Neural Spike Train Data Research Articles

Estimating high-dimensional Hawkes process with time-dependent covariates

The Hawkes process models have been recently become a popular tool for modeling and analysis of neural spike train data. Despite this popularity, existing methodological and theoretical work has mainly focused on models without assumption of time-varying covariates, such as stimulus drive. In this article, motivated by neuronal spike trains study in the presence of stimuli, we propose a new Hawkes process model, where covariates are included in the intensity function. We consider the problem of simultaneous variable selection and estimation for the Hawkes process in the high-dimensional regime. Estimation of the intensity function of the high-dimensional point process is considered within a nonparametric framework, applying B-splines and the SCAD penalty for matters of sparsity. We apply the Doob-Kolmogorov inequality to establish the consistency of the resulting estimators. Finally, we illustrate the performance of our proposal through simulation and demonstrate its utility by applying it to the neuron spike train data set.

Removing nonlinear misalignment in neuronal spike trains using the Fisher-Rao registration framework

BackgroundThe temporal precision in neural spike train data is critically important for understanding functional mechanism in the nervous systems. However, the timing variability of spiking activity can be highly nonlinear in practical observations due to behavioral variability or unobserved/unobservable cognitive states. New methodIn this study, we propose to adopt a powerful nonlinear method, referred to as the Fisher-Rao Registration (FRR), to remove such nonlinear phase variability in discrete neuronal spike trains. We also develop a smoothing procedure on the discrete spike train data in order to use the FRR framework. Comparison with existing methodsWe systematically compare the FRR with the state-of-the-art linear and nonlinear methods in terms of model efficiency and effectiveness. ResultsWe show that the FRR has superior performance and the advantages are well illustrated with simulation and real experimental data. ConclusionsIt is found the FRR framework provides more appropriate alignment performance to understand the temporal variability in neuronal spike trains.

Wavelet spectra for multivariate point processes

SummaryWavelets provide the flexibility for analysing stochastic processes at different scales. In this article we apply them to multivariate point processes as a means of detecting and analysing unknown nonstationarity, both within and across component processes. To provide statistical tractability, a temporally smoothed wavelet periodogram is developed and shown to be equivalent to a multi-wavelet periodogram. Under a stationarity assumption, the distribution of the temporally smoothed wavelet periodogram is demonstrated to be asymptotically Wishart, with the centrality matrix and degrees of freedom readily computable from the multi-wavelet formulation. Distributional results extend to wavelet coherence, a time-scale measure of inter-process correlation. This statistical framework is used to construct a test for stationarity in multivariate point processes. The methods are applied to neural spike-train data, where it is shown to detect and characterize time-varying dependency patterns.

Biologically Plausible Sequence Learning with Spiking Neural Networks

Motivated by the celebrated discrete-time model of nervous activity outlined by McCulloch and Pitts in 1943, we propose a novel continuous-time model, the McCulloch-Pitts network (MPN), for sequence learning in spiking neural networks. Our model has a local learning rule, such that the synaptic weight updates depend only on the information directly accessible by the synapse. By exploiting asymmetry in the connections between binary neurons, we show that MPN can be trained to robustly memorize multiple spatiotemporal patterns of binary vectors, generalizing the ability of the symmetric Hopfield network to memorize static spatial patterns. In addition, we demonstrate that the model can efficiently learn sequences of binary pictures as well as generative models for experimental neural spike-train data. Our learning rule is consistent with spike-timing-dependent plasticity (STDP), thus providing a theoretical ground for the systematic design of biologically inspired networks with large and robust long-range sequence storage capacity.

A Copula-Based Granger Causality Measure for the Analysis of Neural Spike Train Data.

In systems neuroscience, it is becoming increasingly common to record the activity of hundreds of neurons simultaneously via electrode arrays. The ability to accurately measure the causal interactions among multiple neurons in the brain is crucial to understanding how neurons work in concert to generate specific brain functions. The development of new statistical methods for assessing causal influence between spike trains is still an active field of neuroscience research. Here, we suggest a copula-based Granger causality measure for the analysis of neural spike train data. This method is built upon our recent work on copula Granger causality for the analysis of continuous-valued time series by extending it to point-process neural spike train data. The proposed method is therefore able to reveal nonlinear and high-order causality in the spike trains while retaining all the computational advantages such as model-free, efficient estimation, and variability assessment of Granger causality. The performance of our algorithm can be further boosted with time-reversed data. Our method performed well on extensive simulations, and was then demonstrated on neural activity simultaneously recorded from primary visual cortex of a monkey performing a contour detection task.

Generalized Mahalanobis depth in point process and its application in neural coding

In this paper, we propose to generalize the notion of depth in temporal point process observations. The new depth is defined as a weighted product of two probability terms: (1) the number of events in each process, and (2) the center-outward ranking on the event times conditioned on the number of events. In this study, we adopt the Poisson distribution for the first term and the Mahalanobis depth for the second term. We propose an efficient bootstrapping approach to estimate parameters in the defined depth. In the case of Poisson process, the observed events are order statistics where the parameters can be estimated robustly with respect to sample size. We demonstrate the use of the new depth by ranking realizations from a Poisson process. We also test the new method in classification problems using simulations as well as real neural spike train data. It is found that the new framework provides more accurate and robust classifications as compared to commonly used likelihood methods.

Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions

Hawkes () introduced a powerful multivariate point process model of mutually exciting processes to explain causal structure in data. In this article, it is shown that the Granger causality structure of such processes is fully encoded in the corresponding link functions of the model. A new nonparametric estimator of the link functions based on a time‐discretized version of the point process is introduced by using an infinite order autoregression. Consistency of the new estimator is derived. The estimator is applied to simulated data and to neural spike train data from the spinal dorsal horn of a rat.

A Functional Connectivity Analysis Toolbox for Multiple Spike Trains Data: �ToolConnect�

A Functional Connectivity Analysis Toolbox for Multiple Spike Trains Data: �ToolConnect�

TOOLCONNECT: A powerful toolbox for functional connectivity analysis of in vitro neural networks

Event Abstract Back to Event TOOLCONNECT: A powerful toolbox for functional connectivity analysis of in vitro neural networks Vito P. Pastore1*, Aleksandar Godjoski1, Sergio Martinoia1 and Paolo Massobrio1 1 University of Genova, Department of Informatics, Bioengineering, Robotics, System Engineering , Italy Motivation One of the goal of contemporary neuroscience is to study the interplay between topology, structure, functional-effective connectivity and neuronal dynamics at different level of complexity and on different experimental models (from simple in-vitro networks to whole brain areas). Functional connectivity is defined as the strength of the influence one network member has on another during ongoing behavior [1]. The analysis of multiple neural spike train data recorded from experimental models has gained tremendous relevance recently with the widespread application of Micro-Electrode Arrays (MEAs) [2]. At present, to the best of our knowledge, there is no available dedicated software that puts together a set of different functional connectivity analysis methods. Thus, we developed a user-friendly toolbox [3] in order to provide the researchers community a powerful tool to perform functional connectivity analysis on in-vitro neuronal networks coupled to standard and high-density MEAs, while guaranteeing computational efficiency and high accuracy. Material and Methods We implemented 'ToolConnect' toolbox as a standalone windows Graphical User Interface (GUI) application, using C# and Microsoft Visual Studio with .NET framework 4.5 development environment. The software is designed to be intuitive and straightforward to use. It is based on several windows forms and a friendly and modular GUI through which provides the user with powerful tools to manipulate and analyze data. ToolConnect offers functional connectivity analysis based on two correlation (cross-correlation and partial correlation) and two information theory based methods (transfer entropy and joint entropy). Cross correlation measures the frequency at which one cell fires as a function of time relative to the firing of a spike in another cell [4]. Partial correlation allows to distinguish between direct and indirect connections by removing the portion of the relationship between two spike trains that can be attributed to linear relationships with recorded spike trains from other neurons [5, 6]. Transfer Entropy is an information theoretic measure able to estimate causal relationships between time series taking into account their past activity [7]. Joint Entropy analyzes the cross Inter-Spike-Intervals (cISI): if two neurons are strongly connected the cISI histogram will show a peak and Joint Entropy will be close to zero, otherwise the cISI histogram will be almost flat, and the Joint Entropy will be high. The graphical section offers dedicated interfaces and allows the user to: i) plot the correlograms between each couple of the set of analyzed electrodes (for cross- and partial correlation); ii) manage, thresh and plot the Connectivity Matrix (CM) and the connectivity graph; iii) compute some powerful metrics that allow to extract the main topological features (degree, cluster coefficient, path length). One of the major features of the toolbox is its independence from the acquisition system (e.g. Multi Channel Systems, Qwane Biosciences, 3Brain) and from the MEA layout (number of microelectrodes and spatial organization). Results We designed and developed ToolConnect taking care to satisfy the user-friendliness requirement. According to this, our software has a GUI, which permits also to inexperienced users to perform functional connectivity analysis, to graphically represent the results, hiding the algorithms implementation specifics and software’s code design. Figure 1 shows a screenshot of ToolConnect’s GUI. Figure 2 shows the connectivity graphs obtained from the analysis of cortical networks coupled to the MEA60 and the MEA2100 acquisition systems of Multi Channel Systems (www.multichannelsystems.com; MCS, Reutlingen, Germany) and the BioCam acquisition system of 3Brain Systems. To assess the performances of tool connect we performed functional-connectivity analysis based on the cross-correlation method on hippocampal neuronal networks coupled to the MEA 60 from Multi-Channel Systems (MCS), during spontaneous and stimulus-evoked activity[3]. Discussion To the best of our knowledge, ToolConnect is the first functional connectivity toolbox dedicated to the analysis of multiple spike trains recorded from in-vitro neural networks coupled to MEAs. It provides the user with a complete set of computational and graphical tools of intuitive and straightforward usage through a dedicated and modular GUI. ToolConnect is implemented taking care of the optimization of the resources usage (requested RAM) and the reduction of the computational time. We were able to obtain acceptable performances with computational time lower than 2 minutes (for 10 minutes of recording sampled at 10 kHz). These performances make ToolConnect compatible with high-density recording systems (e.g., the 4096 electrodes of the 3brain system). In this way, it will be possible to perform functional connectivity analysis on neural networks with dimensions of thousands of neurons preserving an acceptable spatial and temporal resolution, hence allowing to obtain realistic and complete information on the dynamics and the topology of such systems.

Introduction to neural spike train data for phase-amplitude analysis

Statistical analysis of spike trains is one of the central problems in neural coding, and can be pursued in several ways. One option is model-based, i.e. assume a parametric or semi-parametric model, such as the Poisson model, for spike train data and use it in decoding spike trains. The other option is metric-based, i.e. choose a metric for comparing the numbers and the placements of spikes in different trains, and does not need a model. A prominent idea in the latter approach is to derive metrics that are based on measurements of time-warpings of spike trains needed in the alignments of corresponding spikes. We propose the use of ideas developed in functional data analysis, namely the definition and separation of phase-amplitude components, as a novel tool for analyzing spike trains and decoding underlying neural signals. For concreteness, we introduce a real spike train dataset taken from experimental recordings of the primary motor cortex of a monkey while performing certain arm movements. To facilitate functional data analysis, one needs to smooth the observed discrete spike trains with Gaussian kernels.

Analysis of spike train data: Alignment and comparisons using the extended Fisher-Rao metric

We present a metric-based framework for analyzing statistical variability of the neural spike train data that was introduced in an earlier paper on this section [14]. Treating the smoothed spike trains as functional data, we apply the extended Fisher-Rao Riemannian metric, first introduced in Srivastava et al. [9], to perform: (1) pairwise alignment of spike functions, (2) averaging of multiple functions, and (3) alignment of spike functions to the mean. The last item results in separation phase and amplitude components from the functional data. Further, we utilize proper metrics on these components for classification of activities represented by spike trains. This approach is based on the square-root slope function (SRSF) representation of functions that transforms the Fisher-Rao metric into the standard $\mathbb{L}^{2}$ metric and, thus, simplifies computations. We compare our registration results with some current methods and demonstrate an application of our approach in neural decoding to infer motor behaviors.

Estimating synaptic connections from multiple spike trains based on a coupled escape rate model

An approach to study the mechanism of information processing in a neural circuit is to identify synaptic connectivity between neurons. As recent advances in experimental techniques facilitate simultaneous recording of a large population of neurons, estimation of synaptic connectivity from multiple neural spike train data has become a major goal in computational neuroscience. Although it is important to develop an accurate method, it is difficult to validate a method on the basis of experimental data because of the lack of knowledge regarding synaptic connectivity. In this contribution, we have developed a method to estimate synaptic connection on the basis of a coupled escape rate model (CERM), which is an extension of the escape rate model [1]. The strength of the synaptic connection was determined by maximizing the likelihood function. We applied this method as well as model-free methods (transfer entropy and cross-correlation [2]) to synthetic spike train data. The synthetic data were generated by a cortical network model, which consisted of thousands of Hodgkin-Huxley type neurons [3]. These methods are applied to the spike data generated by the cortical network model with different topologies of synaptic connectivity (regular, small-world, and random). It should be noted that the true connectivity is known and the estimation performance can be evaluated by the receiver operating characteristic (ROC) analysis. Our results demonstrated that all methods gave better results for nonrandom (regular and small-world) networks than for random networks. Furthermore, CERM is considered to be the optimal method because it does not involve binning and requires smallest observation length. Therefore, despite high computational costs, CERM is a most suitable method to estimate synaptic connections from multiple spike train data.

Robust analysis of semiparametric renewal process models

A rate model is proposed for a modulated renewal process comprising a single long sequence, where the covariate process may not capture the dependencies in the sequence as in standard intensity models. We consider partial likelihood-based inferences under a semiparametric multiplicative rate model, which has been widely studied in the context of independent and identical data. Under an intensity model, gap times in a single long sequence may be used naively in the partial likelihood with variance estimation utilizing the observed information matrix. Under a rate model, the gap times cannot be treated as independent and studying the partial likelihood is much more challenging. We employ a mixing condition in the application of limit theory for stationary sequences to obtain consistency and asymptotic normality. The estimator's variance is quite complicated owing to the unknown gap times dependence structure. We adapt block bootstrapping and cluster variance estimators to the partial likelihood. Simulation studies and an analysis of a semiparametric extension of a popular model for neural spike train data demonstrate the practical utility of the rate approach in comparison with the intensity approach.

The potential of corticomuscular and intermuscular coherence for research on human motor control

The potential of corticomuscular and intermuscular coherence for research on human motor control

State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data

Precise spike coordination between the spiking activities of multiple neurons is suggested as an indication of coordinated network activity in active cell assemblies. Spike correlation analysis aims to identify such cooperative network activity by detecting excess spike synchrony in simultaneously recorded multiple neural spike sequences. Cooperative activity is expected to organize dynamically during behavior and cognition; therefore currently available analysis techniques must be extended to enable the estimation of multiple time-varying spike interactions between neurons simultaneously. In particular, new methods must take advantage of the simultaneous observations of multiple neurons by addressing their higher-order dependencies, which cannot be revealed by pairwise analyses alone. In this paper, we develop a method for estimating time-varying spike interactions by means of a state-space analysis. Discretized parallel spike sequences are modeled as multi-variate binary processes using a log-linear model that provides a well-defined measure of higher-order spike correlation in an information geometry framework. We construct a recursive Bayesian filter/smoother for the extraction of spike interaction parameters. This method can simultaneously estimate the dynamic pairwise spike interactions of multiple single neurons, thereby extending the Ising/spin-glass model analysis of multiple neural spike train data to a nonstationary analysis. Furthermore, the method can estimate dynamic higher-order spike interactions. To validate the inclusion of the higher-order terms in the model, we construct an approximation method to assess the goodness-of-fit to spike data. In addition, we formulate a test method for the presence of higher-order spike correlation even in nonstationary spike data, e.g., data from awake behaving animals. The utility of the proposed methods is tested using simulated spike data with known underlying correlation dynamics. Finally, we apply the methods to neural spike data simultaneously recorded from the motor cortex of an awake monkey and demonstrate that the higher-order spike correlation organizes dynamically in relation to a behavioral demand.

The Ising decoder: reading out the activity of large neural ensembles

The Ising model has recently received much attention for the statistical description of neural spike train data. In this paper, we propose and demonstrate its use for building decoders capable of predicting, on a millisecond timescale, the stimulus represented by a pattern of neural activity. After fitting to a training dataset, the Ising decoder can be applied "online" for instantaneous decoding of test data. While such models can be fit exactly using Boltzmann learning, this approach rapidly becomes computationally intractable as neural ensemble size increases. We show that several approaches, including the Thouless-Anderson-Palmer (TAP) mean field approach from statistical physics, and the recently developed Minimum Probability Flow Learning (MPFL) algorithm, can be used for rapid inference of model parameters in large-scale neural ensembles. Use of the Ising model for decoding, unlike other problems such as functional connectivity estimation, requires estimation of the partition function. As this involves summation over all possible responses, this step can be limiting. Mean field approaches avoid this problem by providing an analytical expression for the partition function. We demonstrate these decoding techniques by applying them to simulated neural ensemble responses from a mouse visual cortex model, finding an improvement in decoder performance for a model with heterogeneous as opposed to homogeneous neural tuning and response properties. Our results demonstrate the practicality of using the Ising model to read out, or decode, spatial patterns of activity comprised of many hundreds of neurons.

Multivariate autoregressive modeling and granger causality analysis of multiple spike trains.

Recent years have seen the emergence of microelectrode arrays and optical methods allowing simultaneous recording of spiking activity from populations of neurons in various parts of the nervous system. The analysis of multiple neural spike train data could benefit significantly from existing methods for multivariate time-series analysis which have proven to be very powerful in the modeling and analysis of continuous neural signals like EEG signals. However, those methods have not generally been well adapted to point processes. Here, we use our recent results on correlation distortions in multivariate Linear-Nonlinear-Poisson spiking neuron models to derive generalized Yule-Walker-type equations for fitting ‘‘hidden” Multivariate Autoregressive models. We use this new framework to perform Granger causality analysis in order to extract the directed information flow pattern in networks of simulated spiking neurons. We discuss the relative merits and limitations of the new method.

Causal pattern recovery from neural spike train data using the Snap Shot Score

We present a new approach to learning directed information flow networks from multi-channel spike train data. A novel scoring function, the Snap Shot Score, is used to assess potential networks with respect to their quality of causal explanation for the data. Additionally, we suggest a generic concept of plausibility in order to assess network learning techniques under partial observability conditions. Examples demonstrate the assessment of networks with the Snap Shot Score, and neural network simulations show its performance in complex situations with partial observability. We discuss the application of the new score to real data and indicate how it can be modified to suit other neural data types.

Functional clustering algorithm for the analysis of dynamic network data.

We formulate a technique for the detection of functional clusters in discrete event data. The advantage of this algorithm is that no prior knowledge of the number of functional groups is needed, as our procedure progressively combines data traces and derives the optimal clustering cutoff in a simple and intuitive manner through the use of surrogate data sets. In order to demonstrate the power of this algorithm to detect changes in network dynamics and connectivity, we apply it to both simulated neural spike train data and real neural data obtained from the mouse hippocampus during exploration and slow-wave sleep. Using the simulated data, we show that our algorithm performs better than existing methods. In the experimental data, we observe state-dependent clustering patterns consistent with known neurophysiological processes involved in memory consolidation.

An integrative analysis platform for multiple neural spike train data

In neuroscience research, multiple electrodes are used to record simultaneous spiking activity of many neurons lossless in real time. Accordingly, to analyze the data from multiple electrodes, many algorithms and computer programs have been developed. Since these programs are developed by commercial companies or academic institutes independently, the lack of common standard makes the talks between them difficult. In one integrative analysis, when several of them are needed, neuroscience researchers are usually exhausted by the program switching and data transformation. In this paper, we developed an integrative workflow-based platform for multiple neural spike train data analysis, namely MEA-Platform. MEA-Platform is a Java-based software platform, which provides (1) a general application development interface to integrate or bridge other programs and (2) a workflow mechanism to operate them and make them talk easily. At the moment, many algorithms and tools abstracted from MEA-Tools, Spike manager and DATA-MEAns are integrated. They together provide comprehensive functionalities of data normalization, statistics and result reporting, which are indispensable for a complete analysis of multiple neural spike train data. Because the interface developed is very general and flexible, new analysis tools can be integrated effectively as required. MEA-Platform implies an ideal environment for integrative neuroscience research.