A generalized linear model for estimating spectrotemporal receptive fields from responses to natural sounds

In the auditory system, the stimulus-response properties of single neurons are often described in terms of the spectrotemporal receptive field (STRF), a linear kernel relating the spectrogram of the sound stimulus to the instantaneous firing rate of the neuron. Several algorithms have been used to estimate STRFs from responses to natural stimuli; these algorithms differ in their functional models, cost functions, and regularization methods. Here, we characterize the stimulus-response function of auditory neurons using a generalized linear model (GLM). In this model, each cell's input is described by: 1) a stimulus filter (STRF); and 2) a post-spike filter, which captures dependencies on the neuron's spiking history. The output of the model is given by a series of spike trains rather than instantaneous firing rate, allowing the prediction of spike train responses to novel stimuli. We fit the model by maximum penalized likelihood to the spiking activity of zebra finch auditory midbrain neurons in response to conspecific vocalizations (songs) and modulation limited (ml) noise. We compare this model to normalized reverse correlation (NRC), the traditional method for STRF estimation, in terms of predictive power and the basic tuning properties of the estimated STRFs. We find that a GLM with a sparse prior predicts novel responses to both stimulus classes significantly better than NRC. Importantly, we find that STRFs from the two models derived from the same responses can differ substantially and that GLM STRFs are more consistent between stimulus classes than NRC STRFs. These results suggest that a GLM with a sparse prior provides a more accurate characterization of spectrotemporal tuning than does the NRC method when responses to complex sounds are studied in these neurons.     

Characterizing the fine structure of a neural sensory code through information distortion

We present an application of the information distortion approach to neural coding. The approach allows the discovery of neural symbols and the corresponding stimulus space of a neuron or neural ensemble simultaneously and quantitatively, making few assumptions about the nature of either code or relevant features. The neural codebook is derived by quantizing sensory stimuli and neural responses into small reproduction sets, and optimizing the quantization to minimize the information distortion function. The application of this approach to the analysis of coding in sensory interneurons involved a further restriction of the space of allowed quantizers to a smaller family of parametric distributions. We show that, for some cells in this system, a significant amount of information is encoded in patterns of spikes that would not be discovered through analyses based on linear stimulus-response measures.     

Decorrelation of Neural-Network Activity by Inhibitory Feedback

Correlations in spike-train ensembles can seriously impair the encoding of information by their spatio-temporal structure. An inevitable source of correlation in finite neural networks is common presynaptic input to pairs of neurons. Recent studies demonstrate that spike correlations in recurrent neural networks are considerably smaller than expected based on the amount of shared presynaptic input. Here, we explain this observation by means of a linear network model and simulations of networks of leaky integrate-and-fire neurons. We show that inhibitory feedback efficiently suppresses pairwise correlations and, hence, population-rate fluctuations, thereby assigning inhibitory neurons the new role of active decorrelation. We quantify this decorrelation by comparing the responses of the intact recurrent network (feedback system) and systems where the statistics of the feedback channel is perturbed (feedforward system). Manipulations of the feedback statistics can lead to a significant increase in the power and coherence of the population response. In particular, neglecting correlations within the ensemble of feedback channels or between the external stimulus and the feedback amplifies population-rate fluctuations by orders of magnitude. The fluctuation suppression in homogeneous inhibitory networks is explained by a negative feedback loop in the one-dimensional dynamics of the compound activity. Similarly, a change of coordinates exposes an effective negative feedback loop in the compound dynamics of stable excitatory-inhibitory networks. The suppression of input correlations in finite networks is explained by the population averaged correlations in the linear network model: In purely inhibitory networks, shared-input correlations are canceled by negative spike-train correlations. In excitatory-inhibitory networks, spike-train correlations are typically positive. Here, the suppression of input correlations is not a result of the mere existence of correlations between excitatory (E) and inhibitory (I) neurons, but a consequence of a particular structure of correlations among the three possible pairings (EE, EI, II).     

Dynamic Alignment Models for Neural Coding

Recently, there have been remarkable advances in modeling the relationships between the sensory environment, neuronal responses, and behavior. However, most models cannot encompass variable stimulus-response relationships such as varying response latencies and state or context dependence of the neural code. Here, we consider response modeling as a dynamic alignment problem and model stimulus and response jointly by a mixed pair hidden Markov model (MPH). In MPHs, multiple stimulus-response relationships (e.g., receptive fields) are represented by different states or groups of states in a Markov chain. Each stimulus-response relationship features temporal flexibility, allowing modeling of variable response latencies, including noisy ones. We derive algorithms for learning of MPH parameters and for inference of spike response probabilities. We show that some linear-nonlinear Poisson cascade (LNP) models are a special case of MPHs. We demonstrate the efficiency and usefulness of MPHs in simulations of both jittered and switching spike responses to white noise and natural stimuli. Furthermore, we apply MPHs to extracellular single and multi-unit data recorded in cortical brain areas of singing birds to showcase a novel method for estimating response lag distributions. MPHs allow simultaneous estimation of receptive fields, latency statistics, and hidden state dynamics and so can help to uncover complex stimulus response relationships that are subject to variable timing and involve diverse neural codes.     

The influence of cortical feature maps on the encoding of the orientation of a short line

The inhomogeneous distribution of the receptive fields of cortical neurons influences the cortical representation of the orientation of short lines seen in visual images. We construct a model of the response of populations of neurons in the human primary visual cortex by combining realistic response properties of individual neurons and cortical maps of orientation and location preferences. The encoding error, which characterizes the difference between the parameters of a visual stimulus and their cortical representation, is calculated using Fisher information as the square root of the variance of a statistically efficient estimator. The error of encoding orientation varies considerably with the location and orientation of the short line stimulus as modulated by the underlying orientation preference map. The average encoding error depends only weakly on the structure of the orientation preference map and is much smaller than the human error of estimating orientation measured psychophysically. From this comparison we conclude that the actual mechanism of orientation perception does not make efficient use of all the information available in the neuronal responses and that it is the decoding of visual information from neuronal responses that limits psychophysical performance. Action Editor: Terrence Sejnowski     

Correlation-distortion based identification of Linear-Nonlinear-Poisson models

Linear-Nonlinear-Poisson (LNP) models are a popular and powerful tool for describing encoding (stimulus-response) transformations by single sensory as well as motor neurons. Recently, there has been rising interest in the second- and higher-order correlation structure of neural spike trains, and how it may be related to specific encoding relationships. The distortion of signal correlations as they are transformed through particular LNP models is predictable and in some cases analytically tractable and invertible. Here, we propose that LNP encoding models can potentially be identified strictly from the correlation transformations they induce, and develop a computational method for identifying minimum-phase single-neuron temporal kernels under white and colored random Gaussian excitation. Unlike reverse-correlation or maximum-likelihood, correlation-distortion based identification does not require the simultaneous observation of stimulus-response pairs—only their respective second order statistics. Although in principle filter kernels are not necessarily minimum-phase, and only their spectral amplitude can be uniquely determined from output correlations, we show that in practice this method provides excellent estimates of kernels from a range of parametric models of neural systems. We conclude by discussing how this approach could potentially enable neural models to be estimated from a much wider variety of experimental conditions and systems, and its limitations.     

A critical assessment of different measures of the information carried by correlated neuronal firing

Information theoretic measures have been proposed as a quantitative framework to clarify the role of correlated neuronal activity in the brain. In this paper we review some recent methods that allow precise assessments of the role of correlation in stimulus coding and decoding by the nervous system. We present new results that make explicit links between types of encoding and decoding mechanisms based on correlations. We illustrate the concepts by showing that the spike trains of pairs of neurons in rat somatosensory cortex can be decoded almost perfectly without including knowledge of correlation in the read-out model, although in this neural system correlations between spike times contribute appreciably to stimulus encoding.     

Neural solution to the correction of miss distance in gun fire control system

Multilayer perceptrons trained with the backpropagation algorithm are tested in gun fire control system for error correction and are compared to optimal algorithms based on minimum mean square error. The structure of the proposed neural controller is described and performance results are shown.     

Characteristics of Human Luminance Discrimination and Modeling a Neural Network Based on the Response Properties of the Visual Cortex

Reaction time (RT) and error rate that depend on stimulus duration were measured in a luminance-discrimination reaction time task. Two patches of light with different luminance were presented to participants for ‘short’ (150 ms) or ‘long’ (1 s) period on each trial. When the stimulus duration was ‘short’, the participants responded more rapidly with poorer discrimination performance than they did in the longer duration. The results suggested that different sensory responses in the visual cortices were responsible for the dependence of response speed and accuracy on the stimulus duration during the luminance-discrimination reaction time task. It was shown that the simple winner-take-all-type neural network model receiving transient and sustained stimulus information from the primary visual cortex successfully reproduced RT distributions for correct responses and error rates. Moreover, temporal spike sequences obtained from the model network closely resembled to the neural activity in the monkey prefrontal or parietal area during other visual decision tasks such as motion discrimination and oddball detection tasks.     

Processing of hierarchic stimulus structures has advantages in humans and animals

Carmesin and Schwegler (1994) have determined theoretically that a linear hierarchical stimulus structure can be encoded by a parallel network of minimal complexity. The experiments reported here compare the efficiency with which humans and pigeons process sets of stimulus pairs embodying different inequality structures. Groups of subjects of each species were taught to discriminate all 10 pairwise combinations of 5 stimuli with an operant conditioning method. For one group, the reward/punishment allocations within the pairs agreed with a linear hierarchy. For a second and third group, the reinforcement allocations of one or three, respectively, of the stimulus pairs deviated from such ordering. The time it took the subjects to learn the tasks as well as the final choice latencies and/or error rates increased with the number of deviating inequalities. The results agree with the assumption that both humans and pigeons encode stimulus inequality structures with parallel processing neural networks rather than with a sequentially processing algorithm.     

Estimation of response curves in closed-loop physiological control

Several recent reports have addressed the problem of estimating the response slope from repeated measurements of paired data when both stimulus and response variables are subject to biological variability. These earlier approaches suffer from several drawbacks: useful information about the relationships between the error components in a closed-loop system is not fully utilized; the response intercept cannot be directly estimated; and the normalization procedure required in some methods may fail under certain circumstances. This paper proposes a new, general method of simultaneously estimating the response slope and intercept from corrupted stimulus-response data when the errors in both variables are specifically related by the system structure. A direct extension of the least-squares approach, this method [directed least squares (DLS)] reduces to ordinary least-squares methods when either of the measured variables is error free and to the reduced-major-axis (RMA) method of Kermack and Haldane (Biometrics 37: 30-41, 1950) when the magnitudes of the normalized errors are equal. The DLS estimators are scale invariant, statistically unbiased and always assume the minimum variance. With simple modifications, the method is also applicable to paired data. If, however, the relation between error components is uncertain, then the RMA method is optimal, i.e., having the least possible asymptotic bias and variance. These results are illustrated by using various types of closed-loop respiratory response data.     

Receiver operating characteristic (ROC) analysis of neural code efficacies

 Nerve cell signals are different in form from the stimuli that evoke them and they exhibit complex spatio-temporal characteristics. This defines a neural coding problem which is addressed by two current theories: Multiple Meaning Theory holds that neural signals contain patterns that make statements about combinations of stimulus properties; the Task Dependence Hypothesis suggests that different features of identical neural signals mediate performance in different behavioral tasks. These coding issues were addressed by investigating the representation of sensory information in the distal nervous system after transduction of visual stimuli into bio-electric signals. The objects of study were light-evoked neural responses which had been intracellularly recorded from single retinula (photoreceptor) cells in Limulus lateral eyes. The efficacies with which sensory information was represented by various candidate neural codes were calculated using receiver operating characteristic (ROC) analyses to provide objective indices. The specific visual problem under investigation was discrimination between light flashes whose intensities differed by a very small amount. A wide range of light adaptation states and relative stimulus intensities were explored. Extremely stringent data quality standards were applied which restricted the investigation to cells whose potentials did not exhibit any statistically significant drift during the hours required for data collection. Seven cellular characterizations were simultaneously monitored to detect drift in a given cell’s potentials; these characterizations included the value of the membrane potential and the values of six candidate codes. These codes were: the area under the light-evoked receptor potential (RP), the mean value of the RP, the peak height of the RP, the slope of the onset of the RP, the duration required for the RP to drop from its peak by a given amount, and the duration required for the RP to end. The results were: (1) Light adaptation increases efficacy. (2) Thus, light adaptation trades sensitivity for acuity (as characterized by ROC discriminations). (3) Increasing relative light flash intensity also increases efficacy. (4) The efficacies of the various codes are significantly different and fall in the following order: area?peak=mean?duration-end=slope= duration-drop. These findings further demonstrate that arbitrary characterizations of stimulus-response relationships are very likely to be incomplete. They particularly indicate that many commonly used and quite conventional neural analysis strategies may substantially underestimate system performance. Received: 21 August 1995/Accepted in revised form: 19 April 1996     

Balanced input allows optimal encoding in a stochastic binary neural network model: an analytical study

Recent neurophysiological experiments have demonstrated a remarkable effect of attention on the underlying neural activity that suggests for the first time that information encoding is indeed actively influenced by attention. Single cell recordings show that attention reduces both the neural variability and correlations in the attended condition with respect to the non-attended one. This reduction of variability and redundancy enhances the information associated with the detection and further processing of the attended stimulus. Beyond the attentional paradigm, the local activity in a neural circuit can be modulated in a number of ways, leading to the general question of understanding how the activity of such circuits is sensitive to these relatively small modulations. Here, using an analytically tractable neural network model, we demonstrate how this enhancement of information emerges when excitatory and inhibitory synaptic currents are balanced. In particular, we show that the network encoding sensitivity--as measured by the Fisher information--is maximized at the exact balance. Furthermore, we find a similar result for a more realistic spiking neural network model. As the regime of balanced inputs has been experimentally observed, these results suggest that this regime is functionally important from an information encoding standpoint.     

A nonlinear cascade model for action potential encoding in an insect sensory neuron.

Action potential encoding in the cockroach tactile spine neuron can be represented as a single-input single-output nonlinear dynamic process. We have used a new functional expansion method to characterize the nonlinear behavior of the neural encoder. This method, which yields similar kernels to the Wiener method, is more accurate than the latter and is efficient enough to obtain reasonable kernels in less than 15 min using a personal computer. The input stimulus was band-limited white Gaussian noise and the output consisted of the resulting train of action potentials, which were unitized to give binary values. The kernels and the system input-output signals were used to identify a model for encoding comprising a cascade of dynamic linear, static nonlinear, and dynamic linear components. The two dynamic linear components had repeatable and distinctive forms with the first being low-pass and the second being high-pass. The static nonlinearity was fitted with a fifth-order polynomial function over several input amplitude ranges and had the form of a half-wave rectifier. The complete model gave a good approximation to the output of the neuron when both were subjected to the same novel white noise input signal.     

The effect of negative and positive emotionality on associative memory: an FMRI study

In general, emotion is known to enhance memory processes. However, the effect of emotion on associative memory and the underling neural mechanisms remains largely unexplored. In this study, we explored brain activation during an associative memory task that involved the encoding and retrieval of word and face pairs. The word and face pairs consisted of either negative or positive words with neutral faces. Significant hippocampal activation was observed during both encoding and retrieval, regardless of whether the word was negative or positive. Negative and positive emotionality differentially affected the hemodynamic responses to encoding and retrieval in the amygdala, with increased responses during encoding negative word and face pairs. Furthermore, activation of the amygdala during encoding of negative word and neutral face pairs was inversely correlated with subsequent memory retrieval. These findings suggest that activation of the amygdala induced by negative emotion during encoding may disrupt associative memory performance.     

Stimulus and network dynamics collide in a ratiometric model of the antennal lobe macroglomerular complex

Time is considered to be an important encoding dimension in olfaction, as neural populations generate odour-specific spatiotemporal responses to constant stimuli. However, during pheromone mediated anemotactic search insects must discriminate specific ratios of blend components from rapidly time varying input. The dynamics intrinsic to olfactory processing and those of naturalistic stimuli can therefore potentially collide, thereby confounding ratiometric information. In this paper we use a computational model of the macroglomerular complex of the insect antennal lobe to study the impact on ratiometric information of this potential collision between network and stimulus dynamics. We show that the model exhibits two different dynamical regimes depending upon the connectivity pattern between inhibitory interneurons (that we refer to as fixed point attractor and limit cycle attractor), which both generate ratio-specific trajectories in the projection neuron output population that are reminiscent of temporal patterning and periodic hyperpolarisation observed in olfactory antennal lobe neurons. We compare the performance of the two corresponding population codes for reporting ratiometric blend information to higher centres of the insect brain. Our key finding is that whilst the dynamically rich limit cycle attractor spatiotemporal code is faster and more efficient in transmitting blend information under certain conditions it is also more prone to interference between network and stimulus dynamics, thus degrading ratiometric information under naturalistic input conditions. Our results suggest that rich intrinsically generated network dynamics can provide a powerful means of encoding multidimensional stimuli with high accuracy and efficiency, but only when isolated from stimulus dynamics. This interference between temporal dynamics of the stimulus and temporal patterns of neural activity constitutes a real challenge that must be successfully solved by the nervous system when faced with naturalistic input.     

Beyond GLMs: A Generative Mixture Modeling Approach to Neural System Identification

Generalized linear models (GLMs) represent a popular choice for the probabilistic characterization of neural spike responses. While GLMs are attractive for their computational tractability, they also impose strong assumptions and thus only allow for a limited range of stimulus-response relationships to be discovered. Alternative approaches exist that make only very weak assumptions but scale poorly to high-dimensional stimulus spaces. Here we seek an approach which can gracefully interpolate between the two extremes. We extend two frequently used special cases of the GLM—a linear and a quadratic model—by assuming that the spike-triggered and non-spike-triggered distributions can be adequately represented using Gaussian mixtures. Because we derive the model from a generative perspective, its components are easy to interpret as they correspond to, for example, the spike-triggered distribution and the interspike interval distribution. The model is able to capture complex dependencies on high-dimensional stimuli with far fewer parameters than other approaches such as histogram-based methods. The added flexibility comes at the cost of a non-concave log-likelihood. We show that in practice this does not have to be an issue and the mixture-based model is able to outperform generalized linear and quadratic models.     

Spatial interactions and stimulus-response relations of unit responses evoked by somato-sensory stimuli in the feline caudal medullary reticular formation

Responses of neurons in the bulbar reticular area to separate and simultaneous stimulation of the forelimbs were recorded extracellularly in chloralose-anaesthetized cats. On increasing the stimulus intensity the number of spikes per response increased while the initial latency and interspike intervals decreased in accordance with the functional property of the neuron. Responses evoked by simultaneous stimulation displayed more spikes and a shorter latency than those evoked by separate stimuli of corresponding intensities. The differences in the responses evoked simultaneously and the sums of responses evoked separately showed characteristic distributions as a function of the latter. Three types of distribution were distinguished. The results indicate that stimulus-response relations play a determining role in the mechanism of spatial integration.     

Discriminative Learning of Receptive Fields from Responses to Non-Gaussian Stimulus Ensembles

Analysis of sensory neurons'' processing characteristics requires simultaneous measurement of presented stimuli and concurrent spike responses. The functional transformation from high-dimensional stimulus space to the binary space of spike and non-spike responses is commonly described with linear-nonlinear models, whose linear filter component describes the neuron''s receptive field. From a machine learning perspective, this corresponds to the binary classification problem of discriminating spike-eliciting from non-spike-eliciting stimulus examples. The classification-based receptive field (CbRF) estimation method proposed here adapts a linear large-margin classifier to optimally predict experimental stimulus-response data and subsequently interprets learned classifier weights as the neuron''s receptive field filter. Computational learning theory provides a theoretical framework for learning from data and guarantees optimality in the sense that the risk of erroneously assigning a spike-eliciting stimulus example to the non-spike class (and vice versa) is minimized. Efficacy of the CbRF method is validated with simulations and for auditory spectro-temporal receptive field (STRF) estimation from experimental recordings in the auditory midbrain of Mongolian gerbils. Acoustic stimulation is performed with frequency-modulated tone complexes that mimic properties of natural stimuli, specifically non-Gaussian amplitude distribution and higher-order correlations. Results demonstrate that the proposed approach successfully identifies correct underlying STRFs, even in cases where second-order methods based on the spike-triggered average (STA) do not. Applied to small data samples, the method is shown to converge on smaller amounts of experimental recordings and with lower estimation variance than the generalized linear model and recent information theoretic methods. Thus, CbRF estimation may prove useful for investigation of neuronal processes in response to natural stimuli and in settings where rapid adaptation is induced by experimental design.