Understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience. However, an optimal approach of assessing these interactions has not been established, as existing methods either do not consider the inherent point process nature of spike trains or are based on parametric assumptions that may lead to wrong inferences if not met. This work presents a framework, grounded in the field of information dynamics, for the model-free, continuous-time estimation of both undirected (symmetric) and directed (causal) interactions between pairs of spike trains. The framework decomposes the overall information exchanged dynamically between two point processes X and Y as the sum of the dynamic mutual information (dMI) between the histories of X and Y, plus the transfer entropy (TE) along the directions X->Y and Y->X. Building on recent work which derived theoretical expressions and consistent estimators for the TE in continuous time, we develop algorithms for estimating efficiently all measures in our framework through nearest neighbor statistics. These algorithms are validated in simulations of independent and coupled spike train processes, showing the accuracy of dMI and TE in the assessment of undirected and directed interactions even for weakly coupled and short realizations, and proving the superiority of the continuous-time estimator over the discrete-time method. Then, the usefulness of the framework is illustrated in a real data scenario of recordings from in-vitro preparations of spontaneously-growing cultures of cortical neurons, where we show the ability of dMI and TE to identify how the networks of undirected and directed spike train interactions change their topology through maturation of the neuronal cultures.
Neurons in the central nervous system communicate with each other with the help of series of Action Potentials, or spike trains. Various studies have shown that neurons encode information in different features of spike trains, such as the fine temporal structure, mean firing rate, synchrony etc. An important step in understanding the encoding of information by neurons, is to obtain a reliable measure of correlation between different spike trains. In this paper, two new binless similarity measures for spike trains are proposed. The performance of the new measures are compared with some existing…
We propose a statistical method for modeling the non-Poisson variability of spike trains observed in a wide range of brain regions. Central to our approach is the assumption that the variance and the mean of interspike intervals are related by a power function characterized by two parameters: the scale factor and exponent. It is shown that this single assumption allows the variability of spike trains to have an arbitrary scale and various dependencies on the firing rate in the spike count statistics, as well as in the interval statistics, depending on the two parameters of the power function. …
Statistical analysis and inferences on spike trains are one of the central topics in neural coding. It is of great interest to understand the underlying distribution and geometric structure of given spike train data. However, a fundamental obstacle is that the space of all spike trains is not an Euclidean space, and non-Euclidean metrics have been commonly used in the literature to characterize the variability and pattern in neural observations. Over the past few years, two Euclidean-like metrics were independently developed to measure distance in the spike train space. An important benefit of…
We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained f…
There is extensive evidence that biological neural networks encode information in the precise timing of the spikes generated and transmitted by neurons, which offers several advantages over rate-based codes. Here we adopt a vector space formulation of spike train sequences and introduce a new liquid state machine (LSM) network architecture and a new forward orthogonal regression algorithm to learn an input-output signal mapping or to decode the brain activity. The proposed algorithm uses precise spike timing to select the presynaptic neurons relevant to each learning task. We show that using p…
In neural systems, synaptic plasticity is usually driven by spike trains. Due to the inherent noises of neurons, synapses and networks, spike trains typically exhibit externally uncontrollable variability such as spatial heterogeneity and temporal stochasticity, resulting in variability of synapses, which we call efficacy variability. Spike patterns with the same population rate but inducing different efficacy variability may result in neuronal networks with sharply different structures and functions. However, how the variability of spike trains influences the efficacy variability remains uncl…
A new learning scheme called time divergence-convergence (TDC) is proposed for two-layer dynamic synapse neural networks (DSNN). DSNN is an artificial neural network model, in which the synaptic transmission is modeled by a dynamic process and the information between neurons are transmitted through spike timing. In TDC, the intra-layer neurons of a DSNN are trained to map input spike trains to a higher dimension of spike trains called a feature-domain, and the output neurons are trained to build the desired spike trains by processing the spike timing of intralayer neurons. The DSNN performance…
Humans perform remarkably well in many cognitive tasks including pattern recognition. However, the neuronal mechanisms underlying this process are not well understood. Nevertheless, artificial neural networks, inspired in brain circuits, have been designed and used to tackle spatio-temporal pattern recognition tasks. In this paper we present a multineuronal spike pattern detection structure able to autonomously implement online learning and recognition of parallel spike sequences (i.e., sequences of pulses belonging to different neurons/neural ensembles). The operating principle of this struct…
Interval jitter and spike resampling methods are used to analyze the time scale on which temporal correlations occur. They allow the computation of jitter corrected cross correlograms and the performance of an associated statistically robust hypothesis test to decide whether observed correlations at a given time scale are significant. Currently used Monte Carlo methods approximate the probability distribution of coincidences. They require generating $N_{\rm MC}$ simulated spike trains of length $T$ and calculating their correlation with another spike train up to lag $τ_{\max}$. This is computa…
Background: Measures of spike train synchrony are widely used in both experimental and computational neuroscience. Time-scale independent and parameter-free measures, such as the ISI-distance, the SPIKE-distance and SPIKE-synchronization, are preferable to time-scale parametric measures, since by adapting to the local firing rate they take into account all the time-scales of a given dataset. New Method: In data containing multiple time-scales (e.g. regular spiking and bursts) one is typically less interested in the smallest time-scales and a more adaptive approach is needed. Here we propose th…
Understanding information processing in the brain requires the ability to determine the functional connectivity between the different regions of the brain. We present a method using transfer entropy to extract this flow of information between brain regions from spike-train data commonly obtained in neurological experiments. Transfer entropy is a statistical measure based in information theory that attempts to quantify the information flow from one process to another, and has been applied to find connectivity in simulated spike-train data. Due to statistical error in the estimator, inferring fu…
Observations of finely-timed spike relationships in population recordings have been used to support partial reconstruction of neural microcircuit diagrams. In this approach, fine-timescale components of paired spike train interactions are isolated and subsequently attributed to synaptic parameters. Recent perturbation studies strengthen the case for such an inference, yet the complete set of measurements needed to calibrate statistical models are unavailable. To address this gap, we study features of pairwise spiking in a large-scale in vivo dataset where presynaptic neurons were explicitly de…
Modern well-performing approaches to neural decoding are based on machine learning models such as decision tree ensembles and deep neural networks. The wide range of algorithms that can be utilized to learn from neural spike trains, which are essentially time-series data, results in the need for diverse and challenging benchmarks for neural decoding, similar to the ones in the fields of computer vision and natural language processing. In this work, we propose a spike train classification benchmark, based on open-access neural activity datasets and consisting of several learning tasks such as s…
Quantifying spike train synchrony and directionality: Measures and Applications
Institute for Complex Systems (ISC), National Research Council (CNR)（复杂系统研究所，国家研究委员会）；National Institute of Nuclear Physics (INFN), Florence Section（国家核物理研究所，佛罗伦萨分部）
Statistical analysis and inference on spike trains is one of the central topics in the neural coding. It is of great interest to understand the underlying structure of given neural data. Based on the metric distances between spike trains, recent investigations have introduced the notion of an average or prototype spike train to characterize the template pattern in the neural activity. However, as those metrics lack certain Euclidean properties, the defined averages are nonunique, and do not share the conventional properties of a mean. In this article, we propose a new framework to define the m…
In many animal sensory pathways, the transformation from external stimuli to spike trains is essentially deterministic. In this context, a new mathematical framework for coding and reconstruction, based on a biologically plausible model of the spiking neuron, is presented. The framework considers encoding of a signal through spike trains generated by an ensemble of neurons via a standard convolve-then-threshold mechanism. Neurons are distinguished by their convolution kernels and threshold values. Reconstruction is posited as a convex optimization minimizing energy. Formal conditions under whi…
Measures of spike train synchrony have proven a valuable tool in both experimental and computational neuroscience. Particularly useful are time-resolved methods such as the ISI- and the SPIKE-distance, which have already been applied in various bivariate and multivariate contexts. Recently, SPIKE-Synchronization was proposed as another time-resolved synchronization measure. It is based on Event-Synchronization and has a very intuitive interpretation. Here, we present a detailed analysis of the mathematical properties of these three synchronization measures. For example, we were able to obtain …
Statistical similarities between neuronal spike trains could reveal significant information on complex underlying processing. In general, the similarity between synchronous spike trains is somewhat easy to identify. However, the similar patterns also potentially appear in an asynchronous manner. However, existing methods for their identification tend to converge slowly, and cannot be applied to short sequences. In response, we propose Hellinger distance measure based on empirical probabilities, which we show to be as accurate as existing techniques, yet faster to converge for synthetic as well…
Understanding how the brain functions is one of the biggest challenges of our time. The analysis of experimentally recorded neural firing patterns (spike trains) plays a crucial role in addressing this problem. Here, the PySpike library is introduced, a Python package for spike train analysis providing parameter-free and time-scale independent measures of spike train synchrony. It allows to compute similarity and dissimilarity profiles, averaged values and distance matrices. Although mainly focusing on neuroscience, PySpike can also be applied in other contexts like climate research or social …
Background: It is commonly assumed in neuronal coding that repeated presentations of a stimulus to a coding neuron elicit similar responses. One common way to assess similarity are spike train distances. These can be divided into spike-resolved, such as the Victor-Purpura and the van Rossum distance, and time-resolved, e.g. the ISI-, the SPIKE- and the RI-SPIKE-distance. New Method: We use independent steady-rate Poisson processes as surrogates for spike trains with fixed rate and no timing information to address two basic questions: How does the sensitivity of the different spike train distan…
Spike generation in neurons produces a temporal point process, whose statistics is governed by intrinsic phenomena and the external incoming inputs to be coded. In particular, spike-evoked adaptation currents support a slow temporal process that conditions spiking probability at the present time according to past activity. In this work, we study the statistics of interspike interval correlations arising in such non-renewal spike trains, for a neuron model that reproduces different spike modes in a small adaptation scenario. We found that correlations are stronger as the neuron fires at a parti…
The current state-of-the-art in neurophysiological data collection allows for simultaneous recording of tens to hundreds of neurons, for which point processes are an appropriate statistical modelling framework. However, existing point process models lack multivariate generalizations which are both flexible and computationally tractable. This paper introduces a multivariate generalization of the Skellam process with resetting (SPR), a point process tailored to model individual neural spike trains. The multivariate SPR (MSPR) is biologically justified as it mimics the process of neural integrati…
Neural noise sets a limit to information transmission in sensory systems. In several areas, the spiking response (to a repeated stimulus) has shown a higher degree of regularity than predicted by a Poisson process. However, a simple model to explain this low variability is still lacking. Here we introduce a new model, with a correction to Poisson statistics, which can accurately predict the regularity of neural spike trains in response to a repeated stimulus. The model has only two parameters, but can reproduce the observed variability in retinal recordings in various conditions. We show analy…
Learning synaptic weights of spiking neural network (SNN) models that can reproduce target spike trains from provided neural firing data is a central problem in computational neuroscience and spike-based computing. The discovery of the optimal weight values can be posed as a supervised learning task wherein the weights of the model network are chosen to maximize the similarity between the target spike trains and the model outputs. It is still largely unknown whether optimizing spike train similarity of highly recurrent SNNs produces weight matrices similar to those of the ground truth model. T…
We present a hidden Markov model that describes variation in an animal's position associated with varying levels of activity in action potential spike trains of individual place cell neurons. The model incorporates a coarse-graining of position, which we find to be a more parsimonious description of the system than other models. We use a sequential Monte Carlo algorithm for Bayesian inference of model parameters, including the state space dimension, and we explain how to estimate position from spike train observations (decoding). We obtain greater accuracy over other methods in the conditions …
Background: Spike trains of multiple neurons can be analyzed following the summed population (SP) or the labeled line (LL) hypothesis. Responses to external stimuli are generated by a neuronal population as a whole or the individual neurons have encoding capacities of their own. The SPIKE-distance estimated either for a single, pooled spike train over a population or for each neuron separately can serve to quantify these responses. New Method: For the SP case we compare three algorithms that search for the most discriminative subpopulation over all stimulus pairs. For the LL case we introduce …
The ability to record from increasingly large numbers of neurons, and the increasing attention being paid to large scale neural network simulations, demands computationally fast algorithms to compute relevant statistical measures. We present an O(n) algorithm for calculating the Kendall correlation of spike trains, a correlation measure that is becoming especially recognized as an important tool in neuroscience. We show that our method is around 50 times faster than the O (n ln n) method which is a current standard for quickly computing the Kendall correlation. In addition to providing a faste…
Statistical Mechanics of Spike Trains: Self-Consistent Activity Ensembles and Phase Transitions
Université Paris Cité（巴黎西岱大学）；Institute of Psychiatry and Neuroscience of Paris (IPNP)（巴黎精神病学与神经科学研究所）；INSERM U1266（法国国家健康与医学研究院 U1266）；Hôpital Fondation Adolphe de Rothschild（阿道夫·德·罗斯柴尔德基金会医院）；Medical University of Gdańsk（格但斯克医科大学）；Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Laboratoire de Physique Théorique de la Matière Condensée, LPTMC（凝聚态物质理论物理实验室）；Institut Universitaire de France (IUF)（法兰西学院）；LIB, Sorbonne Université, INSERM, CNRS（索邦大学、法国国家健康与医学研究院、法国国家科学研究中心 LIB）；Institute of Theoretical and Applied Informatics, Polish Academy of Sciences（波兰科学院理论与应用信息学研究所）；International Centre for Theory of Quantum Technologies (ICTQT), University of Gdansk（格但斯克大学量子技术理论国际中心）
