An approximate method for Bayesian entropy estimation for a discrete random variable

Yokota, Yasunari

doi:10.1109/iembs.2004.1403100

Cited by 7 publications

(13 citation statements)

References 6 publications

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“…It can be seen that both of the curves, estimated from the time series of the instantaneous phase at narrowband, contain a small linear segment in which the slope converges to constant values as the number of data points increase (number of data points is from 8,000 to 10,000 in this plot). Such a result is consistent with a paper published in 2005 by Yokota [32] , who reported that the entropy value estimated by the conventional Shannon method will not get close to the true value until the samples reach 5,000.…”

Section: Convergence Of Directional Index Calculation Over 8000 Datasupporting

confidence: 82%

Directional Indicator on Neural Oscillations as a Measure of Synaptic Plasticity in Chronic Unpredictable Stress Rats

Zhang¹,

Zheng²,

Quan³

et al. 2011

Neurosignals

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To examine whether the directionality index of neural information flow (NIF) over specific oscillatory bands is useful in measuring synaptic plasticity, we employed the IM approach to determine the direction of NIF between the cortex and thalamus in normal and stressed animals. The experiment was performed by inducing long-term potentiation (LTP) of the thalamocortical pathway after recording local field potential (LFP). Additionally, comparison of IM measurement between broad- and narrowbands was performed, while a numerical study was also carried out for assessing the number of data points. The results show that the instantaneous phases extracted from narrowband vary monotonically, while these phases are jagged in broadband. Our data show that there is a predominant driving effect (coupling directional index d >0) from the thalamus to the frontal cortex in normal animals; however, the value of d is significantly reduced in the chronic stressed group in both the delta and theta bands. Furthermore, the field LTP data show that chronic stress decreases medial prefrontal cortex synaptic plasticity, which is certainly in line with the LFP findings. Together, these data suggest that using an IM algorithm, the directionality index of NIF in specific oscillatory frequency bands will probably be used as a measure of synaptic plasticity.

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Section: Convergence Of Directional Index Calculation Over 8000 Datasupporting

confidence: 82%

Directional Indicator on Neural Oscillations as a Measure of Synaptic Plasticity in Chronic Unpredictable Stress Rats

Zhang¹,

Zheng²,

Quan³

et al. 2011

Neurosignals

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“…If our key mechanism would not be used, this approximate entropy estimator could be used with the other information of message such as source identification, location information, or sensory data themselves for distinguishing unusual events. We pursued to simplify the entropy estimation considering limited capacity of nodes and result in accurate estimation, thus we used an approximate method for Bayesian entropy estimation [9]. Entropy estimation is one of statistical approaches used for distribution comparison where the measurements involved are discrete values.…”

Section: Approximate Entropy Estimator For a Discrete Random Variablementioning

confidence: 99%

“…M-ary entropy function H for a discrete random variable X which takes M sorts of values {a 1 log . Thus, in conventional entropy estimation, occurrence probabilities r of values a are estimated by the maximal likelihood estimation method, i.e., ř = n/N, in which values a are assumed to be included respectively for n ≡ (n 1 ,...,n M ) in the observed sample set of size N. However, unfortunately, the conventional entropy estimator is not optimum in the meaning of least square error [9].…”

Section: Approximate Entropy Estimator For a Discrete Random Variablementioning

confidence: 99%

“…Thus, we use basically the approximated Bayesian entropy estimator [9] as shown in equation (1), instead of the conventional estimator. In the equation (1), the previous work of [9] revealed that s i =0.5 (i=1,...,M), as center, and K=20 were sufficient from the viewpoint of approximation precision, and numerical experiments of [9] demonstrated that the proposed entropy estimation improved the estimation precision of entropy remarkably in comparison to conventional entropy estimation.…”

Section: Approximate Entropy Estimator For a Discrete Random Variablementioning

confidence: 99%

“…The x-axis of this figure is estimate round as time goes on. For the calculation of approximate entropy Bayes H , we use s i =0.5 and K=20 as recommended in [9], M=5 due to 5 key spaces and N=100 or N=500. At each estimate round, the calculation of Bayes H is performed with the new 100 or 500 packets, that is N = δ as the worst case in the view of detection speed.…”

Section: Detection Accuracy and Scalabilitymentioning

confidence: 99%

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Overlapped Detection Via Approximate Entropy Estimation Against Flooding Attack in Mobile Sensor Networks

Kim

Chae

2006

Computational Science – ICCS 2006

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Abstract. To achieve security in sensor networks, it is important to be able to defend against flooding attack recently considered as an extremely threatening attack. In this paper, we propose a flooding attack detection method as the first defense step, through approximate entropy estimation reflecting resource constraints of sensors. Each detector performs both basic estimation for its own region and overlapped estimation for its own and neighbor regions, against the mobility of attack node. Also, in order to enhance the accuracy of detection even in the various deployments of attack agents, we deploy hierarchically detectors according to network topology. This detector by entropy estimation is simplified by only multiplication calculation instead of logarithm, in addition to providing higher estimation precision of entropy compared to the conventional entropy estimation. Our simulation results indicate that this hierarchical defense is a feasible method, being especially promising for accurate decision through overlapped detection even in frequent handoffs of mobile attack agents.

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Information flow among neural networks with Bayesian estimation

Ouyang

et al. 2007

Chin. Sci. Bull.

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Estimating the interaction among neural networks is an interesting issue in neuroscience. Some methods have been proposed to estimate the coupling strength among neural networks; however, few estimations of the coupling direction (information flow) among neural networks have been attempted. It is known that Bayesian estimator is based on a priori knowledge and a probability of event occurrence. In this paper, a new method is proposed to estimate coupling directions among neural networks with conditional mutual information that is estimated by Bayesian estimation. First, this method is applied to analyze the simulated EEG series generated by a nonlinear lumped-parameter model. In comparison with the conditional mutual information with Shannon entropy, it is found that this method is more successful in estimating the coupling direction, and is insensitive to the length of EEG series. Therefore, this method is suitable to analyze a short time series in practice. Second, we demonstrate how this method can be applied to the analysis of human intracranial epileptic electroencephalogram (EEG) recordings, and to indicate the coupling directions among neural networks. Therefore, this method helps to elucidate the epileptic focus localization.phase synchronization, coupling direction, conditional mutual information, Bayesian estimation, epileptic EEG The synchronization analysis in the dynamical system has been a focus of attention in various disciplines [1] . Synchronization phenomena have been found in physical systems and biological systems. A typical example is the cardio respiratory interaction [2] . The synchronization between brain areas is associated with human motion [3] , sleep [4] , learning [5] and consciousness [6] . However, excessive synchronization is likely to result in epileptic seizures [7] . Therefore, it is necessary to develop a method to detect the synchronization occurrences, in particular the coupling direction between brain areas. Rosenblum and his colleagues [1,2] put forward two methods to identify the coupling direction: evolution map approach (EMA) and instantaneous period approach (IPA). The two methods detect a driving or casual relationship through the phase dynamics between two channel signals. EMA and IPA have been successfully utilized to detect the coupling direction between the heart and lungs. As the heart rate and respiration signals are regular (periodical) and less noisy, the EMA and IPA can obtain clear results. It is noted that since the EMA is sensitive to noises, it is not suitable for analyzing noisy and nonstationary EEG recordings. In refs. [8,9], state-space and phase-dynamics approaches have been proposed to detect the weak coupling direction. The same drawbacks as those of EPA and IPA exist.A directionality index based on conditional mutual information is proposed and applied to the instantaneous phases of weakly coupled oscillators [10] , with which the coupling direction between oscillators can be identified. This method is abbreviated to IM in this paper. The adva...

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An approximate method for Bayesian entropy estimation for a discrete random variable

Cited by 7 publications

References 6 publications

Directional Indicator on Neural Oscillations as a Measure of Synaptic Plasticity in Chronic Unpredictable Stress Rats

Directional Indicator on Neural Oscillations as a Measure of Synaptic Plasticity in Chronic Unpredictable Stress Rats

Overlapped Detection Via Approximate Entropy Estimation Against Flooding Attack in Mobile Sensor Networks

Information flow among neural networks with Bayesian estimation

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