewpoint models that is inconsistent, and may therefore lead to an incorrect implementation. This paper defines an approach that helps designers to relate different viewpoints to each other. Thereby, it helps to enforce the consistency of the overall design. The results of this paper are expected to be particularly interesting for Model Driven Architecture (MDA) projects, since the proposed models can be used for the explicit definition of the models and relationships between models in an MDA trajectory
Markov models for fMRI correlation structure: is brain functional connectivity small world, or decomposable into networks?
Correlations in the signal observed via functional Magnetic Resonance Imaging
(fMRI), are expected to reveal the interactions in the underlying neural
populations through hemodynamic response. In particular, they highlight
distributed set of mutually correlated regions that correspond to brain
networks related to different cognitive functions. Yet graph-theoretical
studies of neural connections give a different picture: that of a highly
integrated system with small-world properties: local clustering but with short
pathways across the complete structure. We examine the conditional independence
properties of the fMRI signal, i.e. its Markov structure, to find realistic
assumptions on the connectivity structure that are required to explain the
observed functional connectivity. In particular we seek a decomposition of the
Markov structure into segregated functional networks using decomposable graphs:
a set of strongly-connected and partially overlapping cliques. We introduce a
new method to efficiently extract such cliques on a large, strongly-connected
graph. We compare methods learning different graph structures from functional
connectivity by testing the goodness of fit of the model they learn on new
data. We find that summarizing the structure as strongly-connected networks can
give a good description only for very large and overlapping networks. These
results highlight that Markov models are good tools to identify the structure
of brain connectivity from fMRI signals, but for this purpose they must reflect
the small-world properties of the underlying neural systems
Distributional Equivalence and Structure Learning for Bow-free Acyclic Path Diagrams
We consider the problem of structure learning for bow-free acyclic path
diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG
models that allow for certain hidden variables. We present a first method for
this problem using a greedy score-based search algorithm. We also prove some
necessary and some sufficient conditions for distributional equivalence of BAPs
which are used in an algorithmic ap- proach to compute (nearly) equivalent
model structures. This allows us to infer lower bounds of causal effects. We
also present applications to real and simulated datasets using our publicly
available R-package
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