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Register a new userRetinal metric: a stimulus distance measure derived from population neural responses
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The ability of the organism to distinguish between various stimuli is limited by the structure and noise in the population code of its sensory neurons. Here we infer a distance measure on the stimulus space directly from the recorded activity of 100 neurons in the salamander retina. In contrast to previously used measures of stimulus similarity, this neural metric tells us how distinguishable a pair of stimulus clips is to the retina, given the noise in the neural population response. We show that the retinal distance strongly deviates from Euclidean, or any static metric, yet has a simple structure: we identify the stimulus features that the neural population is jointly sensitive to, and show the SVM-like kernel function relating the stimulus and neural response spaces. We show that the non-Euclidean nature of the retinal distance has important consequences for neural decoding.
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Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. To be able to infer a model for this distribution from large-scale neural recordings, we introduce a stimulus-dependent maximum entropy (SDME) model---a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. The model is able to capture the single-cell response properties as well as the correlations in neural spiking due to shared stimulus and due to effective neuron-to-neuron connections. Here we show that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. As a result, the SDME model gives a more accurate account of single cell responses and in particular outperforms uncoupled models in reproducing the distributions of codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like surprise and information transmission in a neural population.
Adaptation in the retina is thought to optimize the encoding of natural light signals into sequences of spikes sent to the brain. However, adaptation also entails computational costs: adaptive code is intrinsically ambiguous, because output symbols cannot be trivially mapped back to the stimuli without the knowledge of the adaptive state of the encoding neuron. It is thus important to learn which statistical changes in the input do, and which do not, invoke adaptive responses, and ask about the reasons for potential limits to adaptation. We measured the ganglion cell responses in the tiger salamander retina to controlled changes in the second (contrast), third (skew) and fourth (kurtosis) moments of the light intensity distribution of spatially uniform temporally independent stimuli. The skew and kurtosis of the stimuli were chosen to cover the range observed in natural scenes. We quantified adaptation in ganglion cells by studying two-dimensional linear-nonlinear models that capture well the retinal encoding properties across all stimuli. We found that the retinal ganglion cells adapt to contrast, but exhibit remarkably invariant behavior to changes in higher-order statistics. Finally, by theoretically analyzing optimal coding in LN-type models, we showed that the neural code can maintain a high information rate without dynamic adaptation despite changes in stimulus skew and kurtosis.
We present a theoretical application of an optimal experiment design (OED) methodology to the development of mathematical models to describe the stimulus-response relationship of sensory neurons. Although there are a few related studies in the computational neuroscience literature on this topic, most of them are either involving non-linear static maps or simple linear filters cascaded to a static non-linearity. Although the linear filters might be appropriate to demonstrate some aspects of neural processes, the high level of non-linearity in the nature of the stimulus-response data may render them inadequate. In addition, modelling by a static non-linear input - output map may mask important dynamical (time-dependent) features in the response data. Due to all those facts a non-linear continuous time dynamic recurrent neural network that models the excitatory and inhibitory membrane potential dynamics is preferred. The main goal of this research is to estimate the parametric details of this model from the available stimulus-response data. In order to design an efficient estimator an optimal experiment design scheme is proposed which computes a pre-shaped stimulus to maximize a certain measure of Fisher Information Matrix. This measure depends on the estimated values of the parameters in the current step and the optimal stimuli are used in a maximum likelihood estimation procedure to find an estimate of the network parameters. This process works as a loop until a reasonable convergence occurs. The response data is discontinuous as it is composed of the neural spiking instants which is assumed to obey the Poisson statistical distribution. Thus the likelihood functions depend on the Poisson statistics. In order to validate the approach and evaluate its performance, a comparison with another approach on estimation based on randomly generated stimuli is also presented.
Although perceptual (dis)similarity between sensory stimuli seems akin to distance, measuring the Euclidean distance between vector representations of auditory stimuli is a poor estimator of subjective dissimilarity. In hearing, nonlinear response patterns, interactions between stimulus components, temporal effects, and top-down modulation transform the information contained in incoming frequency-domain stimuli in a way that seems to preserve some notion of distance, but not that of familiar Euclidean space. This work proposes that transformations applied to auditory stimuli during hearing can be modeled as a function mapping stimulus points to their representations in a perceptual space, inducing a Riemannian distance metric. A dataset was collected in a subjective listening experiment, the results of which were used to explore approaches (biologically inspired, data-driven, and combinations thereof) to approximating the perceptual map. Each of the proposed measures achieved comparable or stronger correlations with subjective ratings (r ~ 0.8) compared to state-of-the-art audio quality measures.
Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are only selective for a small number of linear projections of a potentially high-dimensional input. Here we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g. naturalistic) stimulus distribution, we review several inference methods, focussing in particular on two information-theory-based approaches (maximization of stimulus energy or of noise entropy) and a likelihood-based approach (Bayesian spike-triggered covariance, extensions of generalized linear models). We analyze the formal connection between the likelihood-based and information-based approaches to show how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.
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