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16
Information Geometry on Hierarchy of Probability Distributions
, 2001
"... An exponential family or mixture family of probability distributions has a natural hierarchical structure. This paper gives an “orthogonal” decomposition of such a system based on information geometry. A typical example is the decomposition of stochastic dependency among a number of random variables ..."
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Cited by 106 (8 self)
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An exponential family or mixture family of probability distributions has a natural hierarchical structure. This paper gives an “orthogonal” decomposition of such a system based on information geometry. A typical example is the decomposition of stochastic dependency among a number of random variables. In general, they have a complex structure of dependencies. Pairwise dependency is easily represented by correlation, but it is more difficult to measure effects of pure triplewise or higher order interactions (dependencies) among these variables. Stochastic dependency is decomposed quantitatively into an “orthogonal” sum of pairwise, triplewise, and further higher order dependencies. This gives a new invariant decomposition of joint entropy. This problem is important for extracting intrinsic interactions in firing patterns of an ensemble of neurons and for estimating its functional connections. The orthogonal decomposition is given in a wide class of hierarchical structures including both exponential and mixture families. As an example, we decompose the dependency in a higher order Markov chain into a sum of those in various lower order Markov chains.
Statistical assessment of timevarying dependency between two neurons
 J Neurophysiol
, 2005
"... The joint peristimulus time histogram (JPSTH) provides a visual representation of the dynamics of correlated activity for a pair of neurons. There are many ways to adjust the JPSTH for the timevarying firingrate modulation of each neuron, and then to define a suitable measure of timevarying corre ..."
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Cited by 20 (4 self)
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The joint peristimulus time histogram (JPSTH) provides a visual representation of the dynamics of correlated activity for a pair of neurons. There are many ways to adjust the JPSTH for the timevarying firingrate modulation of each neuron, and then to define a suitable measure of timevarying correlated activity. Our approach is to introduce a statistical model for the timevarying joint spiking activity so that the joint firing rate can be estimated more efficiently. We have applied an adaptive smoothing method, which has been shown to be effective in capturing sudden changes in firing rate, to the ratio of joint firing probability to the probability of firing predicted by independence. A Bootstrap procedure, applicable to both Poisson and nonPoisson data, was used to define a statistical significance test of whether a large ratio could be due to chance alone. A numerical simulation showed that the Bootstrapbased significance test has very nearly the correct rejection probability, and can have markedly better power to detect departures from independence than does an approach based on testing contiguous bins in the JPSTH. In a companion paper (Cai et al. 2004b) we show how this formulation can accommodate latency and timevarying excitability effects, which can confound spike timing effects.
0.2 Synchronous Activity in Cat Visual Cortex Encodes Collinear and Cocircular Contours
"... The primary visual cortex has been viewed as a network of filters or feature detectors (Hubel and Weisel, 1962), but how these features are integrated for object recognition and segmentation is still under debate. Synchronous neural activity has been proposed as a possible foundation for perceiving ..."
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Cited by 17 (2 self)
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The primary visual cortex has been viewed as a network of filters or feature detectors (Hubel and Weisel, 1962), but how these features are integrated for object recognition and segmentation is still under debate. Synchronous neural activity has been proposed as a possible foundation for perceiving coherent, structured visual stimuli (Singer and Gray, 1995). We explored how contour information in primary visual cortex might be embedded in the simultaneous activity of multiple cells. We found that synchrony even exists between cells with wholly different orientation preferences, and that the membership in synchronous groups was stimulusdependent. Our results suggest that synchrony is more reliable than response rates in
Information Geometry on Hierarchical Decomposition of Stochastic Interactions
 IEEE Transaction on Information Theory
, 1999
"... A joint probability distribution represents stochastic dependency among a number of random variables. They in general have complex structure of dependencies. A pairwise dependency is easily represented by correlation, but it is more difficult to extract triplewise or higherorder interactions (depen ..."
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Cited by 14 (3 self)
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A joint probability distribution represents stochastic dependency among a number of random variables. They in general have complex structure of dependencies. A pairwise dependency is easily represented by correlation, but it is more difficult to extract triplewise or higherorder interactions (dependencies) among these variables. They form a hierarchy of dependencies. The present paper decomposes the higher order dependency into an "orthogonal " sum of pairwise, triplewise and further higherorder dependencies, by using Information Geometry. This naturally gives a new invariant decomposition of joint entropy. This problem is important for extracting intrinsic interactions in firing patterns of an ensemble of neurons and for estimating its functional connections. The results are generalized to give an orthogonal decomposition in a wide class of hierarchical structures. As an example, we decompose higher order Markov chains into various lower order Markov 1 chains. This type of decompo...
InformationGeometric Decomposition in Spike Analysis
 Diettrich, S. Becker, Z. Ghahramani (Eds.), NIPS
, 2001
"... We present an informationgeometric measure to systematically investigate neuronal firing patterns, taking account not only of the secondorder but also of higherorder interactions. We begin with the case of two neurons for illustration and show how to test whether or not any pairwise correlati ..."
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Cited by 7 (3 self)
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We present an informationgeometric measure to systematically investigate neuronal firing patterns, taking account not only of the secondorder but also of higherorder interactions. We begin with the case of two neurons for illustration and show how to test whether or not any pairwise correlation in one period is significantly different from that in the other period. In order to test such a hypothesis of different firing rates, the correlation term needs to be singled out `orthogonally' to the firing rates, where the null hypothesis might not be of independent firing. This method is also shown to directly associate neural firing with behavior via their mutual information, which is decomposed into two types of information, conveyed by mean firing rate and coincident firing, respectively.
Cooperative and Competitive Interactions Facilitate Stereo Computations in Macaque Primary Visual Cortex
, 2009
"... Inferring depth from binocular disparities is a difficult problem for the visual system because local features in the left and righteye images must be matched correctly to solve this “stereo correspondence problem. ” Cortical architecture and computational studies suggest that lateral interactions ..."
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Cited by 7 (4 self)
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Inferring depth from binocular disparities is a difficult problem for the visual system because local features in the left and righteye images must be matched correctly to solve this “stereo correspondence problem. ” Cortical architecture and computational studies suggest that lateral interactions among neurons could help resolve local uncertainty about disparity encoded in individual neurons by incorporating contextual constraints. We found that correlated activity among pairs of neurons in primary visual cortex depended both on disparitytuning relationships and the stimuli displayed within the receptive fields of the neurons. Nearby pairs of neurons with distinct disparity tuning exhibited a decrease in spike correlation at competing disparities soon after response onset. Distant neuronal pairs of similar disparity tuning exhibited an increase in spike correlation at mutually preferred disparities. The observed correlated activity and response dynamics suggests that local competitive and distant cooperative interactions improve disparity tuning of individual neurons over time. Such interactions could represent a neural substrate for the principal constraints underlying cooperative stereo algorithms.
Conditional modeling and the jitter method of spike resampling
 Journal of Neurophysiology (2011), Published online
"... Spike Resampling, ” [14] and provides further details, comments, references, and equations that were omitted from this main text in the interest of brevity. To ease referencing, the sectioning of the report follows that of the main text. A few of our remarks in the supplement may be of interest to ..."
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Cited by 6 (1 self)
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Spike Resampling, ” [14] and provides further details, comments, references, and equations that were omitted from this main text in the interest of brevity. To ease referencing, the sectioning of the report follows that of the main text. A few of our remarks in the supplement may be of interest to a broad audience. For quick identification, these highlevel remarks are bordered by a left vertical bar, like the one to the left of this paragraph. The bulk of this document, however, contains technical details about the various simulations and data analyses presented in the main text. These would primarily be of interest to a reader who was hoping to reproduce our methods exactly. There is also a selfcontained Mathematical Appendix at the end of the supplement that provides a more formal treatment of jitter. 1
Statistical Identification of Synchronous Spiking
"... 3 Spike trains and firing rate 5 3.1 Point processes, conditional intensities, and firing rates.............. 7 ..."
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Cited by 4 (3 self)
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3 Spike trains and firing rate 5 3.1 Point processes, conditional intensities, and firing rates.............. 7
A Framework for Evaluating Pairwise and Multiway Synchrony Among StimulusDriven Neurons
"... Several authors have discussed previously the use of loglinear models, often called maximum entropy models, for analyzing spike train data to detect synchrony. The usual loglinear modeling techniques, however, do not allow for timevarying firing rates that typically appear in stimulusdriven (or ac ..."
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Cited by 4 (2 self)
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Several authors have discussed previously the use of loglinear models, often called maximum entropy models, for analyzing spike train data to detect synchrony. The usual loglinear modeling techniques, however, do not allow for timevarying firing rates that typically appear in stimulusdriven (or actiondriven) neurons, nor do they incorporate nonPoisson history effects or covariate effects. We generalize the usual approach, combining point process regression models of individualneuron activity with loglinear models of multiway synchronous interaction. The methods are illustrated with results found in spike trains recorded simultaneously from primary visual cortex. We then go on to assess the amount of data needed to reliably detect multiway spiking.
reactivation
"... A binless correlation measure reduces the variability of memory ..."
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