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111
Correlated firing in macaque visual area MT: Time scales and relationship to behavior
 Journal of Neuroscience
, 2001
"... We studied the simultaneous activity of pairs of neurons recorded with a single electrode in visual cortical area MT while monkeys performed a direction discrimination task. Previously, we reported the strength of interneuronal correlation of spike count on the time scale of the behavioral epoch (2 ..."
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Cited by 36 (1 self)
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We studied the simultaneous activity of pairs of neurons recorded with a single electrode in visual cortical area MT while monkeys performed a direction discrimination task. Previously, we reported the strength of interneuronal correlation of spike count on the time scale of the behavioral epoch (2 sec) and noted its potential impact on signal pooling (Zohary et al., 1994). We have now examined correlation at longer and shorter time scales and found that pairwise crosscorrelation was predominantly short term (10–100 msec). Narrow, central peaks in the spike train crosscorrelograms were largely responsible for correlated spike counts on the time scale of the behavioral epoch. Longerterm (many seconds to minutes) changes in the responsiveness of single neurons were observed in autocorrelations; however, these slow changes in time were on average uncorrelated between neurons. Knowledge of the limited time A fundamental problem in sensory neuroscience is to understand how psychophysical performance is related to the signaling capacities of single sensory neurons. It is now widely recognized that no satisfactory solution to this problem can be achieved in the absence of detailed knowledge concerning correlated firing within the pool of sensory neurons contributing to a particular psychophysical judgment (Johnson et al., 1973; Johnson, 1980;
Neuronal Tuning: To Sharpen or Broaden?
, 1999
"... Sensory and motor variables are typically represented by a population of broadly tuned neurons. A coarser representation with broader tuning can often improve coding accuracy, but sometimes the accuracy may also improve with sharper tuning. The theoretical analysis here shows that the relationship b ..."
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Cited by 30 (1 self)
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Sensory and motor variables are typically represented by a population of broadly tuned neurons. A coarser representation with broader tuning can often improve coding accuracy, but sometimes the accuracy may also improve with sharper tuning. The theoretical analysis here shows that the relationship between tuning width and accuracy depends crucially on the dimension of the encoded variable. A general rule is derived for how the Fisher information scales with the tuning width, regardless of the exact shape of the tuning function, the probability distribution of spikes, and allowing some correlated noise between neurons. These results demonstrate a universal dimensionality effect in neural population coding.
Synergy, Redundancy, and Independence in Population Codes
 The Journal of Neuroscience
, 2003
"... A key issue in understanding the neural code for an ensemble of neurons is the nature and strength of correlations between neurons and how these correlations are related to the stimulus. The issue is complicated by the fact that there is not a single notion of independence or lack of correlation. We ..."
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Cited by 29 (0 self)
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A key issue in understanding the neural code for an ensemble of neurons is the nature and strength of correlations between neurons and how these correlations are related to the stimulus. The issue is complicated by the fact that there is not a single notion of independence or lack of correlation. We distinguish three kinds: (1) activity independence; (2) conditional independence; and (3) information independence. Each notion is related to an information measure: the information between cells, the information between cells given the stimulus, and the synergy of cells about the stimulus, respectively. We show that these measures form an interrelated framework for evaluating contributions of signal and noise correlations to the joint information conveyed about the stimulus and that at least two of the three measures must be calculated to characterize a population code. This framework is compared with others recently proposed in the literature. In addition, we distinguish questions about how information is encoded by a population of neurons from how that information can be decoded. Although information theory is natural and powerful for questions of encoding, it is not sufficient for characterizing the process of decoding. Decoding fundamentally requires an error measure that quantifies the importance of the deviations of estimated stimuli from actual stimuli. Because there is no a priori choice of error measure, questions about decoding cannot be put on the same level of generality as for encoding.
Neural Noise and MovementRelated Codes in the Macaque Supplementary Motor Area
 The Journal of Neuroscience
, 2003
"... We analyzed the variability of spike counts and the coding capacity of simultaneously recorded pairs of neurons in the macaque supplementary motor area (SMA). We analyzed the meanvariance functions for single neurons, as well as signal and noise correlations between pairs of neurons. All three stat ..."
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Cited by 26 (2 self)
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We analyzed the variability of spike counts and the coding capacity of simultaneously recorded pairs of neurons in the macaque supplementary motor area (SMA). We analyzed the meanvariance functions for single neurons, as well as signal and noise correlations between pairs of neurons. All three statistics showed a strong dependence on the bin width chosen for analysis. Changes in the correlation structure of single neuron spike trains over different bin sizes affected the meanvariance function, and signal and noise correlations between pairs of neurons were much smaller at small bin widths, increasing monotonically with the width of the bin. Analyses in the frequency domain showed that the noise between pairs of neurons, on average, was most strongly correlated at low frequencies, which explained the increase in noise correlation with increasing bin width. The coding performance was analyzed to determine whether the temporal precision of spike arrival times and the interactions within and between neurons could improve the prediction of the upcoming movement. We found that in �62 % of neuron pairs, the arrival times of spikes at a resolution between 66 and 40 msec carried more information than spike counts in a 200 msec bin. In addition, in 19 % of neuron pairs, inclusion of within (11%) or betweenneuron (8%) correlations in spike trains improved decoding accuracy. These results suggest that in some SMA neurons elements of the spatiotemporal pattern of activity may be relevant for neural coding. Key words: spike count variability; correlated noise; monkey; decoding; temporal code; rate code
A Unified Approach to the Study of Temporal, Correlational and Rate Coding
"... We demonstrate that the information contained in the spike occurrence times of a population of neurons can be broken up into a series of terms, each of which reflect something about potential coding mechanisms. This is possible in the coding r'egime in which few spikes are emitted in the relevan ..."
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Cited by 25 (6 self)
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We demonstrate that the information contained in the spike occurrence times of a population of neurons can be broken up into a series of terms, each of which reflect something about potential coding mechanisms. This is possible in the coding r'egime in which few spikes are emitted in the relevant time window. This approach allows us to study the additional information contributed by spike timing beyond that present in the spike counts; to examine the contributions to the whole information of different statistical properties of spike trains, such as firing rates and correlation functions; and forms the basis for a new quantitative procedure for the analysis of simultaneous multiple neuron recordings. It also provides theoretical constraints upon neural coding strategies. We find a transition between two coding r'egimes, depending upon the size of the relevant observation timescale. For time windows shorter than the timescale of the stimulusinduced response fluctuations, t...
Nonlinear Population Codes
, 2004
"... Theoretical and experimental studies of distributed neuronal representations of sensory and behavioral variables usually assume that the tuning of the mean firing rates is the main source of information. However, recent theoretical studies have investigated the effect of crosscorrelations in the tr ..."
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Cited by 24 (2 self)
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Theoretical and experimental studies of distributed neuronal representations of sensory and behavioral variables usually assume that the tuning of the mean firing rates is the main source of information. However, recent theoretical studies have investigated the effect of crosscorrelations in the trialtotrial fluctuations of the neuronal responses on the accuracy of the representation. Assuming that only the firstorder statistics of the neuronal responses are tuned to the stimulus, these studies have shown that in the presence of correlations, similar to those observed experimentally in cortical ensembles of neurons, the amount of information in the population is limited, yielding nonzero error levels even in the limit of infinitely large populations of neurons. In this letter, we study correlated neuronal populations whose higherorder statistics, and in particular response variances, are also modulated by the stimulus. We ask two questions: Does the correlated noise limit the accuracy of the neuronal representation of the stimulus? and, How can a biological mechanism extract most of the information embedded in the higherorder statistics of the neuronal responses? Specifically, we address these questions in the context of a population of neurons coding an angular variable. We show that the information embedded in the variances grows linearly with the population size despite the presence of strong correlated noise. This information cannot be extracted by linear readout schemes, including the linear population vector. Instead, we propose a bilinear readout scheme that involves spatial decorrelation, quadratic nonlinearity, and population vector summation. We show that this nonlinear population vector scheme yields accurate estimates of stimulus parameters, with an efficiency that grows linearly with the population size. This code can be implemented using biologically plausible neurons.
Representational Accuracy of Stochastic Neural Populations
, 2001
"... this article that the choice of a variability model has a major, nontrivial impact on the encoding properties of the neural population. The immense variability of individual response parameters, such as tuning widths or correlation coef#cients, has also been neglected in most previous work. Although ..."
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Cited by 24 (4 self)
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this article that the choice of a variability model has a major, nontrivial impact on the encoding properties of the neural population. The immense variability of individual response parameters, such as tuning widths or correlation coef#cients, has also been neglected in most previous work. Although these parameter variations are always found in empirical data, they were considered functionally insignificant, and hence theoretical studies have almost always assumed uniform parameters throughout the population. We will show here that this uniform case is unfavorable in the sense that the introduction of parameter variability improves the encoding performance
ME (2000) Spatialtemporal distribution of whiskerevoked activity in rat somatosensory cortex and the coding of stimulus location
 J Neurosci
"... Rats use their facial vibrissae (“whiskers”) to locate and identify objects. To learn about the neural coding of contact between whiskers and objects, we investigated the representation of singlevibrissa deflection by populations of cortical neurons. Microelectrode arrays, arranged in a geometric 1 ..."
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Cited by 20 (0 self)
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Rats use their facial vibrissae (“whiskers”) to locate and identify objects. To learn about the neural coding of contact between whiskers and objects, we investigated the representation of singlevibrissa deflection by populations of cortical neurons. Microelectrode arrays, arranged in a geometric 10 � 10 grid, were inserted into the thalamorecipient layers of “barrel cortex” (the vibrissal region of somatosensory cortex) in urethaneanesthetized rats, and neuronal activity across large sets of barrelcolumns was measured. Typically, 5 msec after deflection of a whisker a 0.2 mm 2 focus of activity emerged. It rapidly expanded, doubling in size by 7 msec, before retracting and disappearing 28–59 msec after stimulus onset. The total territory engaged by the stimulus ranged from 0.5 to 2.9 mm 2 (2–11 barrels). Stimulus site dictated the domain of activity. To quantify the coding of whisker location, we applied the population d�
Modelbased decoding, information estimation, and changepoint detection in multineuron spike trains
 UNDER REVIEW, NEURAL COMPUTATION
, 2007
"... Understanding how stimulus information is encoded in spike trains is a central problem in computational neuroscience. Decoding methods provide an important tool for addressing this problem, by allowing us to explicitly read out the information contained in spike responses. Here we introduce several ..."
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Cited by 19 (12 self)
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Understanding how stimulus information is encoded in spike trains is a central problem in computational neuroscience. Decoding methods provide an important tool for addressing this problem, by allowing us to explicitly read out the information contained in spike responses. Here we introduce several decoding methods based on pointprocess neural encoding models (i.e. “forward ” models that predict spike responses to novel stimuli). These models have concave loglikelihood functions, allowing for efficient fitting via maximum likelihood. Moreover, we may use the likelihood of the observed spike trains under the model to perform optimal decoding. We present: (1) a tractable algorithm for computing the maximum a posteriori (MAP) estimate of the stimulus — the most probable stimulus to have generated the observed single or multiplespike train response, given some prior distribution over the stimulus; (2) a Gaussian approximation to the posterior distribution, which allows us to quantify the fidelity with which various stimulus features are encoded; (3) an efficient method for estimating the mutual information between the stimulus and the response; and (4) a framework for the detection of changepoint times (e.g. the time at which the stimulus undergoes a change in mean or variance), by marginalizing over the posterior distribution of stimuli. We show several examples illustrating the performance of these estimators with simulated data.
Population Coding with Correlation and an Unfaithful Model
 Neural Computation
, 2001
"... The present study investigates a population decoding paradigm in which the maximum likelihood inference is based on an unfaithful decoding model (UMLI). This is usually the case for neural population decoding because the encoding process of the brain is not exactly known, or because a simplified ..."
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Cited by 17 (1 self)
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The present study investigates a population decoding paradigm in which the maximum likelihood inference is based on an unfaithful decoding model (UMLI). This is usually the case for neural population decoding because the encoding process of the brain is not exactly known, or because a simplified decoding model is preferred for saving computational cost. We consider an unfaithful decoding model which neglects the pairwise correlation between neuronal activities, and prove that UMLI is asymptotically efficient when the neuronal correlation is uniform or of limitedrange. The performance of UMLI is compared with that of the maximum likelihood inference based on a faithful model and that of the center of mass decoding method. It turns out that UMLI has advantages of decreasing the computational complexity remarkablely and maintaining a highlevel decoding accuracy at the same time. Moreover, UMLI can be implemented by a biologically feasible recurrent network (Pouget et al., ...