Finding the event structure of neuronal spike trains

Neurons in sensory systems convey information about physical stimuli in their spike trains. In vitro, single neurons respond precisely and reliably to the repeated injection of the same fluctuating current, producing regions of elevated firing rate, termed events. Analysis of these spike trains reveals that multiple distinct spike patterns can be identified as trial-to-trial correlations between spike times (Fellous, Tiesinga, Thomas, & Sejnowski, 2004 ). Finding events in data with realistic spiking statistics is challenging because events belonging to different spike patterns may overlap. We propose a method for finding spiking events that uses contextual information to disambiguate which pattern a trial belongs to. The procedure can be applied to spike trains of the same neuron across multiple trials to detect and separate responses obtained during different brain states. The procedure can also be applied to spike trains from multiple simultaneously recorded neurons in order to identify volleys of near-synchronous activity or to distinguish between excitatory and inhibitory neurons. The procedure was tested using artificial data as well as recordings in vitro in response to fluctuating current waveforms.     

Fuzzy characterization of spike synchrony in parallel spike trains

We present a framework for characterizing spike (and spike-train) synchrony in parallel neuronal spike trains that is based on the identification of spikes with what we call influence maps: real-valued functions that describe an influence region around the corresponding spike times within which possibly graded (i.e., fuzzy) synchrony with other spikes is defined. We formalize two models of synchrony in this framework: the bin-based model (the almost exclusively applied model in the field) and a novel, alternative model based on a continuous, graded notion of synchrony, aimed at overcoming the drawbacks of the bin-based model. We study the task of identifying frequent (and synchronous) neuronal patterns from parallel spike trains in our framework, formalized as an instance of what we call the fuzzy frequent pattern mining problem (a generalization of standard frequent pattern mining) and briefly evaluate our synchrony models on this task.     

Detection of hidden structures in nonstationary spike trains

We propose an algorithm for simultaneously estimating state transitions among neural states and nonstationary firing rates using a switching state-space model (SSSM). This algorithm enables us to detect state transitions on the basis of not only discontinuous changes in mean firing rates but also discontinuous changes in the temporal profiles of firing rates (e.g., temporal correlation). We construct estimation and learning algorithms for a nongaussian SSSM, whose nongaussian property is caused by binary spike events. Local variational methods can transform the binary observation process into a quadratic form. The transformed observation process enables us to construct a variational Bayes algorithm that can determine the number of neural states based on automatic relevance determination. Additionally, our algorithm can estimate model parameters from single-trial data using a priori knowledge about state transitions and firing rates. Synthetic data analysis reveals that our algorithm has higher performance for estimating nonstationary firing rates than previous methods. The analysis also confirms that our algorithm can detect state transitions on the basis of discontinuous changes in temporal correlation, which are transitions that previous hidden Markov models could not detect. We also analyze neural data recorded from the medial temporal area. The statistically detected neural states probably coincide with transient and sustained states that have been detected heuristically. Estimated parameters suggest that our algorithm detects the state transitions on the basis of discontinuous changes in the temporal correlation of firing rates. These results suggest that our algorithm is advantageous in real-data analysis.     

Optimizing time histograms for non-Poissonian spike trains

The time histogram is a fundamental tool for representing the inhomogeneous density of event occurrences such as neuronal firings. The shape of a histogram critically depends on the size of the bins that partition the time axis. In most neurophysiological studies, however, researchers have arbitrarily selected the bin size when analyzing fluctuations in neuronal activity. A rigorous method for selecting the appropriate bin size was recently derived so that the mean integrated squared error between the time histogram and the unknown underlying rate is minimized (Shimazaki & Shinomoto, 2007 ). This derivation assumes that spikes are independently drawn from a given rate. However, in practice, biological neurons express non-Poissonian features in their firing patterns, such that the spike occurrence depends on the preceding spikes, which inevitably deteriorate the optimization. In this letter, we revise the method for selecting the bin size by considering the possible non-Poissonian features. Improvement in the goodness of fit of the time histogram is assessed and confirmed by numerically simulated non-Poissonian spike trains derived from the given fluctuating rate. For some experimental data, the revised algorithm transforms the shape of the time histogram from the Poissonian optimization method.     

Bayesian estimation of stimulus responses in Poisson spike trains

A Bayesian method is developed for estimating neural responses to stimuli, using likelihood functions incorporating the assumption that spike trains follow either pure Poisson statistics or Poisson statistics with a refractory period. The Bayesian and standard estimates of the mean and variance of responses are similar and asymptotically converge as the size of the data sample increases. However, the Bayesian estimate of the variance of the variance is much lower. This allows the Bayesian method to provide more precise interval estimates of responses. Sensitivity of the Bayesian method to the Poisson assumption was tested by conducting simulations perturbing the Poisson spike trains with noise. This did not affect Bayesian estimates of mean and variance to a significant degree, indicating that the Bayesian method is robust. The Bayesian estimates were less affected by the presence of noise than estimates provided by the standard method.     

Parameters of spike trains observed in a short time window

We study the estimation of statistical moments of interspike intervals based on observation of spike counts in many independent short time windows. This scenario corresponds to the situation in which a target neuron occurs. It receives information from many neurons and has to respond within a short time interval. The precision of the estimation procedures is examined. As the model for neuronal activity, two examples of stationary point processes are considered: renewal process and doubly stochastic Poisson process. Both moment and maximum likelihood estimators are investigated. Not only the mean but also the coefficient of variation is estimated. In accordance with our expectations, numerical studies confirm that the estimation of mean interspike interval is more reliable than the estimation of coefficient of variation. The error of estimation increases with increasing mean interspike interval, which is equivalent to decreasing the size of window (less events are observed in a window) and with decreasing the number of neurons (lower number of windows).     

Estimating information rates with confidence intervals in neural spike trains

Information theory provides a natural set of statistics to quantify the amount of knowledge a neuron conveys about a stimulus. A related work (Kennel, Shlens, Abarbanel, & Chichilnisky, 2005) demonstrated how to reliably estimate, with a Bayesian confidence interval, the entropy rate from a discrete, observed time series. We extend this method to measure the rate of novel information that a neural spike train encodes about a stimulus--the average and specific mutual information rates. Our estimator makes few assumptions about the underlying neural dynamics, shows excellent performance in experimentally relevant regimes, and uniquely provides confidence intervals bounding the range of information rates compatible with the observed spike train. We validate this estimator with simulations of spike trains and highlight how stimulus parameters affect its convergence in bias and variance. Finally, we apply these ideas to a recording from a guinea pig retinal ganglion cell and compare results to a simple linear decoder.     

Improved similarity measures for small sets of spike trains

Multiple measures have been developed to quantify the similarity between two spike trains. These measures have been used for the quantification of the mismatch between neuron models and experiments as well as for the classification of neuronal responses in neuroprosthetic devices and electrophysiological experiments. Frequently only a few spike trains are available in each class. We derive analytical expressions for the small-sample bias present when comparing estimators of the time-dependent firing intensity. We then exploit analogies between the comparison of firing intensities and previously used spike train metrics and show that improved spike train measures can be successfully used for fitting neuron models to experimental data, for comparisons of spike trains, and classification of spike train data. In classification tasks, the improved similarity measures can increase the recovered information. We demonstrate that when similarity measures are used for fitting mathematical models, all previous methods systematically underestimate the noise. Finally, we show a striking implication of this deterministic bias by reevaluating the results of the single-neuron prediction challenge.     

Generation of synthetic spike trains with defined pairwise correlations

Recent technological advances as well as progress in theoretical understanding of neural systems have created a need for synthetic spike trains with controlled mean rate and pairwise cross-correlation. This report introduces and analyzes a novel algorithm for the generation of discretized spike trains with arbitrary mean rates and controlled cross correlation. Pairs of spike trains with any pairwise correlation can be generated, and higher-order correlations are compatible with common synaptic input. Relations between allowable mean rates and correlations within a population are discussed. The algorithm is highly efficient, its complexity increasing linearly with the number of spike trains generated and therefore inversely with the number of cross-correlated pairs.     

Detection of syntonies between multiple spike trains using a coarse-grain binarization of spike count distributions

At very short timescales neuronal spike trains may be compared to binary streams where each neuron gives at most one spike per bin and therefore its state can be described by a binary variable. Time-averaged activity like the mean firing rate can be generally used on longer timescales to describe the dynamics; nevertheless, enlarging the space of the possible states up to the continuum may seriously bias the true statistics if the sampling is not accurate. We propose a simple transformation on binary variables which allows us to fix the dimensionality of the space to sample and to vary the temporal resolution of the analysis. For each time length interactions among simultaneously recorded neurons are evaluated using log-linear models. We illustrate how to use this method by analysing two different sets of data, recorded respectively in the temporal cortex of freely moving rats and in the inferotemporal cortex of behaving monkeys engaged in a visual fixation task. A detailed study of the interactions is provided for both samples. In both datasets we find that some assemblies share robust interactions, invariant at different time lengths, while others cooperate only at delimited time resolutions, yet the size of the samples is too small to allow an unbiased estimate of all possible interactions. We conclude that an extensive application of our method to larger samples of data, together with the development of techniques to correct the bias in the estimate of the coefficients, would provide significant information about the structure of the interactions in populations of neurons.     

On deterministic chaos in software reliability growth models

Software reliability growth models attempt to forecast the future reliability of a software system, based on observations of the historical occurrences of failures. This allows management to estimate the failure rate of the system in field use, and to set release criteria based on these forecasts. However, the current software reliability growth models have never proven to be accurate enough for widespread industry use. One possible reason is that the model forms themselves may not accurately capture the underlying process of fault injection in software; it has been suggested that fault injection is better modeled as a chaotic process rather than a random one. This possibility, while intriguing, has not yet been evaluated in large-scale, modern software reliability growth datasets.We report on an analysis of four software reliability growth datasets, including ones drawn from the Android and Mozilla open-source software communities. These are the four largest software reliability growth datasets we are aware of in the public domain, ranging from 1200 to over 86,000 observations. We employ the methods of nonlinear time series analysis to test for chaotic behavior in these time series; we find that three of the four do show evidence of such behavior (specifically, a multifractal attractor). Finally, we compare a deterministic time series forecasting algorithm against a statistical one on both datasets, to evaluate whether exploiting the apparent chaotic behavior might lead to more accurate reliability forecasts.     

Estimating the entropy rate of spike trains via Lempel-Ziv complexity

Normalized Lempel-Ziv complexity, which measures the generation rate of new patterns along a digital sequence, is closely related to such important source properties as entropy and compression ratio, but, in contrast to these, it is a property of individual sequences. In this article, we propose to exploit this concept to estimate (or, at least, to bound from below) the entropy of neural discharges (spike trains). The main advantages of this method include fast convergence of the estimator (as supported by numerical simulation) and the fact that there is no need to know the probability law of the process generating the signal. Furthermore, we present numerical and experimental comparisons of the new method against the standard method based on word frequencies, providing evidence that this new approach is an alternative entropy estimator for binned spike trains.     

周期微扰动作用下神經元放电行为的控制研究

对直流和混沌电流激励下的Hodgkin—Huxley(H—H)神经元，将周期的微扰动信号分别作用于神经元的不同离子通道，控制神经元放电行为．数值结果表明：作用于不同离子通道的微扰动控制信号，引起完全不同的神经元放电行为；如这些扰动信号可以使神经元从周期性放电转变为抛物线型簇放电、从混沌放电转变为周期放电。     

Short-term synaptic plasticity can enhance weak signal detectability in nonrenewal spike trains

We study the encoding of weak signals in spike trains with interspike interval (ISI) correlations and the signals' subsequent detection in sensory neurons. Motivated by the observation of negative ISI correlations in auditory and electrosensory afferents, we assess the theoretical performance limits of an individual detector neuron receiving a weak signal distributed across multiple afferent inputs. We assess the functional role of ISI correlations in the detection process using statistical detection theory and derive two sequential likelihood ratio detector models: one for afferents with renewal statistics; the other for afferents with negatively correlated ISIs. We suggest a mechanism that might enable sensory neurons to implicitly compute conditional probabilities of presynaptic spikes by means of short-term synaptic plasticity. We demonstrate how this mechanism can enhance a postsynaptic neuron's sensitivity to weak signals by exploiting the correlation structure of the input spike trains. Our model not only captures fundamental aspects of early electrosensory signal processing in weakly electric fish, but may also bear relevance to the mammalian auditory system and other sensory modalities.     

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.     

Fusion of ANNs as decoder of retinal spike trains for scene reconstruction

Applied Intelligence - The retina is one of the most developed sensing organs in the human body. However, the knowledge on the coding and decoding of the retinal neurons are still rather limited....     

Testing for and estimating latency effects for poisson and non-poisson spike trains

Determining the variations in response latency of one or several neurons to a stimulus is of interest in different contexts. Two common problems concern correlating latency with a particular behavior, for example, the reaction time to a stimulus, and adjusting tools for detecting synchronization between two neurons. We use two such problems to illustrate the latency testing and estimation methods developed in this article. Our test for latencies is a formal statistical test that produces a p-value. It is applicable for Poisson and non-Poisson spike trains via use of the bootstrap. Our estimation method is model free, it is fast and easy to implement, and its performance compares favorably to other methods currently available.     

Logical methods to obtain deterministic reliability estimates for systems

We consider the construction of deterministic integral estimates of sucessive failure and recovery times of a system. The mathematical model of system reliability is described by a dynamic automaton using the mathematical apparatus of many-valued and infinite-valued logic.Translated from Kibernetika, No. 5, pp. 104–111, September–October, 1990.     

Estimating parameters of generalized integrate-and-fire neurons from the maximum likelihood of spike trains

When a neuronal spike train is observed, what can we deduce from it about the properties of the neuron that generated it? A natural way to answer this question is to make an assumption about the type of neuron, select an appropriate model for this type, and then choose the model parameters as those that are most likely to generate the observed spike train. This is the maximum likelihood method. If the neuron obeys simple integrate-and-fire dynamics, Paninski, Pillow, and Simoncelli (2004) showed that its negative log-likelihood function is convex and that, at least in principle, its unique global minimum can thus be found by gradient descent techniques. Many biological neurons are, however, known to generate a richer repertoire of spiking behaviors than can be explained in a simple integrate-and-fire model. For instance, such a model retains only an implicit (through spike-induced currents), not an explicit, memory of its input; an example of a physiological situation that cannot be explained is the absence of firing if the input current is increased very slowly. Therefore, we use an expanded model (Mihalas & Niebur, 2009 ), which is capable of generating a large number of complex firing patterns while still being linear. Linearity is important because it maintains the distribution of the random variables and still allows maximum likelihood methods to be used. In this study, we show that although convexity of the negative log-likelihood function is not guaranteed for this model, the minimum of this function yields a good estimate for the model parameters, in particular if the noise level is treated as a free parameter. Furthermore, we show that a nonlinear function minimization method (r-algorithm with space dilation) usually reaches the global minimum.     

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.