Statistical dependencies in the responses of sensory neurons govern both the amount of stimulus information conveyed and the means by which downstream neurons can extract it. Although a variety of measurements indicate the existence of such dependencies 1-3 , their origin and importance for neural coding are poorly understood. Here we analyse the functional significance of correlated firing in a complete population of macaque parasol retinal ganglion cells using a model of multi-neuron spike responses 4,5 . The model, with parameters fit directly to physiological data, simultaneously captures both the stimulus dependence and detailed spatio-temporal correlations in population responses, and provides two insights into the structure of the neural code. First, neural encoding at the population level is less noisy than one would expect from the variability of individual neurons: spike times are more precise, and can be predicted more accurately when the spiking of neighbouring neurons is taken into account. Second, correlations provide additional sensory information: optimal, model-based decoding that exploits the response correlation structure extracts 20% more information about the visual scene than decoding under the assumption of independence, and preserves 40% more visual information than optimal linear decoding 6 . This model-based approach reveals the role of correlated activity in the retinal coding of visual stimuli, and provides a general framework for understanding the importance of correlated activity in populations of neurons.How does the spiking activity of a neural population represent the sensory environment? The answer depends critically on the structure of neuronal correlations, or the tendency of groups of neurons to fire temporally coordinated spike patterns. The statistics of such patterns have been studied in a variety of brain areas, and their significance in the processing and representation of sensory information has been debated extensively 2,3,7-13 .Author Information Reprints and permissions information is available at www.nature.com/reprints. Correspondence and requests for materials should be addressed to J.W.P. (E-mail: pillow@gatsby.ucl.ac.uk). Full Methods and any associated references are available in the online version of the paper at www.nature.com/nature.Supplementary Information is linked to the online version of the paper at www.nature.com/nature. Previous studies have examined visual coding by pairs of neurons 11 and the statistics of simultaneous firing patterns in larger neural populations 14,15 . However, no previous approach has addressed how correlated spiking activity in complete neural populations depends on the pattern of visual stimulation, or has answered the question of how such dependencies affect the encoding of visual stimuli. NIH Public AccessHere we introduce a model-based methodology for studying this problem. We describe the encoding of stimuli in the spike trains of a neural population with a generalized linear model (Fig. 1a), a generalization of th...
SUMMARY We present a modular approach for analyzing calcium imaging recordings of large neuronal ensembles. Our goal is to simultaneously identify the locations of the neurons, demix spatially overlapping components, and denoise and deconvolve the spiking activity from the slow dynamics of the calcium indicator. Our approach relies on a constrained nonnegative matrix factorization that expresses the spatiotemporal fluorescence activity as the product of a spatial matrix that encodes the spatial footprint of each neuron in the optical field and a temporal matrix that characterizes the calcium concentration of each neuron over time. This framework is combined with a novel constrained deconvolution approach that extracts estimates of neural activity from fluorescence traces, to create a spatiotemporal processing algorithm that requires minimal parameter tuning. We demonstrate the general applicability of our method by applying it to in vitro and in vivo multineuronal imaging data, whole-brain light-sheet imaging data, and dendritic imaging data.
We present some new results on the nonparametric estimation of entropy and mutual information. First, we use an exact local expansion of the entropy function to prove almost sure consistency and central limit theorems for three of the most commonly used discretized information estimators. The setup is related to Grenander's method of sieves and places no assumptions on the underlying probability measure generating the data. Second, we prove a converse to these consistency theorems, demonstrating that a misapplication of the most common estimation techniques leads to an arbitrarily poor estimate of the true information, even given unlimited data. This "inconsistency" theorem leads to an analytical approximation of the bias, valid in surprisingly small sample regimes and more accurate than the usual Finally, we note a very useful connection between the bias of entropy estimators and a certain polynomial approximation problem. By casting bias calculation problems in this approximation theory framework, we obtain the best possible generalization of known asymptotic bias results. More interesting, this framework leads to an estimator with some nice properties: the estimator comes equipped with rigorous bounds on the maximum error over all possible underlying probability distributions, and this maximum error turns out to be surprisingly small. We demonstrate the application of this new estimator on both real and simulated data.
The activity of motor cortex (MI) neurons conveys movement intent sufficiently well to be used as a control signal to operate artificial devices, but until now this has called for extensive training or has been confined to a limited movement repertoire. Here we show how activity from a few (7-30) MI neurons can be decoded into a signal that a monkey is able to use immediately to move a computer cursor to any new position in its workspace (14 degrees x 14 degrees visual angle). Our results, which are based on recordings made by an electrode array that is suitable for human use, indicate that neurally based control of movement may eventually be feasible in paralysed humans.
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