Construction of point process adaptive filter algorithms for neural systems using sequential Monte Carlo methods

Neural Manifold Constraint for Spike Prediction Models Under Behavioral Reinforcement

Spike prediction models effectively predict downstream spike trains from upstream neural activity for neural prostheses. Such prostheses could potentially restore damaged neural communication pathways using predicted patterns to guide electrical stimulations on downstream. Since the ground truth of downstream neural activity is unavailable for subjects with the damage, reinforcement learning (RL) with behavior-level rewards becomes necessary for model training. However, existing models do not involve any constraint on the generated firing patterns and neglect the correlations among neural activities. Thus, the model outputs can greatly deviate from the natural range of neural activities, causing concerns for clinical usage. This study proposes the neural manifold constraint to solve this problem, shaping RL-generated spike trains in the feature space. The constraint terms describe the first and second order statistics of the neural manifold estimated from neural recordings during subjects' freely moving period. Then, the models can be optimized within the neural manifold by behavioral reinforcement. We test the method to predict primary motor cortex (M1) spikes from medial prefrontal (mPFC) spikes when rats perform the two-lever discrimination task. Results show that the neural activity generated by constrained models resembles the real M1 recordings. Compared with models without constraints, our approach achieves similar behavioral success rates, but reduces the mean squared error of neural firing by 61%. The constraints also increase the model's robustness across data segments and induce realistic neural correlations. Our method provides a promising tool to restore transregional communication with high behavioral performance and more realistic microscopic patterns.

Time-varying generalized linear models: characterizing and decoding neuronal dynamics in higher visual areas

To create a behaviorally relevant representation of the visual world, neurons in higher visual areas exhibit dynamic response changes to account for the time-varying interactions between external (e.g., visual input) and internal (e.g., reward value) factors. The resulting high-dimensional representational space poses challenges for precisely quantifying individual factors' contributions to the representation and readout of sensory information during a behavior. The widely used point process generalized linear model (GLM) approach provides a powerful framework for a quantitative description of neuronal processing as a function of various sensory and non-sensory inputs (encoding) as well as linking particular response components to particular behaviors (decoding), at the level of single trials and individual neurons. However, most existing variations of GLMs assume the neural systems to be time-invariant, making them inadequate for modeling nonstationary characteristics of neuronal sensitivity in higher visual areas. In this review, we summarize some of the existing GLM variations, with a focus on time-varying extensions. We highlight their applications to understanding neural representations in higher visual areas and decoding transient neuronal sensitivity as well as linking physiology to behavior through manipulation of model components. This time-varying class of statistical models provide valuable insights into the neural basis of various visual behaviors in higher visual areas and hold significant potential for uncovering the fundamental computational principles that govern neuronal processing underlying various behaviors in different regions of the brain.

Online Estimating Pairwise Neuronal Functional Connectivity in Brain-Machine Interface

Neurons respond to external stimuli and form functional networks through pairwise interactions. A neural encoding model can describe a single neuron's behavior, and brain-machine interfaces (BMIs) provide a platform to investigate how neurons adapt, functionally connect, and encode movement. Movement modulation and pairwise functional connectivity are modeled as high-dimensional tuning states, estimated from neural spike train observations. However, accurate estimation of this neural state vector can be challenging as pairwise neural interactions are highly dimensional, change in different temporal scales from movement, and could be non-stationary. We propose an Adam-based gradient descent method to online estimate high-dimensional pairwise neuronal functional connectivity and single neuronal tuning adaptation simultaneously. By minimizing negative log-likelihood based on point process observation, the proposed method adaptively adjusts the learning rate for each dimension of the neural state vectors by employing momentum and regularizer. We test the method on real recordings of two rats performing the brain control mode of a two-lever discrimination task. Our results show that our method outperforms existing methods, especially when the state is sparse. Our method is more stable and faster for an online scenario regardless of the parameter initializations. Our method provides a promising tool to track and build the time-variant functional neural connectivity, which dynamically forms the functional network and results in better brain control.

Tracking Fast Neural Adaptation by Globally Adaptive Point Process Estimation for Brain-Machine Interface

Brain-machine interfaces (BMIs) help the disabled restore body functions by translating neural activity into digital commands to control external devices. Neural adaptation, where the brain signals change in response to external stimuli or movements, plays an important role in BMIs. When subjects purely use neural activity to brain-control a prosthesis, some neurons will actively explore a new tuning property to accomplish the movement task. The prediction of this neural tuning property can help subjects adapt more efficiently to brain control and maintain a good decoding performance. Existing prediction methods track the slow change of the tuning property in the manual control, which is not suitable for the fast neural adaptation in brain control. In order to identify the active neurons in brain control and track their tuning property changes, we propose a globally adaptive point process method (GaPP) to estimate the neural modulation state from spike trains, decompose the states into the hyper preferred direction and reconstruct the kinematics in a dual-model framework. We implement the method on real data from rats performing a two-lever discrimination task under manual control and brain control. The results show our method successfully predicts the neural modulation state and identifies the neurons that become active in brain control. Compared to the existing method, ours tracks the fast changes of the hyper preferred direction from manual control to brain control more accurately and efficiently and reconstructs the kinematics better and faster.

Parameter Estimation in Multiple Dynamic Synaptic Coupling Model Using Bayesian Point Process State-Space Modeling Framework

It is of great interest to characterize the spiking activity of individual neurons in a cell ensemble. Many different mechanisms, such as synaptic coupling and the spiking activity of itself and its neighbors, drive a cell's firing properties. Though this is a widely studied modeling problem, there is still room to develop modeling solutions by simplifications embedded in previous models. The first shortcut is that synaptic coupling mechanisms in previous models do not replicate the complex dynamics of the synaptic response. The second is that the number of synaptic connections in these models is an order of magnitude smaller than in an actual neuron. In this research, we push this barrier by incorporating a more accurate model of the synapse and propose a system identification solution that can scale to a network incorporating hundreds of synaptic connections. Although a neuron has hundreds of synaptic connections, only a subset of these connections significantly contributes to its spiking activity. As a result, we assume the synaptic connections are sparse, and to characterize these dynamics, we propose a Bayesian point-process state-space model that lets us incorporate the sparsity of synaptic connections within the regularization technique into our framework. We develop an extended expectation-maximization. algorithm to estimate the free parameters of the proposed model and demonstrate the application of this methodology to the problem of estimating the parameters of many dynamic synaptic connections. We then go through a simulation example consisting of the dynamic synapses across a range of parameter values and show that the model parameters can be estimated using our method. We also show the application of the proposed algorithm in the intracellular data that contains 96 presynaptic connections and assess the estimation accuracy of our method using a combination of goodness-of-fit measures.

Characterizing and dissociating multiple time-varying modulatory computations influencing neuronal activity

In many brain areas, sensory responses are heavily modulated by factors including attentional state, context, reward history, motor preparation, learned associations, and other cognitive variables. Modelling the effect of these modulatory factors on sensory responses has proven challenging, mostly due to the time-varying and nonlinear nature of the underlying computations. Here we present a computational model capable of capturing and dissociating multiple time-varying modulatory effects on neuronal responses on the order of milliseconds. The model’s performance is tested on extrastriate perisaccadic visual responses in nonhuman primates. Visual neurons respond to stimuli presented around the time of saccades differently than during fixation. These perisaccadic changes include sensitivity to the stimuli presented at locations outside the neuron’s receptive field, which suggests a contribution of multiple sources to perisaccadic response generation. Current computational approaches cannot quantitatively characterize the contribution of each modulatory source in response generation, mainly due to the very short timescale on which the saccade takes place. In this study, we use a high spatiotemporal resolution experimental paradigm along with a novel extension of the generalized linear model framework (GLM), termed the sparse-variable GLM, to allow for time-varying model parameters representing the temporal evolution of the system with a resolution on the order of milliseconds. We used this model framework to precisely map the temporal evolution of the spatiotemporal receptive field of visual neurons in the middle temporal area during the execution of a saccade. Moreover, an extended model based on a factorization of the sparse-variable GLM allowed us to disassociate and quantify the contribution of individual sources to the perisaccadic response. Our results show that our novel framework can precisely capture the changes in sensitivity of neurons around the time of saccades, and provide a general framework to quantitatively track the role of multiple modulatory sources over time.

The sensory responses of neurons in many brain areas, particularly those in higher prefrontal or parietal areas, are strongly influenced by factors including task rules, attentional state, context, reward history, motor preparation, learned associations, and other cognitive variables. These modulations often occur in combination, or on fast timescales which present a challenge for both experimental and modelling approaches aiming to describe the underlying mechanisms or computations. Here we present a computational model capable of capturing and dissociating multiple time-varying modulatory effects on spiking responses on the order of milliseconds. The model’s performance is evaluated by testing its ability to reproduce and dissociate multiple changes in visual sensitivity occurring in extrastriate visual cortex around the time of rapid eye movements. No previous model is capable of capturing these changes with as fine a resolution as that presented here. Our model both provides specific insight into the nature and time course of changes in visual sensitivity around the time of eye movements, and offers a general framework applicable to a wide variety of contexts in which sensory processing is modulated dynamically by multiple time-varying cognitive or behavioral factors, to understand the neuronal computations underpinning these modulations and make predictions about the underlying mechanisms.

Efficient Decoding of Multi-Dimensional Signals From Population Spiking Activity Using a Gaussian Mixture Particle Filter

New recording technologies and the potential for closed-loop experiments have led to an increasing demand for computationally efficient and accurate algorithms to decode population spiking activity in multi-dimensional spaces. Exact point process filters can accurately decode low-dimensional signals, but are computationally intractable for high-dimensional signals. Approximate Gaussian filters are computationally efficient, but are inaccurate when the signals have complex distributions and nonlinear dynamics. Even particle filter methods tend to become inefficient and inaccurate when the filter distribution has multiple peaks. Here, we develop a new point process filter algorithm that combines the computational efficiency of approximate Gaussian methods with a numerical accuracy that exceeds standard particle filters. We use a mixture of Gaussian model for the posterior at each time step, allowing for an analytic solution to the computationally expensive filter integration step. During non-spike intervals, the filter needs only to update the mean, covariance, and mixture weight of each component. At spike times, a sampling procedure is used to update the filtering distribution and find the number of Gaussian mixture components necessary to maintain an accurate approximation. We illustrate the application of this algorithm to the problem of decoding a rat's position and velocity in a maze from hippocampal place cell data using both 2-D and 4-D decoders.

Nonlinear Modeling of Neural Interaction for Spike Prediction Using the Staged Point-Process Model

Neurons communicate nonlinearly through spike activities. Generalized linear models (GLMs) describe spike activities with a cascade of a linear combination across inputs, a static nonlinear function, and an inhomogeneous Bernoulli or Poisson process, or Cox process if a self-history term is considered. This structure considers the output nonlinearity in spike generation but excludes the nonlinear interaction among input neurons. Recent studies extend GLMs by modeling the interaction among input neurons with a quadratic function, which considers the interaction between every pair of input spikes. However, quadratic effects may not fully capture the nonlinear nature of input interaction. We therefore propose a staged point-process model to describe the nonlinear interaction among inputs using a few hidden units, which follows the idea of artificial neural networks. The output firing probability conditioned on inputs is formed as a cascade of two linear-nonlinear (a linear combination plus a static nonlinear function) stages and an inhomogeneous Bernoulli process. Parameters of this model are estimated by maximizing the log likelihood on output spike trains. Unlike the iterative reweighted least squares algorithm used in GLMs, where the performance is guaranteed by the concave condition, we propose a modified Levenberg-Marquardt (L-M) algorithm, which directly calculates the Hessian matrix of the log likelihood, for the nonlinear optimization in our model. The proposed model is tested on both synthetic data and real spike train data recorded from the dorsal premotor cortex and primary motor cortex of a monkey performing a center-out task. Performances are evaluated by discrete-time rescaled Kolmogorov-Smirnov tests, where our model statistically outperforms a GLM and its quadratic extension, with a higher goodness-of-fit in the prediction results. In addition, the staged point-process model describes nonlinear interaction among input neurons with fewer parameters than quadratic models, and the modified L-M algorithm also demonstrates fast convergence.

Real-time particle filtering and smoothing algorithms for detecting abrupt changes in neural ensemble spike activity

Sequential change-point detection from time series data is a common problem in many neuroscience applications, such as seizure detection, anomaly detection, and pain detection. In our previous work (Chen Z, Zhang Q, Tong AP, Manders TR, Wang J. J Neural Eng 14: 036023, 2017), we developed a latent state-space model, known as the Poisson linear dynamical system, for detecting abrupt changes in neuronal ensemble spike activity. In online brain-machine interface (BMI) applications, a recursive filtering algorithm is used to track the changes in the latent variable. However, previous methods have been restricted to Gaussian dynamical noise and have used Gaussian approximation for the Poisson likelihood. To improve the detection speed, we introduce non-Gaussian dynamical noise for modeling a stochastic jump process in the latent state space. To efficiently estimate the state posterior that accommodates non-Gaussian noise and non-Gaussian likelihood, we propose particle filtering and smoothing algorithms for the change-point detection problem. To speed up the computation, we implement the proposed particle filtering algorithms using advanced graphics processing unit computing technology. We validate our algorithms, using both computer simulations and experimental data for acute pain detection. Finally, we discuss several important practical issues in the context of real-time closed-loop BMI applications. NEW & NOTEWORTHY Sequential change-point detection is an important problem in closed-loop neuroscience experiments. This study proposes novel sequential Monte Carlo methods to quickly detect the onset and offset of a stochastic jump process that drives the population spike activity. This new approach is robust with respect to spike sorting noise and varying levels of signal-to-noise ratio. The GPU implementation of the computational algorithm allows for parallel processing in real time.

Modeling, Detecting, and Tracking Freezing of Gait in Parkinson Disease Using Inertial Sensors

In this paper, we develop new methods to automatically detect the onset and duration of freezing of gait (FOG) in people with Parkinson disease (PD) in real time, using inertial sensors. We first build a physical model that describes the trembling motion during the FOG events. Then, we design a generalized likelihood ratio test framework to develop a two-stage detector for determining the zero-velocity and trembling events during gait. Thereafter, to filter out falsely detected FOG events, we develop a point-process filter that combines the output of the detectors with information about the speed of the foot, provided by a foot-mounted inertial navigation system. We computed the probability of FOG by using the point-process filter to determine the onset and duration of the FOG event. Finally, we validate the performance of the proposed system design using real data obtained from people with PD who performed a set of gait tasks. We compare our FOG detection results with an existing method that only uses accelerometer data. The results indicate that our method yields 81.03% accuracy in detecting FOG events and a threefold decrease in the false-alarm rate relative to the existing method.

From point process observations to collective neural dynamics: Nonlinear Hawkes process GLMs, low-dimensional dynamics and coarse graining

This review presents a perspective on capturing collective dynamics in recorded neuronal ensembles based on multivariate point process models, inference of low-dimensional dynamics and coarse graining of spatiotemporal measurements. A general probabilistic framework for continuous time point processes reviewed, with an emphasis on multivariate nonlinear Hawkes processes with exogenous inputs. A point process generalized linear model (PP-GLM) framework for the estimation of discrete time multivariate nonlinear Hawkes processes is described. The approach is illustrated with the modeling of collective dynamics in neocortical neuronal ensembles recorded in human and non-human primates, and prediction of single-neuron spiking. A complementary approach to capture collective dynamics based on low-dimensional dynamics ("order parameters") inferred via latent state-space models with point process observations is presented. The approach is illustrated by inferring and decoding low-dimensional dynamics in primate motor cortex during naturalistic reach and grasp movements. Finally, we briefly review hypothesis tests based on conditional inference and spatiotemporal coarse graining for assessing collective dynamics in recorded neuronal ensembles.

Tracking Neural Modulation Depth by Dual Sequential Monte Carlo Estimation on Point Processes for Brain-Machine Interfaces

Classic brain-machine interface (BMI) approaches decode neural signals from the brain responsible for achieving specific motor movements, which subsequently command prosthetic devices. Brain activities adaptively change during the control of the neuroprosthesis in BMIs, where the alteration of the preferred direction and the modulation of the gain depth are observed. The static neural tuning models have been limited by fixed codes, resulting in a decay of decoding performance over the course of the movement and subsequent instability in motor performance. To achieve stable performance, we propose a dual sequential Monte Carlo adaptive point process method, which models and decodes the gradually changing modulation depth of individual neuron over the course of a movement. We use multichannel neural spike trains from the primary motor cortex of a monkey trained to perform a target pursuit task using a joystick. Our results show that our computational approach successfully tracks the neural modulation depth over time with better goodness-of-fit than classic static neural tuning models, resulting in smaller errors between the true kinematics and the estimations in both simulated and real data. Our novel decoding approach suggests that the brain may employ such strategies to achieve stable motor output, i.e., plastic neural tuning is a feature of neural systems. BMI users may benefit from this adaptive algorithm to achieve more complex and controlled movement outcomes.

Monte Carlo point process estimation of electromyographic envelopes from motor cortical spikes for brain-machine interfaces

OBJECTIVE

Representation of movement in the motor cortex (M1) has been widely studied in brain-machine interfaces (BMIs). The electromyogram (EMG) has greater bandwidth than the conventional kinematic variables (such as position, velocity), and is functionally related to the discharge of cortical neurons. As the stochastic information of EMG is derived from the explicit spike time structure, point process (PP) methods will be a good solution for decoding EMG directly from neural spike trains. Previous studies usually assume linear or exponential tuning curves between neural firing and EMG, which may not be true.

APPROACH

In our analysis, we estimate the tuning curves in a data-driven way and find both the traditional functional-excitatory and functional-inhibitory neurons, which are widely found across a rat's motor cortex. To accurately decode EMG envelopes from M1 neural spike trains, the Monte Carlo point process (MCPP) method is implemented based on such nonlinear tuning properties.

MAIN RESULTS

Better reconstruction of EMG signals is shown on baseline and extreme high peaks, as our method can better preserve the nonlinearity of the neural tuning during decoding. The MCPP improves the prediction accuracy (the normalized mean squared error) 57% and 66% on average compared with the adaptive point process filter using linear and exponential tuning curves respectively, for all 112 data segments across six rats. Compared to a Wiener filter using spike rates with an optimal window size of 50 ms, MCPP decoding EMG from a point process improves the normalized mean square error (NMSE) by 59% on average.

SIGNIFICANCE

These results suggest that neural tuning is constantly changing during task execution and therefore, the use of spike timing methodologies and estimation of appropriate tuning curves needs to be undertaken for better EMG decoding in motor BMIs.

Sparse Spectro-Temporal Receptive Fields Based on Multi-Unit and High-Gamma Responses in Human Auditory Cortex

Spectro-Temporal Receptive Fields (STRFs) were estimated from both multi-unit sorted clusters and high-gamma power responses in human auditory cortex. Intracranial electrophysiological recordings were used to measure responses to a random chord sequence of Gammatone stimuli. Traditional methods for estimating STRFs from single-unit recordings, such as spike-triggered-averages, tend to be noisy and are less robust to other response signals such as local field potentials. We present an extension to recently advanced methods for estimating STRFs from generalized linear models (GLM). A new variant of regression using regularization that penalizes non-zero coefficients is described, which results in a sparse solution. The frequency-time structure of the STRF tends toward grouping in different areas of frequency-time and we demonstrate that group sparsity-inducing penalties applied to GLM estimates of STRFs reduces the background noise while preserving the complex internal structure. The contribution of local spiking activity to the high-gamma power signal was factored out of the STRF using the GLM method, and this contribution was significant in 85 percent of the cases. Although the GLM methods have been used to estimate STRFs in animals, this study examines the detailed structure directly from auditory cortex in the awake human brain. We used this approach to identify an abrupt change in the best frequency of estimated STRFs along posteromedial-to-anterolateral recording locations along the long axis of Heschl's gyrus. This change correlates well with a proposed transition from core to non-core auditory fields previously identified using the temporal response properties of Heschl's gyrus recordings elicited by click-train stimuli.

Clusterless Decoding of Position from Multiunit Activity Using a Marked Point Process Filter

Point process filters have been applied successfully to decode neural signals and track neural dynamics. Traditionally these methods assume that multiunit spiking activity has already been correctly spike-sorted. As a result, these methods are not appropriate for situations where sorting cannot be performed with high precision, such as real-time decoding for brain-computer interfaces. Because the unsupervised spike-sorting problem remains unsolved, we took an alternative approach that takes advantage of recent insights into clusterless decoding. Here we present a new point process decoding algorithm that does not require multiunit signals to be sorted into individual units. We use the theory of marked point processes to construct a function that characterizes the relationship between a covariate of interest (in this case, the location of a rat on a track) and features of the spike waveforms. In our example, we use tetrode recordings, and the marks represent a four-dimensional vector of the maximum amplitudes of the spike waveform on each of the four electrodes. In general, the marks may represent any features of the spike waveform. We then use Bayes's rule to estimate spatial location from hippocampal neural activity. We validate our approach with a simulation study and experimental data recorded in the hippocampus of a rat moving through a linear environment. Our decoding algorithm accurately reconstructs the rat's position from unsorted multiunit spiking activity. We then compare the quality of our decoding algorithm to that of a traditional spike-sorting and decoding algorithm. Our analyses show that the proposed decoding algorithm performs equivalent to or better than algorithms based on sorted single-unit activity. These results provide a path toward accurate real-time decoding of spiking patterns that could be used to carry out content-specific manipulations of population activity in hippocampus or elsewhere in the brain.

Neural coding for effective rehabilitation

Successful neurological rehabilitation depends on accurate diagnosis, effective treatment, and quantitative evaluation. Neural coding, a technology for interpretation of functional and structural information of the nervous system, has contributed to the advancements in neuroimaging, brain-machine interface (BMI), and design of training devices for rehabilitation purposes. In this review, we summarized the latest breakthroughs in neuroimaging from microscale to macroscale levels with potential diagnostic applications for rehabilitation. We also reviewed the achievements in electrocorticography (ECoG) coding with both animal models and human beings for BMI design, electromyography (EMG) interpretation for interaction with external robotic systems, and robot-assisted quantitative evaluation on the progress of rehabilitation programs. Future rehabilitation would be more home-based, automatic, and self-served by patients. Further investigations and breakthroughs are mainly needed in aspects of improving the computational efficiency in neuroimaging and multichannel ECoG by selection of localized neuroinformatics, validation of the effectiveness in BMI guided rehabilitation programs, and simplification of the system operation in training devices.

Neural decoding using a parallel sequential Monte Carlo method on point processes with ensemble effect

Sequential Monte Carlo estimation on point processes has been successfully applied to predict the movement from neural activity. However, there exist some issues along with this method such as the simplified tuning model and the high computational complexity, which may degenerate the decoding performance of motor brain machine interfaces. In this paper, we adopt a general tuning model which takes recent ensemble activity into account. The goodness-of-fit analysis demonstrates that the proposed model can predict the neuronal response more accurately than the one only depending on kinematics. A new sequential Monte Carlo algorithm based on the proposed model is constructed. The algorithm can significantly reduce the root mean square error of decoding results, which decreases 23.6% in position estimation. In addition, we accelerate the decoding speed by implementing the proposed algorithm in a massive parallel manner on GPU. The results demonstrate that the spike trains can be decoded as point process in real time even with 8000 particles or 300 neurons, which is over 10 times faster than the serial implementation. The main contribution of our work is to enable the sequential Monte Carlo algorithm with point process observation to output the movement estimation much faster and more accurately.

A unified approach to linking experimental, statistical and computational analysis of spike train data

A fundamental issue in neuroscience is how to identify the multiple biophysical mechanisms through which neurons generate observed patterns of spiking activity. In previous work, we proposed a method for linking observed patterns of spiking activity to specific biophysical mechanisms based on a state space modeling framework and a sequential Monte Carlo, or particle filter, estimation algorithm. We have shown, in simulation, that this approach is able to identify a space of simple biophysical models that were consistent with observed spiking data (and included the model that generated the data), but have yet to demonstrate the application of the method to identify realistic currents from real spike train data. Here, we apply the particle filter to spiking data recorded from rat layer V cortical neurons, and correctly identify the dynamics of an slow, intrinsic current. The underlying intrinsic current is successfully identified in four distinct neurons, even though the cells exhibit two distinct classes of spiking activity: regular spiking and bursting. This approach – linking statistical, computational, and experimental neuroscience – provides an effective technique to constrain detailed biophysical models to specific mechanisms consistent with observed spike train data.

An overview of Bayesian methods for neural spike train analysis

Neural spike train analysis is an important task in computational neuroscience which aims to understand neural mechanisms and gain insights into neural circuits. With the advancement of multielectrode recording and imaging technologies, it has become increasingly demanding to develop statistical tools for analyzing large neuronal ensemble spike activity. Here we present a tutorial overview of Bayesian methods and their representative applications in neural spike train analysis, at both single neuron and population levels. On the theoretical side, we focus on various approximate Bayesian inference techniques as applied to latent state and parameter estimation. On the application side, the topics include spike sorting, tuning curve estimation, neural encoding and decoding, deconvolution of spike trains from calcium imaging signals, and inference of neuronal functional connectivity and synchrony. Some research challenges and opportunities for neural spike train analysis are discussed.

Markov chain Monte Carlo methods for state-space models with point process observations

This letter considers how a number of modern Markov chain Monte Carlo (MCMC) methods can be applied for parameter estimation and inference in state-space models with point process observations. We quantified the efficiencies of these MCMC methods on synthetic data, and our results suggest that the Reimannian manifold Hamiltonian Monte Carlo method offers the best performance. We further compared such a method with a previously tested variational Bayes method on two experimental data sets. Results indicate similar performance on the large data sets and superior performance on small ones. The work offers an extensive suite of MCMC algorithms evaluated on an important class of models for physiological signal analysis.

Approximate Methods for State-Space Models

State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace's method, an asymptotic series expansion, to approximate the state's conditional mean and variance, together with a Gaussian conditional distribution. This Laplace-Gaussian filter (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulations and with real data. We find that the LGF can deliver superior results in a small fraction of the computing time.

Inferring synaptic inputs given a noisy voltage trace via sequential Monte Carlo methods

We discuss methods for optimally inferring the synaptic inputs to an electrotonically compact neuron, given intracellular voltage-clamp or current-clamp recordings from the postsynaptic cell. These methods are based on sequential Monte Carlo techniques ("particle filtering"). We demonstrate, on model data, that these methods can recover the time course of excitatory and inhibitory synaptic inputs accurately on a single trial. Depending on the observation noise level, no averaging over multiple trials may be required. However, excitatory inputs are consistently inferred more accurately than inhibitory inputs at physiological resting potentials, due to the stronger driving force associated with excitatory conductances. Once these synaptic input time courses are recovered, it becomes possible to fit (via tractable convex optimization techniques) models describing the relationship between the sensory stimulus and the observed synaptic input. We develop both parametric and nonparametric expectation-maximization (EM) algorithms that consist of alternating iterations between these synaptic recovery and model estimation steps. We employ a fast, robust convex optimization-based method to effectively initialize the filter; these fast methods may be of independent interest. The proposed methods could be applied to better understand the balance between excitation and inhibition in sensory processing in vivo.

A sequential Monte Carlo approach to estimate biophysical neural models from spikes

Realistic computational models of neuronal activity typically involve many variables and parameters, most of which remain unknown or poorly constrained. Moreover, experimental observations of the neuronal system are typically limited to the times of action potentials, or spikes. One important component of developing a computational model is the optimal incorporation of these sparse experimental data. Here, we use point process statistical theory to develop a procedure for estimating parameters and hidden variables in neuronal computational models given only the observed spike times. We discuss the implementation of a sequential Monte Carlo method for this procedure and apply it to three simulated examples of neuronal spiking activity. We also address the issues of model identification and misspecification, and show that accurate estimates of model parameters and hidden variables are possible given only spike time data.

Computing confidence intervals for point process models

Characterizing neural spiking activity as a function of intrinsic and extrinsic factors is important in neuroscience. Point process models are valuable for capturing such information; however, the process of fully applying these models is not always obvious. A complete model application has four broad steps: specification of the model, estimation of model parameters given observed data, verification of the model using goodness of fit, and characterization of the model using confidence bounds. Of these steps, only the first three have been applied widely in the literature, suggesting the need to dedicate a discussion to how the time-rescaling theorem, in combination with parametric bootstrap sampling, can be generally used to compute confidence bounds of point process models. In our first example, we use a generalized linear model of spiking propensity to demonstrate that confidence bounds derived from bootstrap simulations are consistent with those computed from closed-form analytic solutions. In our second example, we consider an adaptive point process model of hippocampal place field plasticity for which no analytical confidence bounds can be derived. We demonstrate how to simulate bootstrap samples from adaptive point process models, how to use these samples to generate confidence bounds, and how to statistically test the hypothesis that neural representations at two time points are significantly different. These examples have been designed as useful guides for performing scientific inference based on point process models.

Neuronal spike train analysis in likelihood space

BACKGROUND

Conventional methods for spike train analysis are predominantly based on the rate function. Additionally, many experiments have utilized a temporal coding mechanism. Several techniques have been used for analyzing these two sources of information separately, but using both sources in a single framework remains a challenging problem. Here, an innovative technique is proposed for spike train analysis that considers both rate and temporal information.

METHODOLOGY/PRINCIPAL FINDINGS

Point process modeling approach is used to estimate the stimulus conditional distribution, based on observation of repeated trials. The extended Kalman filter is applied for estimation of the parameters in a parametric model. The marked point process strategy is used in order to extend this model from a single neuron to an entire neuronal population. Each spike train is transformed into a binary vector and then projected from the observation space onto the likelihood space. This projection generates a newly structured space that integrates temporal and rate information, thus improving performance of distribution-based classifiers. In this space, the stimulus-specific information is used as a distance metric between two stimuli. To illustrate the advantages of the proposed technique, spiking activity of inferior temporal cortex neurons in the macaque monkey are analyzed in both the observation and likelihood spaces. Based on goodness-of-fit, performance of the estimation method is demonstrated and the results are subsequently compared with the firing rate-based framework.

CONCLUSIONS/SIGNIFICANCE

From both rate and temporal information integration and improvement in the neural discrimination of stimuli, it may be concluded that the likelihood space generates a more accurate representation of stimulus space. Further, an understanding of the neuronal mechanism devoted to visual object categorization may be addressed in this framework as well.

Online variational inference for state-space models with point-process observations

We present a variational Bayesian (VB) approach for the state and parameter inference of a state-space model with point-process observations, a physiologically plausible model for signal processing of spike data. We also give the derivation of a variational smoother, as well as an efficient online filtering algorithm, which can also be used to track changes in physiological parameters. The methods are assessed on simulated data, and results are compared to expectation-maximization, as well as Monte Carlo estimation techniques, in order to evaluate the accuracy of the proposed approach. The VB filter is further assessed on a data set of taste-response neural cells, showing that the proposed approach can effectively capture dynamical changes in neural responses in real time.

Value encoding in single neurons in the human amygdala during decision making

A growing consensus suggests that the brain makes simple choices by assigning values to the stimuli under consideration and then comparing these values to make a decision. However, the network involved in computing the values has not yet been fully characterized. Here, we investigated whether the human amygdala plays a role in the computation of stimulus values at the time of decision making. We recorded single neuron activity from the amygdala of awake patients while they made simple purchase decisions over food items. We found 16 amygdala neurons, located primarily in the basolateral nucleus that responded linearly to the values assigned to individual items.

Model-Based Decoding, Information Estimation, and Change-Point Detection Techniques for Multineuron Spike Trains

One of the central problems in systems neuroscience is to understand how neural spike trains convey sensory information. Decoding methods, which provide an explicit means for reading out the information contained in neural spike responses, offer a powerful set of tools for studying the neural coding problem. Here we develop several decoding methods based on point-process neural encoding models, or forward models that predict spike responses to stimuli. These models have concave log-likelihood functions, which allow efficient maximum-likelihood model fitting and stimulus decoding. We present several applications of the encoding model framework to the problem of decoding stimulus information from population spike responses: (1) a tractable algorithm for computing the maximum a posteriori (MAP) estimate of the stimulus, the most probable stimulus to have generated an observed single- or multiple-neuron spike train response, given some prior distribution over the stimulus; (2) a gaussian approximation to the posterior stimulus distribution that can be used 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 spike trains emitted by a neural population; and (4) a framework for the detection of change-point times (the time at which the stimulus undergoes a change in mean or variance) by marginalizing over the posterior stimulus distribution. We provide several examples illustrating the performance of these estimators with simulated and real neural data.

Extended Kalman filtering of point process observation

A temporal point process is a stochastic time series of binary events that occurs in continuous time. In computational neuroscience, the point process is used to model neuronal spiking activity; however, estimating the model parameters from spike train is a challenging problem. The state space point process filtering theory is a new technique for the estimation of the states and parameters. In order to use the stochastic filtering theory for the states of neuronal system with the Gaussian assumption, we apply the extended Kalman filter. In this regard, the extended Kalman filtering equations are derived for the point process observation. We illustrate the new filtering algorithm by estimating the effect of visual stimulus on the spiking activity of object selective neurons from the inferior temporal cortex of macaque monkey. Based on the goodness-offit assessment, the extended Kalman filter provides more accurate state estimate than the conventional methods.

Efficient Markov chain Monte Carlo methods for decoding neural spike trains

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 log concave 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 "hit-and-run" algorithm performed better than other MCMC methods. Using these algorithms, we show that for this latter class of priors, the posterior mean estimate can have a considerably lower average error than MAP, whereas for gaussian priors, the two estimators have roughly equal efficiency. We also address the application of MCMC methods for extracting nonmarginal properties of the posterior distribution. For example, by using MCMC to calculate the mutual information between the stimulus and response, we verify the validity of a computationally efficient Laplace approximation to this quantity for gaussian priors in a wide range of model parameters; this makes direct model-based computation of the mutual information tractable even in the case of large observed neural populations, where methods based on binning the spike train fail. Finally, we consider the effect of uncertainty in the GLM parameters on the posterior estimators.

Instantaneous estimation of motor cortical neural encoding for online brain-machine interfaces

Recently, the authors published a sequential decoding algorithm for motor brain-machine interfaces (BMIs) that infers movement directly from spike trains and produces a new kinematic output every time an observation of neural activity is present at its input. Such a methodology also needs a special instantaneous neuronal encoding model to relate instantaneous kinematics to every neural spike activity. This requirement is unlike the tuning methods commonly used in computational neuroscience, which are based on time windows of neural and kinematic data. This paper develops a novel, online, encoding model that uses the instantaneous kinematic variables (position, velocity and acceleration in 2D or 3D space) to estimate the mean value of an inhomogeneous Poisson model. During BMI decoding the mapping from neural spikes to kinematics is one to one and easy to implement by simply reading the spike times directly. Due to the high temporal resolution of the encoding, the delay between motor cortex neurons and kinematics needs to be estimated in the encoding stage. Mutual information is employed to select the optimal time index defined as the lag for which the spike event is maximally informative with respect to the kinematics. We extensively compare the windowed tuning models with the proposed method. The big difference between them resides in the high firing rate portion of the tuning curve, which is rather important for BMI-decoding performance. This paper shows that implementing such an instantaneous tuning model in sequential Monte Carlo point process estimation based on spike timing provides statistically better kinematic reconstructions than the linear and exponential spike-tuning models.

Estimating a State-Space Model from Point Process Observations: A Note on Convergence

Physiological signals such as neural spikes and heartbeats are discrete events in time, driven by continuous underlying systems. A recently introduced data-driven model to analyze such a system is a state-space model with point process observations, parameters of which and the underlying state sequence are simultaneously identified in a maximum likelihood setting using the expectation-maximization (EM) algorithm. In this note, we observe some simple convergence properties of such a setting, previously un-noticed. Simulations show that the likelihood is unimodal in the unknown parameters, and hence the EM iterations are always able to find the globally optimal solution.

A new look at state-space models for neural data

State space methods have proven indispensable in neural data analysis. However, common methods for performing inference in state-space models with non-Gaussian 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 state-space 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 spatially-varying firing rates.

Assimilating seizure dynamics

Observability of a dynamical system requires an understanding of its state-the collective values of its variables. However, existing techniques are too limited to measure all but a small fraction of the physical variables and parameters of neuronal networks. We constructed models of the biophysical properties of neuronal membrane, synaptic, and microenvironment dynamics, and incorporated them into a model-based predictor-controller framework from modern control theory. We demonstrate that it is now possible to meaningfully estimate the dynamics of small neuronal networks using as few as a single measured variable. Specifically, we assimilate noisy membrane potential measurements from individual hippocampal neurons to reconstruct the dynamics of networks of these cells, their extracellular microenvironment, and the activities of different neuronal types during seizures. We use reconstruction to account for unmeasured parts of the neuronal system, relating micro-domain metabolic processes to cellular excitability, and validate the reconstruction of cellular dynamical interactions against actual measurements. Data assimilation, the fusing of measurement with computational models, has significant potential to improve the way we observe and understand brain dynamics.

Decoding Movement Trajectories Through a T-Maze Using Point Process Filters Applied to Place Field Data from Rat Hippocampal Region CA1

Firing activity from neural ensembles in rat hippocampus has been previously used to determine an animal's position in an open environment and separately to predict future behavioral decisions. However, a unified statistical procedure to combine information about position and behavior in environments with complex topological features from ensemble hippocampal activity has yet to be described. Here we present a two-stage computational framework that uses point process filters to simultaneously estimate the animal's location and predict future behavior from ensemble neural spiking activity. First, in the encoding stage, we linearized a two-dimensional T-maze, and used spline-based generalized linear models to characterize the place-field structure of different neurons. All of these neurons displayed highly specific position-dependent firing, which frequently had several peaks at multiple locations along the maze. When the rat was at the stem of the T-maze, the firing activity of several of these neurons also varied significantly as a function of the direction it would turn at the decision point, as detected by ANOVA. Second, in the decoding stage, we developed a state-space model for the animal's movement along a T-maze and used point process filters to accurately reconstruct both the location of the animal and the probability of the next decision. The filter yielded exact full posterior densities that were highly nongaussian and often multimodal. Our computational framework provides a reliable approach for characterizing and extracting information from ensembles of neurons with spatially specific context or task-dependent firing activity.

Sequential Monte Carlo Point-Process Estimation of Kinematics from Neural Spiking Activity for Brain-Machine Interfaces

Many decoding algorithms for brain machine interfaces' (BMIs) estimate hand movement from binned spike rates, which do not fully exploit the resolution contained in spike timing and may exclude rich neural dynamics from the modeling. More recently, an adaptive filtering method based on a Bayesian approach to reconstruct the neural state from the observed spike times has been proposed. However, it assumes and propagates a gaussian distributed state posterior density, which in general is too restrictive. We have also proposed a sequential Monte Carlo estimation methodology to reconstruct the kinematic states directly from the multichannel spike trains. This letter presents a systematic testing of this algorithm in a simulated neural spike train decoding experiment and then in BMI data. Compared to a point-process adaptive filtering algorithm with a linear observation model and a gaussian approximation (the counterpart for point processes of the Kalman filter), our sequential Monte Carlo estimation methodology exploits a detailed encoding model (tuning function) derived for each neuron from training data. However, this added complexity is translated into higher performance with real data. To deal with the intrinsic spike randomness in online modeling, several synthetic spike trains are generated from the intensity function estimated from the neurons and utilized as extra model inputs in an attempt to decrease the variance in the kinematic predictions. The performance of the sequential Monte Carlo estimation methodology augmented with this synthetic spike input provides improved reconstruction, which raises interesting questions and helps explain the overall modeling requirements better.

Spike inference from calcium imaging using sequential Monte Carlo methods

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., approximately 5-10 s or 5-40 spikes), without the requirement of any simultaneous electrophysiology or imaging experiments.

Characterizing learning by simultaneous analysis of continuous and binary measures of performance

Continuous observations, such as reaction and run times, and binary observations, such as correct/incorrect responses, are recorded routinely in behavioral learning experiments. Although both types of performance measures are often recorded simultaneously, the two have not been used in combination to evaluate learning. We present a state-space model of learning in which the observation process has simultaneously recorded continuous and binary measures of performance. We use these performance measures simultaneously to estimate the model parameters and the unobserved cognitive state process by maximum likelihood using an approximate expectation maximization (EM) algorithm. We introduce the concept of a reaction-time curve and reformulate our previous definitions of the learning curve, the ideal observer curve, the learning trial and between-trial comparisons of performance in terms of the new model. We illustrate the properties of the new model in an analysis of a simulated learning experiment. In the simulated data analysis, simultaneous use of the two measures of performance provided more credible and accurate estimates of the learning than either measure analyzed separately. We also analyze two actual learning experiments in which the performance of rats and of monkeys was tracked across trials by simultaneously recorded reaction and run times and the correct and incorrect responses. In the analysis of the actual experiments, our algorithm gave a straightforward, efficient way to characterize learning by combining continuous and binary measures of performance. This analysis paradigm has implications for characterizing learning and for the more general problem of combining different data types to characterize the properties of a neural system.

A Bayesian statistical analysis of behavioral facilitation associated with deep brain stimulation

Deep brain stimulation (DBS) is an established therapy for Parkinson's Disease and is being investigated as a treatment for chronic depression, obsessive compulsive disorder and for facilitating functional recovery of patients in minimally conscious states following brain injury. For all of these applications, quantitative assessments of the behavioral effects of DBS are crucial to determine whether the therapy is effective and, if so, how stimulation parameters can be optimized. Behavioral analyses for DBS are challenging because subject performance is typically assessed from only a small set of discrete measurements made on a discrete rating scale, the time course of DBS effects is unknown, and between-subject differences are often large. We demonstrate how Bayesian state-space methods can be used to characterize the relationship between DBS and behavior comparing our approach with logistic regression in two experiments: the effects of DBS on attention of a macaque monkey performing a reaction-time task, and the effects of DBS on motor behavior of a human patient in a minimally conscious state. The state-space analysis can assess the magnitude of DBS behavioral facilitation (positive or negative) at specific time points and has important implications for developing principled strategies to optimize DBS paradigms.

Sequential optimal design of neurophysiology experiments

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 high-dimensional 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) that we want to fit to the neuron's activity. We rely on important log concavity and asymptotic normality properties of the posterior to facilitate the required computations. Our algorithm requires only low-rank matrix manipulations and a two-dimensional search to choose the optimal stimulus. The average running time of these operations scales quadratically with the dimensionality of the GLM, making real-time adaptive experimental design feasible even for high-dimensional stimulus and parameter spaces. For example, we require roughly 10 milliseconds on a desktop computer to optimize a 100-dimensional stimulus. Despite using some approximations to make the algorithm efficient, our algorithm asymptotically decreases the uncertainty about the model parameters at a rate equal to the maximum rate predicted by an asymptotic analysis. Simulation results show that picking stimuli by maximizing the mutual information can speed up convergence to the optimal values of the parameters by an order of magnitude compared to using random (nonadaptive) stimuli. Finally, applying our design procedure to real neurophysiology experiments requires addressing the nonstationarities that we would expect to see in neural responses; our algorithm can efficiently handle both fast adaptation due to spike history effects and slow, nonsystematic drifts in a neuron's activity.

A mixed filter algorithm for cognitive state estimation from simultaneously recorded continuous and binary measures of performance

Continuous (reaction times) and binary (correct/ incorrect responses) measures of performance are routinely recorded to track the dynamics of a subject's cognitive state during a learning experiment. Current analyses of experimental data from learning studies do not consider the two performance measures together and do not use the concept of the cognitive state formally to design statistical methods. We develop a mixed filter algorithm to estimate the cognitive state modeled as a linear stochastic dynamical system from simultaneously recorded continuous and binary measures of performance. The mixed filter algorithm has the Kalman filter and the more recently developed recursive filtering algorithm for binary processes as special cases. In the analysis of a simulated learning experiment the mixed filter algorithm provided a more accurate and precise estimate of the cognitive state process than either the Kalman or binary filter alone. In the analysis of an actual learning experiment in which a monkey's performance was tracked by its series of reaction times, and correct and incorrect responses, the mixed filter gave a more complete description of the learning process than either the Kalman or binary filter. These results establish the feasibility of estimating cognitive state from simultaneously recorded continuous and binary performance measures and suggest a way to make practical use of concepts from learning theory in the design of statistical methods for the analysis of data from learning experiments.

Computational mechanisms of mechanosensory processing in the cricket

Crickets and many other orthopteran insects face the challenge of gathering sensory information from the environment from a set of multi-modal sensory organs and transforming these stimuli into patterns of neural activity that can encode behaviorally relevant stimuli. The cercal mechanosensory system transduces low frequency air movements near the animal's body and is involved in many behaviors including escape from predators, orientation with respect to gravity, flight steering, aggression and mating behaviors. Three populations of neurons are sensitive to both the direction and dynamics of air currents:an array of mechanoreceptor-coupled sensory neurons, identified local interneurons and identified projection interneurons. The sensory neurons form a functional map of air current direction within the central nervous system that represents the direction of air currents as three-dimensional spatio-temporal activity patterns. These dynamic activity patterns provide excitatory input to interneurons whose sensitivity and spiking output depend on the location of the neuronal arbors within the sensory map and the biophysical and electronic properties of the cell structure. Sets of bilaterally symmetric interneurons can encode the direction of an air current stimulus by their ensemble activity patterns, functioning much like a Cartesian coordinate system. These interneurons are capable of responding to specific dynamic stimuli with precise temporal patterns of action potentials that may encode these stimuli using temporal encoding schemes. Thus, a relatively simple mechanosensory system employs a variety of complex computational mechanisms to provide the animal with relevant information about its environment.

Analysis of between-trial and within-trial neural spiking dynamics

Recording single-neuron activity from a specific brain region across multiple trials in response to the same stimulus or execution of the same behavioral task is a common neurophysiology protocol. The raster plots of the spike trains often show strong between-trial and within-trial dynamics, yet the standard analysis of these data with the peristimulus time histogram (PSTH) and ANOVA do not consider between-trial dynamics. By itself, the PSTH does not provide a framework for statistical inference. We present a state-space generalized linear model (SS-GLM) to formulate a point process representation of between-trial and within-trial neural spiking dynamics. Our model has the PSTH as a special case. We provide a framework for model estimation, model selection, goodness-of-fit analysis, and inference. In an analysis of hippocampal neural activity recorded from a monkey performing a location-scene association task, we demonstrate how the SS-GLM may be used to answer frequently posed neurophysiological questions including, What is the nature of the between-trial and within-trial task-specific modulation of the neural spiking activity? How can we characterize learning-related neural dynamics? What are the timescales and characteristics of the neuron's biophysical properties? Our results demonstrate that the SS-GLM is a more informative tool than the PSTH and ANOVA for analysis of multiple trial neural responses and that it provides a quantitative characterization of the between-trial and within-trial neural dynamics readily visible in raster plots, as well as the less apparent fast (1-10 ms), intermediate (11-20 ms), and longer (>20 ms) timescale features of the neuron's biophysical properties.

General-Purpose Filter Design for Neural Prosthetic Devices

Brain-driven interfaces depend on estimation procedures to convert neural signals to inputs for prosthetic devices that can assist individuals with severe motor deficits. Previous estimation procedures were developed on an application-specific basis. Here we report a coherent estimation framework that unifies these procedures and motivates new applications of prosthetic devices driven by action potentials, local field potentials (LFPs), electrocorticography (ECoG), electroencephalography (EEG), electromyography (EMG), or optical methods. The brain-driven interface is described as a probabilistic relationship between neural activity and components of a prosthetic device that may take on discrete or continuous values. A new estimation procedure is developed for action potentials, and a corresponding procedure is described for field potentials and optical measurements. We test our framework against dominant approaches in an arm reaching task using simulated traces of ensemble spiking activity from primary motor cortex (MI) and a wheelchair navigation task using simulated traces of EEG-band power. Adaptive filtering is incorporated to demonstrate performance under neuron death and discovery. Finally, we characterize performance under model misspecification using physiologically realistic history dependence in MI spiking. These simulated results predict that the unified framework outperforms previous approaches under various conditions, in the control of position and velocity, based on trajectory and endpoint mean squared errors.