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ABSTRACT: Assessing dependence between two sets of spike trains or between a set of input stimuli and the corresponding generated spike trains is crucial in many neuroscientific applications, such as in analyzing functional connectivity among neural assemblies, and in neural coding. Dependence between two random variables is traditionally assessed in terms of mutual information. However, although well explored in the context of real or vector valued random variables, estimating mutual information still remains a challenging issue when the random variables exist in more exotic spaces such as the space of spike trains. In the statistical literature, on the other hand, the concept of dependence between two random variables has been presented in many other ways, e.g. using copula, or using measures of association such as Spearman's ρ, and Kendall's τ. Although these methods are usually applied on the real line, their simplicity, both in terms of understanding and estimating, make them worth investigating in the context of spike train dependence. In this paper, we generalize the concept of association to any abstract metric spaces. This new approach is an attractive alternative to mutual information, since it can be easily estimated from realizations without binning or clustering. It also provides an intuitive understanding of what dependence implies in the context of realizations. We show that this new methodology effectively captures dependence between sets of stimuli and spike trains. Moreover, the estimator has desirable small sample characteristic, and it often outperforms an existing similar metric based approach.
Neural Networks (IJCNN), The 2011 International Joint Conference on; 09/2011
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ABSTRACT: Estimating divergence between two point processes, i.e. probability laws on the space of spike trains, is an essential tool in many computational neuroscience applications, such as change detection and neural coding. However, the problem of estimating divergence, although well studied in the Euclidean space, has seldom been addressed in a more general setting. Since the space of spike trains can be viewed as a metric space, we address the problem of estimating Jensen-Shannon divergence in a metric space using a nearest neighbor based approach. We empirically demonstrate the validity of the proposed estimator, and compare it against other available methods in the context of two-sample problem.
Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on; 06/2011 · 4.63 Impact Factor
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ABSTRACT: Characterizing the dynamics of neural data by a discrete state variable is desirable in experimental analysis and brain-machine interfaces. Previous successes have used dynamical modeling including Hidden Markov Models, but the methods do not always produce meaningful results without being carefully trained or initialized. We propose unsupervised clustering in the spatio-temporal space of neural data using time embedding and a corresponding distance measure. By defining performance measures, the method parameters are investigated for a set of neural and simulated data with promising results. Our investigations demonstrate a different view of how to extract information to maximize the utility of state estimation.
Engineering in Medicine and Biology Society (EMBC), 2010 Annual International Conference of the IEEE; 10/2010
