Joint work with Philipp Berens, Sebastian Gerwinn, and Alexander Ecker.
New results for population codes of angular variables
The relative merits of different population coding schemes have mostly been analyzed in the framework of stimulus reconstruction using Fisher Information. Here, we consider the case of stimulus discrimination in a two alternative forced choice paradigm and compute neurometric functions in terms of the minimal discrimination error and the Jensen-Shannon information to study neural population codes. In contrast to Fisher information the minimum discrimination error allows an accurate assessment of coding accuracy also for short decoding time windows and highly inhomogeneous populations. We use this framework to study population codes of angular variables for ensembles of Linear-Nonlinear Poisson (LNP) neurons. In particular, we study both the effect of the nonlinearity and the impact of different noise correlations structures on coding accuracy in long versus short decoding time windows. The length of the time window determines the signal-to-noise ratio of the encoding since in our model the mean spike counts of the neurons are proportional to it. While Fisher information is invariant under the length of the time window up to a constant factor, this is not true for realistic decoding errors. First, we reevaluate previously studied population codes with stimulus dependent noise correlations which lead to larger Fisher information than stimulus independent noise correlations. Remarkably, the minimum discrimination error makes the opposite prediction for small time windows. The more critical factor, however, is the shape of the tuning functions. While sharp tuning functions have been shown to be optimal with respect to Fisher information, we find that steep sigmoidal nonlinearities leading to broad box-like tuning functions exhibit superior performance for any finite decoding time window. The smaller the time window and the larger the neural population the larger the advantage of box-like tuning over sharp tuning functions.
Joint work with Denise Berger, Sebastian Louis, Abigail Morrisonand Sonja Gruen
Statistics to Identify Assembly Neurons in Massively Parallel Spike Trains
If the spiking activities of large numbers of neurons are recordedsimultaneously, chances of detecting assembly activity can be expectedto increase. Since such massively parallel recordings are now becomingavailable, specialized methods able to analyze such data for spikecorrelations are needed, as a combinatorial explosion often makesit infeasible to extend methods developed for smaller data sets.By evaluating the distribution of spike counts in coincident spikeevents (complexity) the existence of correlated groups can be detected,but their member neurons cannot be identified. In this presentation,we survey some approaches to actually identify the individual neuronsinvolved in assemblies. The core idea of these approaches is to testwhether a neuron participates in an assembly by relating certainstatistics of those time bins in which a given neuron fires to thesame statistics for all time bins. A p-value can then be derivedby generating several surrogate data sets and computing the samestatistics. We have developed several concrete statistics and comparetheir relative performance on artificial data and recordings from catvisual cortex.
Berger D, Borgelt C, Louis S, Morrison A, Gruen S (2010) Efficient Identification of Assembly Neurons within Massively Parallel Spike Trains. Computational Intelligence and Neuroscience,Volume 2010, Article ID 439648, 18 pages. doi:10.1155/2010/439648
Spike train statistics from a dynamical systems perspective
We review recent results dealing with the analysis of spike train statistics in neural networks models, using methods from dynamical systems (thermodynamic formalism). We discuss why Gibbs distributions are natural candidates and present some consequences at the theoretical and algorithmic level.
Comparing Spike-Time Predictions
Twenty five years ago it would not have been thinkable to have a mathematical model to predict the spike-times of real neuron receiving complex stimuli. By now we know that many different neuron models are able very good predictions. Unfortunately, it is difficult to compare different models or fitting methods because every researcher evaluates the performance with his own spike train metric and his own experimental paradigm. To address this problem, the INCF competition asked researchers in any field to submit their spike-time predictions on a series of benchmark experiments with a fixed set of evaluation criteria. This way it was possible to compare multiple types of models for predicting the spike-times and membrane potential traces of real experiments. Submissions included simple leaky integrate-and-fire models, modified integrate-and-fire models to account for adaptation and refractoriness and even complex Hodgkin and Huxley compartmental models. We will present an overview of what we have learned from three years of these competitions. Another way to compare the published results is to study the relation between the different performance measures. Moreover, we discuss how the results of the competition depend on the choice of the performance measure. To this end, we re-evaluate the submissions using different spike-train metrics, including the previously used coincidence factor as well as the methods of, for instance, Victor and Purpura 1997 or Trucollo et al. 2010. Analytical relations between the different metrics will be discussed.
Joint work with Christian Borgelt (European Centre for Soft Computing, Spain), George Gerstein (University of Pennsylvania, USA), Sebastien Louis (RIKEN, Japan), Markus Diesmann (RIKEN, Japan)
Proper surrogates for spike correlation analysis
In the correlation analysis of experimentally recorded parallel spike trains one has to thoroughly consider the statistical features of the data in order to prevent false positive results [1]. Typically, the complexity of the data prevents us from using analytical expressions for evaluating the significance of observed correlations. Similarly, parametric tests presuppose models that are typically simplifications of the real neuronal data and thus may ignore important features. An alternative to these approaches is to use surrogate data, i.e. modified versions of the original data, to assess the significance of correlation [2]. The objective of surrogate data generation is to leave all statistical features of the original experimental data intact, except those we want to test for; these we wish to destroy.
The main challenge for these methods is to conserve certain features of the spike trains, the two most important being the modulation in firing rate in time, and the inter-spike interval statistics. In this study we make use of operational time to introduce generalizations to spike train manipulations and propose novel surrogates which conserves both features with high precision. Using simulated data sets with well controlled statistical features we compare the new approaches to existent surrogate approaches with respect to the occurrence of false positives and false negatives. Even in the extreme case where firing rates modulate in coherent stepsthe methods based on operational time stay close to the specified signicifance level. The price for this good natured behavior is a decreased sensitivity.
Cortical information coding with spikes trains and field potentials.
Recent studies have shown that in visual and auditory cortices of mammals, the angular phase of the Local Field Potential (LFP) at the time of spike generation adds significant extra information about a sensory stimulus, beyond the one contained in the firing rate alone. In that scenario, the LFP sets a local time scale with respect to which a spike timing code can be ascribed to neurons that otherwise would show a much more imprecise firing pattern relative to an external clock. I will review these results and suggest possible mechanisms to explain the origin of the observed extra information, and how it could be made available for downstream processing.
Spike Sorting
abstract follows
Joint work with Benjamin Staude and Imke Reimer (BCCN Freiburg, Germany), and Sonja Gruen (RIKEN BSI, Wako-shi, Japan)
Higher-order correlations in large neuronal populations
Spiking neurons are known to be quite sensitive for the higher-order correlation structure of their respective input populations [1]. But what is the role of these correlations in cortical information processing?
A prerequisite to answering this question is an appropriate framework to describe the correlation structure of neuronal populations, and an effective method to estimate it from sampled data. Previously suggested approaches suffer from the combinatorial explosion of the number of parameters, which typically grows exponentially with the number of recorded neurons. As a consequence, methods that go beyond pairwise correlations and aim for estimating genuine higher-order effects require vast samples, rendering them essentially inapplicable to populations of more than ~10 neurons.Here, we discuss the compound Poisson process as an intuitive and flexible model for correlated populations of spiking neurons. Based on this generative model, we present novel estimation techniques to infer the correlation structure of a neural population from sampled spike trains [2-4]. Our techniques can provide conclusive evidence for higher-order correlations in rather large populations of ~50 neurons, based on sample sizes that are compatible with current physiological in vivo recording technology. Recent developments aim at coping with certain types of non-Poissonian processes, and with certain types of non-stationarities encountered in spike recordings from behaving animals [5].
Reading out the activity of large neural ensembles: The Ising Decoder
New technologies such as high-density multi-electrode array recording and multiphoton calcium imaging allow the activity of large numbers of neurons to be monitored. However, analysis tools have lagged behind the experimental technology, with most approaches limited to very small population sizes. In this talk, I will outline the Ising Decoder approach to decoding the activity of large ensembles, in the limit of short time windows where neuronal activity can be binarized without loss of information. In this approach, an Ising type model is fit to a set of training data, after which decoding can take place trial by trial (or instant by instant). By taking advantage of recent advances in machine learning approaches for learning model parameters, we have been able to scale our neural population decoder up to relatively large ensembles. We have demonstrated the utility of this approach by using it to analyse the activity of networks of neurones recorded using multi-electrode array recording and two-photon calcium imaging, examining the effect of spike patterns on decoder performance.
Quantifying neural encoding of event timing
Single-neuron firing is often analyzed relative to an external event, such as successful task performance or the delivery of a stimulus. The perievent time histogram (PETH) examines how, on average, neural firing modulates before and after the alignment event. However, the PETH contains no information about the single-trial reliability of the neural response, which is important from the perspective of a target neuron. The concept of using the neural activity to predict the timing of the occurrence of an event, as opposed to using the event to predict the neural response is proposed. We first estimate the likelihood of an observed spike train, under the assumption that it was generated by an inhomogeneous gamma process with rate profile similar to the PETH shifted by a small time. This is used to generate a probability distribution of the event occurrence, using Bayes' rule. By an information theoretic approach, this method yields a single value (in bits) that quantifies the reduction in uncertainty regarding the time of an external event following observation of the spike train. We show that the approach is sensitive to the amplitude of a response, to the level of baseline firing, and to the consistency of a response between trials, all of which are factors that will influence a neuron's ability to code for the time of the event. The technique can provide a useful means not only of determining which of several behavioral events a cell encodes best, but also of permitting objective comparison of different cell populations.
Estimating information in spike trains: why so many methods?
Entropy and information are quantities of interest to neuroscientists, because of their mathematical properties and because they place limits on the performance of a neural system. Estimating these quantities from neural spike trains is much more challenging than estimating other statistics, such as mean and variance. The central difficulty in estimating information is tightly linked to the properties of information that make it a desirable quantity to estimate. This fundamental difficulty can be surmounted through the use of broad classes of models for spike trains, or for how spike trains are related to each other. These model classes vary widely in their character, and consequently, each leads to a different kind of strategy for information estimation. As a result, information estimates are useful not only in situations in which several approaches provide mutually consistent results, but also in situations in which they differ. These ideas are illustrated with examples from the visual and gustatory systems.
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