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1.
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.  相似文献   

2.
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.  相似文献   

3.
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.  相似文献   

4.
Pattern matching is a simple method for studying the properties of information sources based on individual sequences (Wyner et al 1998 IEEE Trans. Inf. Theory 44 2045-56). In particular, the normalized Lempel-Ziv complexity (Lempel and Ziv 1976 IEEE Trans. Inf. Theory 22 75-88), which measures the rate of generation of new patterns along a sequence, is closely related to such important source properties as entropy and information compression ratio. We make use of this concept to characterize the responses of neurons of the primary visual cortex to different kinds of stimulus, including visual stimulation (sinusoidal drifting gratings) and intracellular current injections (sinusoidal and random currents), under two conditions (in vivo and in vitro preparations). Specifically, we digitize the neuronal discharges with several encoding techniques and employ the complexity curves of the resulting discrete signals as fingerprints of the stimuli ensembles. Our results show, for example, that if the neural discharges are encoded with a particular one-parameter method ('interspike time coding'), the normalized complexity remains constant within some classes of stimuli for a wide range of the parameter. Such constant values of the normalized complexity allow then the differentiation of the stimuli classes. With other encodings (e.g. 'bin coding'), the whole complexity curve is needed to achieve this goal. In any case, it turns out that the normalized complexity of the neural discharges in vivo are higher (and hence carry more information in the sense of Shannon) than in vitro for the same kind of stimulus.  相似文献   

5.
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.  相似文献   

6.
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.  相似文献   

7.
Niebur E 《Neural computation》2007,19(7):1720-1738
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.  相似文献   

8.
Lehky SR 《Neural computation》2004,16(7):1325-1343
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.  相似文献   

9.
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.  相似文献   

10.
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.  相似文献   

11.
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).  相似文献   

12.
Estimating the temporal interval entropy of neuronal discharge   总被引:2,自引:0,他引:2  
To better understand the role of timing in the function of the nervous system, we have developed a methodology that allows the entropy of neuronal discharge activity to be estimated from a spike train record when it may be assumed that successive interspike intervals are temporally uncorrelated. The so-called interval entropy obtained by this methodology is based on an implicit enumeration of all possible spike trains that are statistically indistinguishable from a given spike train. The interval entropy is calculated from an analytic distribution whose parameters are obtained by maximum likelihood estimation from the interval probability distribution associated with a given spike train. We show that this approach reveals features of neuronal discharge not seen with two alternative methods of entropy estimation. The methodology allows for validation of the obtained data models by calculation of confidence intervals for the parameters of the analytic distribution and the testing of the significance of the fit between the observed and analytic interval distributions by means of Kolmogorov-Smirnov and Anderson-Darling statistics. The method is demonstrated by analysis of two different data sets: simulated spike trains evoked by either Poissonian or near-synchronous pulsed activation of a model cerebellar Purkinje neuron and spike trains obtained by extracellular recording from spontaneously discharging cultured rat hippocampal neurons.  相似文献   

13.
A procedure for estimating the complexity of synthesized designs from finite-state machine (FSM) specifications is described. Incorporating this estimate in the data path synthesis stage allows a trade-off between data path and control logic, resulting in high quality designs in terms of synthesized logic area. It is shown that the estimation process takes 650 to 3000 times less CPU time than the synthesis procedure  相似文献   

14.
Li  Wei  Joseph Raj  Alex Noel  Tjahjadi  Tardi  Zhuang  Zhemin 《Applied Intelligence》2022,52(13):15164-15176
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....  相似文献   

15.
16.
17.
As multi-electrode and imaging technology begin to provide us with simultaneous recordings of large neuronal populations, new methods for modelling such data must also be developed. We present a model of responses to repeated trials of a sensory stimulus based on thresholded Gaussian processes that allows for analysis and modelling of variability and covariability of population spike trains across multiple time scales. The model framework can be used to specify the values of many different variability measures including spike timing precision across trials, coefficient of variation of the interspike interval distribution, and Fano factor of spike counts for individual neurons, as well as signal and noise correlations and correlations of spike counts across multiple neurons. Using both simulated data and data from different stages of the mammalian auditory pathway, we demonstrate the range of possible independent manipulations of different variability measures, and explore how this range depends on the sensory stimulus. The model provides a powerful framework for the study of experimental and surrogate data and for analyzing dependencies between different statistical properties of neuronal populations.  相似文献   

18.
If (X,T) is a measure-preserving system, a nontrivial partition of X into two sets and f a positive increasing function defined on the positive real numbers, then the limit inferior of the sequence is greater than or equal to the limit inferior of the sequence of quotients of the average complexity of trajectories of length n generated by and nf(log2(n))/log2(n). A similar statement also holds for the limit superior. Received: August 20, 1999.  相似文献   

19.
用例驱动的软件复杂性度量及应用   总被引:1,自引:0,他引:1  
王悠  张熙 《计算机工程与设计》2007,28(11):2543-2546
在用例驱动的软件开发过程中,研究软件复杂性,对于项目规模估算、进度控制及度量、评估都具有积极的意义.从需求获取、分析、设计、测试等阶段详细讨论了整个软件开发过程中如何获取、量化用例层次上的软件复杂度的方法,概括了研究的意义并通过实践进一步验证.根据它对软件可靠性相关指标参数的影响,探讨基于用例的软件可靠性度量分析方法的改进.  相似文献   

20.
In this paper, we define the conditional Rényi entropy and show that the so-called chain rule holds for the Rényi entropy. Then, we introduce a relation for the rate of Rényi entropy and use it to derive the rate of the Rényi entropy for an irreducible-aperiodic Markov chain. We also show that the bound for the Rényi entropy rate is simply the Shannon entropy rate.  相似文献   

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