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31
Spatial Transformations in the Parietal Cortex Using Basis Functions
, 1997
"... Sensorimotor transformations are nonlinear mappings of sensory inputs to motor responses. We explore here the possibility that the responses of single neurons in the parietal cortex serve as basis functions for these transformations. Basis function decomposition is a general method for approximating ..."
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Cited by 100 (7 self)
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Sensorimotor transformations are nonlinear mappings of sensory inputs to motor responses. We explore here the possibility that the responses of single neurons in the parietal cortex serve as basis functions for these transformations. Basis function decomposition is a general method for approximating nonlinear functions that is computationally efficient and well suited for adaptive modification. In particular, the responses of single parietal neurons can be approximated by the product of a Gaussian function of retinal location and a sigmoid function of eye position, called a gain field. A large set of such functions forms a basis set that can be used to perform an arbitrary motor response through a direct projection. We compare this hypothesis with other approaches that are commonly used to model population codes, such as computational maps and vectorial representations. Neither of these alternatives can fully account for the responses of parietal neurons, and they are computationally less efficient for nonlinear transformations. Basis functions also have the advantage of not depending on any coordinate system or reference frame. As a consequence, the position of an object can be represented in multiple reference frames simultaneously, a property consistent with the behavior of hemineglect patients with lesions in the parietal cortex.
Interpreting neuronal population activity by reconstruction: unified framework with application to hippocampal place cells
 J. Neumphysiol
, 1998
"... such as the orientation of a line in the visual field or the location of Two main goals for reconstruction are approached in this the body in space are coded as activity levels in populations of neurons. Reconstruction or decoding is an inverse problem in which paper. The first goal is technical and ..."
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Cited by 98 (6 self)
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such as the orientation of a line in the visual field or the location of Two main goals for reconstruction are approached in this the body in space are coded as activity levels in populations of neurons. Reconstruction or decoding is an inverse problem in which paper. The first goal is technical and is exemplified by the the physical variables are estimated from observed neural activity. population vector method applied to motor cortical activities Reconstruction is useful first in quantifying how much information during various reaching tasks (Georgopoulos et al. 1986, 1989; about the physical variables is present in the population and, second, Schwartz 1994) and the template matching method applied to in providing insight into how the brain might use distributed represen disparity selective cells in the visual cortex (Lehky and Sejnowtations in solving related computational problems such as visual ob ski 1990) and hippocampal place cells during rapid learning of ject recognition and spatial navigation. Two classes of reconstruction place fields in a novel environment (Wilson and McNaughton methods, namely, probabilistic or Bayesian methods and basis func 1993). In these examples, reconstruction extracts information tion methods, are discussed. They include important existing methods from noisy neuronal population activity and transforms it to a
Transfer of Coded Information from Sensory to Motor Networks
, 1995
"... During sensoryguided motor tasks, information must be transferred from arrays of neurons coding target location to motor networks that generate and control movement. We address two basic questions about this information transfer. First, what mechanisms assure that the different neural representatio ..."
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Cited by 87 (14 self)
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During sensoryguided motor tasks, information must be transferred from arrays of neurons coding target location to motor networks that generate and control movement. We address two basic questions about this information transfer. First, what mechanisms assure that the different neural representations align properly so that activity in the sensory network representing target location evokes a motor response generating accurate movement toward the target? Coordinate transformations may be needed to put the sensory data into a form appropriate for use by the motor system. For example, in visually guided reaching the location of a target relative to the body is determined by a combination of the position of its image on the retina and the direction of gaze. What assures that the motor network responds to the appropriate combination of sensory inputs corresponding to target position in body or armcentered coordinates ? To answer these questions, we model a sensory network coding target p...
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 44 (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
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 31 (16 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.
Efficient Markov Chain Monte Carlo methods for decoding population spike trains
 TO APPEAR, NEURAL COMPUTATION
, 2010
"... Stimulus reconstruction or decoding methods provide an important tool for understanding how sensory and motor information is represented in neural activity. We discuss Bayesian decoding methods based on an encoding generalized linear model (GLM) that accurately describes how stimuli are transformed ..."
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Cited by 29 (13 self)
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Stimulus reconstruction or decoding methods provide an important tool for understanding how sensory and motor information is represented in neural activity. We discuss Bayesian decoding methods based on an encoding generalized linear model (GLM) that accurately describes how stimuli are transformed into the spike trains of a group of neurons. The form of the GLM likelihood ensures that the posterior distribution over the stimuli that caused an observed set of spike trains is logconcave so long as the prior is. This allows the maximum a posteriori (MAP) stimulus estimate to be obtained using efficient optimization algorithms. Unfortunately, the MAP estimate can have a relatively large average error when the posterior is highly nonGaussian. Here we compare several Markov chain Monte Carlo (MCMC) algorithms that allow for the calculation of general Bayesian estimators involving posterior expectations (conditional on model parameters). An efficient version of the hybrid Monte Carlo (HMC) algorithm was significantly superior to other MCMC methods for Gaussian priors. When the prior distribution has sharp edges and corners, on the other hand, the “hitandrun” algorithm performed better than other MCMC methods. Using these
A model of movement coordinates in motor cortex: posturedependent changes in the gain and direction of single tuning curves.” Dep. Cognitive and Neural Systems
, 2000
"... This article outlines a methodology for investigating the coordinate systems by which movement variables are encoded in the firing rates of individual motor cortical neurons. Recent neurophysiological experiments have probed the issue of underlying coordinates by examining how cellular preferred dir ..."
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Cited by 18 (1 self)
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This article outlines a methodology for investigating the coordinate systems by which movement variables are encoded in the firing rates of individual motor cortical neurons. Recent neurophysiological experiments have probed the issue of underlying coordinates by examining how cellular preferred directions (as determined by the centerout task! change with posture. Several key experimental findings have resulted that constrain hypotheses about how motor cortical cells encode movement information. But while the significance of shifts in preferred direction is well known and widely accepted, posturedependent changes in the depth of modulation of a cell's tuning curvethat is, gain changeshave not been similarly identified as a means of coordinate inference. This article develops a vector field framework in which the preferred direction and the gain of a cell's tuning curve are viewed as dual components of a unitary response vector. The formalism can be used to compute how each aspect of cell response covaries with posture as a function of the coordinate system in which a given cell is hypothesized to encode its movement information. Such an integrated approach leads to a model of motor cortical cell activity that codifies the following four observations: (i) cell activity correlates with hand movement direction; (ii) cell activity correlates with hand movement speed; (iii) preferred directions vary with posture; and (iv) the modulation depth of tuning curves varies with posture. Finally, the model suggests general methods for testing coordinate hypotheses at the singlecell level and simulates an example protocol for three possible coordinate systems: Cartesian spatial, shouldercentered, and joint angle.
Statistical encoding model for a primary motor cortical brainmachine interface
 IEEE Trans Biomed Eng
"... Abstract—A number of studies of the motor system suggest that the majority of primary motor cortical neurons represent simple movementrelated kinematic and dynamic quantities in their timevarying activity patterns. An example of such an encoding relationship is the cosine tuning of firing rate with ..."
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Cited by 14 (3 self)
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Abstract—A number of studies of the motor system suggest that the majority of primary motor cortical neurons represent simple movementrelated kinematic and dynamic quantities in their timevarying activity patterns. An example of such an encoding relationship is the cosine tuning of firing rate with respect to the direction of hand motion. We present a systematic development of statistical encoding models for movementrelated motor neurons using multielectrode array recordings during a twodimensional (2D) continuous pursuittracking task. Our approach avoids massive averaging of responses by utilizing 2D normalized occupancy plots, cascaded linearnonlinear (LN) system models and a method for describing variability in discrete random systems. We found that the expected firing rate of most movementrelated motor neurons is related to the kinematic values by a linear transformation, with a significant nonlinear distortion in about 1 3 of the neurons. The measured variability of the neural responses is markedly nonPoisson in many neurons and is well captured by a “normalizedGaussian ” statistical model that is defined and introduced here. The statistical model is seamlessly integrated into a nearlyoptimal recursive method for decoding movement from neural responses based on a Sequential Monte Carlo filter. Index Terms—Discrete distribution, LN model, neural decoding, neuroprosthetics, sequential MonteCarlo. I.
A neural model of the cortical representation of egocentric distance
 Cereb Cortex
, 1994
"... Neurons in the visual cortex of monkeys respond selectively to the disparity between the images in the two eyes. Recent recordings have shown that some of the disparityselective neurons in the primary visual cortex and the posterior parietal cortex are modulated by the distance of fixation. A popul ..."
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Cited by 13 (3 self)
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Neurons in the visual cortex of monkeys respond selectively to the disparity between the images in the two eyes. Recent recordings have shown that some of the disparityselective neurons in the primary visual cortex and the posterior parietal cortex are modulated by the distance of fixation. A population of such gainmodulated, disparityselective neurons forms a set of basis functions of horizontal disparity and distance of fixation that can be used as an intermediate representation for computing egocentric distance. This distributed representation is consistent with psychophysical studies of human depth perception; in contrast, neurons explicitly tuned to distance are not consistent with how we perceive distance. In a population model that includes noise in the firing rates of neurons, the perceived distance is
A theory of geometric constraints on neural activity for natural threedimensional movement
 J. Neumsci
, 1999
"... Although the orientation of an arm in space or the static view of an object may be represented by a population of neurons in complex ways, how these variables change with movement often follows simple linear rules, reflecting the underlying geometric constraints in the physical world. A theoretical ..."
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Cited by 8 (1 self)
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Although the orientation of an arm in space or the static view of an object may be represented by a population of neurons in complex ways, how these variables change with movement often follows simple linear rules, reflecting the underlying geometric constraints in the physical world. A theoretical analysis is presented for how such constraints affect the average firing rates of sensory and motor neurons during natural movements with low degrees of freedom, such as a limb movement and rigid object motion. When applied to nonrigid reaching arm movements, the linear theory accounts for cosine directional tuning with linear speed modulation, predicts a curlfree spatial distribution of preferred directions, and also explains why the instantaneous motion of the hand can be recovered from the neural population activity. For threedimensional motion of a rigid object, the theory predicts that, to a first approximation,