4,891 research outputs found
Information transfer of an Ising model on a brain network
We implement the Ising model on a structural connectivity matrix describing
the brain at a coarse scale. Tuning the model temperature to its critical
value, i.e. at the susceptibility peak, we find a maximal amount of total
information transfer between the spin variables. At this point the amount of
information that can be redistributed by some nodes reaches a limit and the net
dynamics exhibits signature of the law of diminishing marginal returns, a
fundamental principle connected to saturated levels of production. Our results
extend the recent analysis of dynamical oscillators models on the connectome
structure, taking into account lagged and directional influences, focusing only
on the nodes that are more prone to became bottlenecks of information. The
ratio between the outgoing and the incoming information at each node is related
to the number of incoming links
Universal Estimation of Directed Information
Four estimators of the directed information rate between a pair of jointly
stationary ergodic finite-alphabet processes are proposed, based on universal
probability assignments. The first one is a Shannon--McMillan--Breiman type
estimator, similar to those used by Verd\'u (2005) and Cai, Kulkarni, and
Verd\'u (2006) for estimation of other information measures. We show the almost
sure and convergence properties of the estimator for any underlying
universal probability assignment. The other three estimators map universal
probability assignments to different functionals, each exhibiting relative
merits such as smoothness, nonnegativity, and boundedness. We establish the
consistency of these estimators in almost sure and senses, and derive
near-optimal rates of convergence in the minimax sense under mild conditions.
These estimators carry over directly to estimating other information measures
of stationary ergodic finite-alphabet processes, such as entropy rate and
mutual information rate, with near-optimal performance and provide alternatives
to classical approaches in the existing literature. Guided by these theoretical
results, the proposed estimators are implemented using the context-tree
weighting algorithm as the universal probability assignment. Experiments on
synthetic and real data are presented, demonstrating the potential of the
proposed schemes in practice and the utility of directed information estimation
in detecting and measuring causal influence and delay.Comment: 23 pages, 10 figures, to appear in IEEE Transactions on Information
Theor
The (in)visible hand in the Libor market: an Information Theory approach
This paper analyzes several interest rates time series from the United
Kingdom during the period 1999 to 2014. The analysis is carried out using a
pioneering statistical tool in the financial literature: the complexity-entropy
causality plane. This representation is able to classify different stochastic
and chaotic regimes in time series. We use sliding temporal windows to assess
changes in the intrinsic stochastic dynamics of the time series. Anomalous
behavior in the Libor is detected, especially around the time of the last
financial crisis, that could be consistent with data manipulation.Comment: PACS 89.65.Gh Econophysics; 74.40.De noise and chao
Parameters estimation for spatio-temporal maximum entropy distributions: application to neural spike trains
We propose a numerical method to learn Maximum Entropy (MaxEnt) distributions
with spatio-temporal constraints from experimental spike trains. This is an
extension of two papers [10] and [4] who proposed the estimation of parameters
where only spatial constraints were taken into account. The extension we
propose allows to properly handle memory effects in spike statistics, for large
sized neural networks.Comment: 34 pages, 33 figure
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