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105
Statistical models for neural encoding, decoding, and optimal stimulus design
 Computational Neuroscience: Progress in Brain Research
, 2006
"... There are two basic problems in the statistical analysis of neural data. The “encoding” problem concerns how information is encoded in neural spike trains: can we predict the spike trains of a neuron (or population of neurons), given an arbitrary stimulus or observed motor response? Conversely, the ..."
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Cited by 31 (15 self)
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There are two basic problems in the statistical analysis of neural data. The “encoding” problem concerns how information is encoded in neural spike trains: can we predict the spike trains of a neuron (or population of neurons), given an arbitrary stimulus or observed motor response? Conversely, the “decoding ” problem concerns how much information is in a spike train: in particular, how well can we estimate the stimulus that gave rise to the spike train? This chapter describes statistical modelbased techniques that in some cases provide a unified solution to these two coding problems. These models can capture stimulus dependencies as well as spike history and interneuronal interaction effects in population spike trains, and are intimately related to biophysicallybased models of integrateandfire type. We describe flexible, powerful likelihoodbased methods for fitting these encoding models and then for using the models to perform optimal decoding. Each of these (apparently quite difficult) tasks turn out to be highly computationally tractable, due to a key concavity property of the model likelihood. Finally, we return to the encoding problem to describe how to use these models to adaptively optimize the stimuli presented to the cell on a trialbytrial basis, in order that we may infer the optimal model parameters as efficiently as possible.
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 30 (17 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
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 30 (20 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.
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 21 (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.
Sequential optimal design of neurophysiology experiments
, 2008
"... Adaptively optimizing experiments has the potential to significantly reduce the number of trials needed to build parametric statistical models of neural systems. However, application of adaptive methods to neurophysiology has been limited by severe computational challenges. Since most neurons are hi ..."
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Cited by 19 (6 self)
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Adaptively optimizing experiments has the potential to significantly reduce the number of trials needed to build parametric statistical models of neural systems. However, application of adaptive methods to neurophysiology has been limited by severe computational challenges. Since most neurons are high dimensional systems, optimizing neurophysiology experiments requires computing highdimensional integrations and optimizations in real time. Here we present a fast algorithm for choosing the most informative stimulus by maximizing the mutual information between the data and the unknown parameters of a generalized linear model (GLM) which we want to fit to the neuron’s activity. We rely on important logconcavity and asymptotic normality properties of the posterior to facilitate the required computations. Our algorithm requires only lowrank matrix manipulations and a 2dimensional search to choose the optimal stimulus. The average running time of these operations scales quadratically with the dimensionality of the GLM, making realtime adaptive experimental design feasible even for highdimensional stimulus and parameter spaces. For example, we
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 16 (11 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
Inferring input nonlinearities in neural encoding models
, 2007
"... Draft to be submitted Abstract. We describe a class of models that can be used to predict how the instantaneous firing rate of a neuron varies in response to a dynamic stimulus. These models are based on learned pointwise nonlinear transforms of the stimulus, followed by a temporal linear filtering ..."
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Cited by 13 (7 self)
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Draft to be submitted Abstract. We describe a class of models that can be used to predict how the instantaneous firing rate of a neuron varies in response to a dynamic stimulus. These models are based on learned pointwise nonlinear transforms of the stimulus, followed by a temporal linear filtering operation on the transformed inputs. In one case, the transformation is the same for all lagtimes. Thus, this “input nonlinearity ” converts the initial numerical representation of the stimulus (e.g. air pressure) to a new representation which is optimal as input to the subsequent linear model (e.g. decibels). We present algorithms for estimating both the input nonlinearity and the linear weights, including regularization techniques, and for quantifying the experimental uncertainty in these estimates. In another approach, the model is generalized to allow a potentially different nonlinear transform of the stimulus value at each lagtime. Although more general, this model is algorithmically more straightforward to fit. However, it contains many more degrees of freedom, and thus requires considerably more data for accurate and precise estimation. The feasibility of these new methods is demonstrated both on synthetic data, and on responses recorded from a neuron in rodent barrel cortex. The models are shown to predict responses to novel data accurately, and to recover several important neuronal response properties. 1
A reproducing kernel Hilbert space framework for spike train signal processing
 Neural Comp
, 2009
"... This paper presents a general framework based on reproducing kernel Hilbert spaces (RKHS) to mathematically describe and manipulate spike trains. The main idea is the definition of inner products to allow spike train signal processing from basic principles while incorporating their statistical descr ..."
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Cited by 11 (7 self)
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This paper presents a general framework based on reproducing kernel Hilbert spaces (RKHS) to mathematically describe and manipulate spike trains. The main idea is the definition of inner products to allow spike train signal processing from basic principles while incorporating their statistical description as point processes. Moreover, because many inner products can be formulated, a particular definition can be crafted to best fit an application. These ideas are illustrated by the definition of a number of spike train inner products. To further elicit the advantages of the RKHS framework, a family of these inner products, called the crossintensity (CI) kernels, is further analyzed in detail. This particular inner product family encapsulates the statistical description from conditional intensity functions of spike trains. The problem of their estimation is also addressed. The simplest of the spike train kernels in this family provides an interesting perspective to other works presented in the literature, as will be illustrated in terms of spike train distance measures. Finally, as an application example, the presented RKHS framework is used to derive from simple principles a clustering algorithm for spike trains.
Spike Inference from Calcium Imaging Using Sequential Monte Carlo Methods
, 2009
"... ABSTRACT As recent advances in calcium sensing technologies facilitate simultaneously imaging action potentials in neuronal populations, complementary analytical tools must also be developed to maximize the utility of this experimental paradigm. Although the observations here are fluorescence movies ..."
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Cited by 11 (4 self)
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ABSTRACT As recent advances in calcium sensing technologies facilitate simultaneously imaging action potentials in neuronal populations, complementary analytical tools must also be developed to maximize the utility of this experimental paradigm. Although the observations here are fluorescence movies, the signals of interest—spike trains and/or time varying intracellular calcium concentrations—are hidden. Inferring these hidden signals is often problematic due to noise, nonlinearities, slow imaging rate, and unknown biophysical parameters. We overcome these difficulties by developing sequential Monte Carlo methods (particle filters) based on biophysical models of spiking, calcium dynamics, and fluorescence. We show that even in simple cases, the particle filters outperform the optimal linear (i.e., Wiener) filter, both by obtaining better estimates and by providing error bars. We then relax a number of our model assumptions to incorporate nonlinear saturation of the fluorescence signal, as well external stimulus and spike history dependence (e.g., refractoriness) of the spike trains. Using both simulations and in vitro fluorescence observations, we demonstrate temporal superresolution by inferring when within a frame each spike occurs. Furthermore, the model parameters may be estimated using expectation maximization with only a very limited amount of data (e.g., ~5–10 s or 5–40 spikes), without the requirement of any simultaneous electrophysiology or imaging experiments.