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112
Mutual information, Fisher information and population coding
 Neural Computation
, 1998
"... In the context of parameter estimation and model selection, it is only quite recently that a direct link between the Fisher information and information theoretic quantities has been exhibited. We give an interpretation of this link within the standard framework of information theory. We show that in ..."
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Cited by 96 (3 self)
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In the context of parameter estimation and model selection, it is only quite recently that a direct link between the Fisher information and information theoretic quantities has been exhibited. We give an interpretation of this link within the standard framework of information theory. We show that in the context of population coding, the mutual information between the activity of a large array of neurons and a stimulus to which the neurons are tuned is naturally related to the Fisher information. In the light of this result we consider the optimization of the tuning curves parameters in the case of neurons responding to a stimulus represented by an angular variable. To appear in Neural Computation Vol. 10, Issue 7, published by the MIT press. 1 Laboratory associated with C.N.R.S. (U.R.A. 1306), ENS, and Universities Paris VI and Paris VII 1 Introduction A natural framework to study how neurons communicate, or transmit information, in the nervous system is information theory (see e...
Bayesian computation in recurrent neural circuits
 Neural Computation
, 2004
"... A large number of human psychophysical results have been successfully explained in recent years using Bayesian models. However, the neural implementation of such models remains largely unclear. In this paper, we show that a network architecture commonly used to model the cerebral cortex can implem ..."
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Cited by 94 (4 self)
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A large number of human psychophysical results have been successfully explained in recent years using Bayesian models. However, the neural implementation of such models remains largely unclear. In this paper, we show that a network architecture commonly used to model the cerebral cortex can implement Bayesian inference for an arbitrary hidden Markov model. We illustrate the approach using an orientation discrimination task and a visual motion detection task. In the case of orientation discrimination, we show that the model network can infer the posterior distribution over orientations and correctly estimate stimulus orientation in the presence of significant noise. In the case of motion detection, we show that the resulting model network exhibits direction selectivity and correctly computes the posterior probabilities over motion direction and position. When used to solve the wellknown random dots motion discrimination task, the model generates responses that mimic the activities of evidenceaccumulating neurons in cortical areas LIP and FEF. The framework introduced in the paper posits a new interpretation of cortical activities in terms of log posterior probabilities of stimuli occurring in the natural world. 1 1
Maximum likelihood estimation of a stochastic integrateandfire neural encoding model
, 2004
"... We examine a cascade encoding model for neural response in which a linear filtering stage is followed by a noisy, leaky, integrateandfire spike generation mechanism. This model provides a biophysically more realistic alternative to models based on Poisson (memoryless) spike generation, and can eff ..."
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Cited by 83 (24 self)
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We examine a cascade encoding model for neural response in which a linear filtering stage is followed by a noisy, leaky, integrateandfire spike generation mechanism. This model provides a biophysically more realistic alternative to models based on Poisson (memoryless) spike generation, and can effectively reproduce a variety of spiking behaviors seen in vivo. We describe the maximum likelihood estimator for the model parameters, given only extracellular spike train responses (not intracellular voltage data). Specifically, we prove that the log likelihood function is concave and thus has an essentially unique global maximum that can be found using gradient ascent techniques. We develop an efficient algorithm for computing the maximum likelihood solution, demonstrate the effectiveness of the resulting estimator with numerical simulations, and discuss a method of testing the model’s validity using timerescaling and density evolution techniques.
Bayesian Population Decoding of Motor Cortical Activity Using a Kalman Filter
, 2006
"... Effective neural motor prostheses require a method for decoding neural activity representing desired movement. In particular, the accurate reconstruction of a continuous motion signal is necessary for the control of devices such as computer cursors, robots, or a patient’s own paralyzed limbs. For su ..."
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Cited by 82 (12 self)
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Effective neural motor prostheses require a method for decoding neural activity representing desired movement. In particular, the accurate reconstruction of a continuous motion signal is necessary for the control of devices such as computer cursors, robots, or a patient’s own paralyzed limbs. For such applications, we developed a realtime system that uses Bayesian inference techniques to estimate hand motion from the firing rates of multiple neurons. In this study, we used recordings that were previously made in the arm area of primary motor cortex in awake behaving monkeys using a chronically implanted multielectrode microarray. Bayesian inference involves computing the posterior probability of the hand motion conditioned on a sequence of observed firing rates; this is formulated in terms of the product of a likelihood and a prior. The likelihood term models the probability of firing rates given a particular hand motion. We found that a linear gaussian model could be used to approximate this likelihood and could be readily learned from a small amount
Population coding of shape in area V4.
 Nature Neuroscience,
, 2002
"... Shape information is distributed across populations of neurons in the ventral pathway of primate visual cortex 1,2 . The population code for shape has to accommodate the virtual infinity of possible objects as well as the variability of a given object's retinal image. This difficult representa ..."
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Cited by 66 (2 self)
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Shape information is distributed across populations of neurons in the ventral pathway of primate visual cortex 1,2 . The population code for shape has to accommodate the virtual infinity of possible objects as well as the variability of a given object's retinal image. This difficult representational problem could be solved by encoding shapes in terms of their component parts Most studies of neural population coding have focused on representation of a single scalar value. A wellknown example is the work showing that neural populations in macaque primary motor cortex (M1) encode arm reach direction Population coding of shape in area V4 Our analysis was based on twodimensional (2D) Gaussian functions in a curvature × angular position domain. For each V4 neuron in our sample, we determined the Gaussian that best described the curvature and position of boundary fragments (embedded in complete shapes) to which the neuron responded. The population response to a given shape was estimated by weighting each Gaussian peak by the corresponding neuron's response to that shape and then summing across neurons. The weighted sum contained peaks representing the major boundary features of the shape. The accuracy of this representation was confirmed by using the population peak values to reconstruct an approximation to the original shape. RESULTS We estimated populationlevel representations of moderately complex silhouettetype shapes in macaque monkey area V4. We based these estimates on the responses of 109 V4 neurons that showed sensitivity to complex shape in preliminary tests. Boundary shape tuning in such cells can be conveniently (though not necessarily uniquely) characterized in terms of boundary curvature and angular position 20 . These dimensions capture the two critical elements of a partsbased representation: part shape (curvature) and part position (specifically objectcentered position 32 ). The stimulus set
A new look at statespace models for neural data
 Journal of Computational Neuroscience
, 2010
"... State space methods have proven indispensable in neural data analysis. However, common methods for performing inference in statespace models with nonGaussian observations rely on certain approximations which are not always accurate. Here we review direct optimization methods that avoid these appro ..."
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Cited by 53 (25 self)
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State space methods have proven indispensable in neural data analysis. However, common methods for performing inference in statespace models with nonGaussian observations rely on certain approximations which are not always accurate. Here we review direct optimization methods that avoid these approximations, but that nonetheless retain the computational efficiency of the approximate methods. We discuss a variety of examples, applying these direct optimization techniques to problems in spike train smoothing, stimulus decoding, parameter estimation, and inference of synaptic properties. Along the way, we point out connections to some related standard statistical methods, including spline smoothing and isotonic regression. Finally, we note that the computational methods reviewed here do not in fact depend on the statespace setting at all; instead, the key property we are exploiting involves the bandedness of certain matrices. We close by discussing some applications of this more general point of view, including Markov chain Monte Carlo methods for neural decoding and efficient estimation of spatiallyvarying firing rates.
Reconstruction of natural scenes from ensemble responses in the lateral geniculate nucleus
 J. Neurosci.
, 1999
"... A major challenge in studying sensory processing is to understand the meaning of the neural messages encoded in the spiking activity of neurons. From the recorded responses in a sensory circuit, what information can we extract about the outside world? Here we used a linear decoding technique to rec ..."
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Cited by 50 (4 self)
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A major challenge in studying sensory processing is to understand the meaning of the neural messages encoded in the spiking activity of neurons. From the recorded responses in a sensory circuit, what information can we extract about the outside world? Here we used a linear decoding technique to reconstruct spatiotemporal visual inputs from ensemble responses in the lateral geniculate nucleus (LGN) of the cat. From the activity of 177 cells, we have reconstructed natural scenes with recognizable moving objects. The quality of reconstruction depends on the number of cells. For each point in space, the quality of reconstruction begins to saturate at six to eight pairs of on and off cells, approaching the estimated coverage factor in the LGN of the cat. Thus, complex visual inputs can be reconstructed with a simple decoding algorithm, and these analyses provide a basis for understanding ensemble coding in the early visual pathway. Key words: LGN; reconstruction; natural scenes; ensemble responses; cat; visual system The foundation of our current knowledge of sensory processing was established by characterizing neuronal responses to various sensory stimuli The decoding approach has been used to study several sensory systems As a step toward understanding visual coding in the natural environment, we used natural scenes as visual stimuli in the current study. Although simple artificial stimuli are very useful in characterizing response properties of sensory neurons, the task of the brain is primarily to process information in the natural environment. Natural scenes are known to have characteristic statistical properties (see, for example, In this study, we reconstructed spatiotemporal natural scenes (movies) from recorded responses in the LGN. The reconstruction algorithm takes into consideration not only the response properties of the neurons, but also the statistics of natural scenes
Commoninput models for multiple neural spiketrain data
 Data, Network: Comput. Neural Syst
, 2006
"... Recent developments in multielectrode recordings enable the simultaneous measurement of the spiking activity of many neurons. Analysis of such multineuronal data is one of the key challenges in computational neuroscience today. In this work, we develop a multivariate pointprocess model in which th ..."
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Cited by 50 (20 self)
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Recent developments in multielectrode recordings enable the simultaneous measurement of the spiking activity of many neurons. Analysis of such multineuronal data is one of the key challenges in computational neuroscience today. In this work, we develop a multivariate pointprocess model in which the observed activity of a network of neurons depends on three terms: 1) the experimentallycontrolled stimulus; 2) the spiking history of the observed neurons; and 3) a latent noise source that corresponds, for example, to “common input ” from an unobserved population of neurons that is presynaptic to two or more cells in the observed population. We develop an expectationmaximization algorithm for fitting the model parameters; here the expectation step is based on a continuoustime implementation of the extended Kalman smoother, and the maximization step involves two concave maximization problems which may be solved in parallel. The techniques developed allow us to solve a variety of inference problems in a straightforward, computationally efficient fashion; for example, we may use the model to predict network activity given an arbitrary stimulus, infer a neuron’s firing rate given the stimulus and the activity of the other observed neurons, and perform optimal stimulus decoding and prediction. We present several detailed simulation studies which explore the strengths and limitations of our approach. 1
On Decoding the Responses of a Population of Neurons from Short Time Windows
, 1999
"... The effectiveness of various stimulus identification (decoding) procedures for extracting the information carried by the responses of a population of neurons to a set of repeatedly presented stimuli is studied analytically, in the limit of short time windows. It is shown that in this limit, the enti ..."
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Cited by 46 (5 self)
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The effectiveness of various stimulus identification (decoding) procedures for extracting the information carried by the responses of a population of neurons to a set of repeatedly presented stimuli is studied analytically, in the limit of short time windows. It is shown that in this limit, the entire information content of the responses can sometimes be decoded, and when this is not the case, the lost information is quantified. In particular, the mutual information extracted by taking into account only the most likely stimulus in each trial turns out to be, if not equal, much closer to the true value than that calculated from all the probabilities that each of the possible stimuli in the set was the actual one. The relation between the mutual information extracted by decoding and the percentage of correct stimulus decodings is also derived analytically in the same limit, showing that the metric content index can be estimated reliably from a few cells recorded from brief periods. Computer simulations as well as the activity of real neurons recorded in the primate hippocampus serve to confirm these results and illustrate the utility and limitations of the approach.
Preplay of future place cell sequences by hippocampal cellular assemblies.
 Nature
, 2011
"... During spatial exploration, hippocampal neurons show a sequential firing pattern in which individual neurons fire specifically at particular locations along the animal's trajectory (place cells We recorded neuronal firing sequences from the CA1 area of the mouse hippocampus ( To quantify the ..."
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Cited by 40 (1 self)
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During spatial exploration, hippocampal neurons show a sequential firing pattern in which individual neurons fire specifically at particular locations along the animal's trajectory (place cells We recorded neuronal firing sequences from the CA1 area of the mouse hippocampus ( To quantify the significance of preplay and to compare it with replay, we created place cell sequence templates according to the spatial order of the peak firing of place cells 3,4,10 on the novel arm during ContigRun (novel arm templates; subpanels c in 24 ; 23 ; Using the familiar track templates and spiking events during FamRest, constructed as above, we determined that 16.2% (P , 10 291 ; data not shown) were significant replay events