Bayesian Inference for Spiking Neuron Models with a Sparsity Prior

Generalized linear models are the most commonly used tools to describe the stimulus selectivity of sensory neurons. Here we present a Bayesian treatment of such models. Using the expectation propagation algorithm, we are able to approximate the full posterior distribution over all weights. In addition, we use a Laplacian prior to favor sparse solutions. Therefore, stimulus features that do not critically influence neural activity will be assigned zero weights and thus be effectively excluded by the model. This feature selection mechanism facilitates both the interpretation of the neuron model as well as its predictive abilities. The posterior distribution can be used to obtain confidence intervals which makes it possible to assess the statistical significance of the solution. In neural data analysis, the available amount of experimental measurements is often limited whereas the parameter space is large. In such a situation, both regularization by a sparsity prior and uncertainty estimates for the model parameters are essential. We apply our method to multi-electrode recordings of retinal ganglion cells and use our uncertainty estimate to test the statistical significance of functional couplings between neurons. Furthermore we used the sparsity of the Laplace prior to select those filters from a spike-triggered covariance analysis that are most informative about the neural response

Statistical Inference for Assessing Functional Connectivity of Neuronal Ensembles With Sparse Spiking Data

The ability to accurately infer functional connectivity between ensemble neurons using experimentally acquired spike train data is currently an important research objective in computational neuroscience. Point process generalized linear models and maximum likelihood estimation have been proposed as effective methods for the identification of spiking dependency between neurons. However, unfavorable experimental conditions occasionally results in insufficient data collection due to factors such as low neuronal firing rates or brief recording periods, and in these cases, the standard maximum likelihood estimate becomes unreliable. The present studies compares the performance of different statistical inference procedures when applied to the estimation of functional connectivity in neuronal assemblies with sparse spiking data. Four inference methods were compared: maximum likelihood estimation, penalized maximum likelihood estimation, using either l2 or l1 regularization, and hierarchical Bayesian estimation based on a variational Bayes algorithm. Algorithmic performances were compared using well-established goodness-of-fit measures in benchmark simulation studies, and the hierarchical Bayesian approach performed favorably when compared with the other algorithms, and this approach was then successfully applied to real spiking data recorded from the cat motor cortex. The identification of spiking dependencies in physiologically acquired data was encouraging, since their sparse nature would have previously precluded them from successful analysis using traditional methods.National Institutes of Health (U.S.) (Grant DP1-OD003646)National Institutes of Health (U.S.) (Grant Grant R01-DA015644)National Institutes of Health (U.S.) (Grant Grant R01-HL08450

Feature detection using spikes: the greedy approach

A goal of low-level neural processes is to build an efficient code extracting the relevant information from the sensory input. It is believed that this is implemented in cortical areas by elementary inferential computations dynamically extracting the most likely parameters corresponding to the sensory signal. We explore here a neuro-mimetic feed-forward model of the primary visual area (VI) solving this problem in the case where the signal may be described by a robust linear generative model. This model uses an over-complete dictionary of primitives which provides a distributed probabilistic representation of input features. Relying on an efficiency criterion, we derive an algorithm as an approximate solution which uses incremental greedy inference processes. This algorithm is similar to 'Matching Pursuit' and mimics the parallel architecture of neural computations. We propose here a simple implementation using a network of spiking integrate-and-fire neurons which communicate using lateral interactions. Numerical simulations show that this Sparse Spike Coding strategy provides an efficient model for representing visual data from a set of natural images. Even though it is simplistic, this transformation of spatial data into a spatio-temporal pattern of binary events provides an accurate description of some complex neural patterns observed in the spiking activity of biological neural networks.Comment: This work links Matching Pursuit with bayesian inference by providing the underlying hypotheses (linear model, uniform prior, gaussian noise model). A parallel with the parallel and event-based nature of neural computations is explored and we show application to modelling Primary Visual Cortex / image processsing. http://incm.cnrs-mrs.fr/perrinet/dynn/LaurentPerrinet/Publications/Perrinet04tau

Low-rank graphical models and Bayesian inference in the statistical analysis of noisy neural data

We develop new methods of Bayesian inference, largely in the context of analysis of neuroscience data. The work is broken into several parts. In the first part, we introduce a novel class of joint probability distributions in which exact inference is tractable. Previously it has been difficult to find general constructions for models in which efficient exact inference is possible, outside of certain classical cases. We identify a class of such models that are tractable owing to a certain "low-rank" structure in the potentials that couple neighboring variables. In the second part we develop methods to quantify and measure information loss in analysis of neuronal spike train data due to two types of noise, making use of the ideas developed in the first part. Information about neuronal identity or temporal resolution may be lost during spike detection and sorting, or precision of spike times may be corrupted by various effects. We quantify the information lost due to these effects for the relatively simple but sufficiently broad class of Markovian model neurons. We find that decoders that model the probability distribution of spike-neuron assignments significantly outperform decoders that use only the most likely spike assignments. We also apply the ideas of the low-rank models from the first section to defining a class of prior distributions over the space of stimuli (or other covariate) which, by conjugacy, preserve the tractability of inference. In the third part, we treat Bayesian methods for the estimation of sparse signals, with application to the locating of synapses in a dendritic tree. We develop a compartmentalized model of the dendritic tree. Building on previous work that applied and generalized ideas of least angle regression to obtain a fast Bayesian solution to the resulting estimation problem, we describe two other approaches to the same problem, one employing a horseshoe prior and the other using various spike-and-slab priors. In the last part, we revisit the low-rank models of the first section and apply them to the problem of inferring orientation selectivity maps from noisy observations of orientation preference. The relevant low-rank model exploits the self-conjugacy of the von Mises distribution on the circle. Because the orientation map model is loopy, we cannot do exact inference on the low-rank model by the forward backward algorithm, but block-wise Gibbs sampling by the forward backward algorithm speeds mixing. We explore another von Mises coupling potential Gibbs sampler that proves to effectively smooth noisily observed orientation maps

Bayesian Inference for Generalized Linear Models for Spiking Neurons

Generalized Linear Models (GLMs) are commonly used statistical methods for modelling the relationship between neural population activity and presented stimuli. When the dimension of the parameter space is large, strong regularization has to be used in order to fit GLMs to datasets of realistic size without overfitting. By imposing properly chosen priors over parameters, Bayesian inference provides an effective and principled approach for achieving regularization. Here we show how the posterior distribution over model parameters of GLMs can be approximated by a Gaussian using the Expectation Propagation algorithm. In this way, we obtain an estimate of the posterior mean and posterior covariance, allowing us to calculate Bayesian confidence intervals that characterize the uncertainty about the optimal solution. From the posterior we also obtain a different point estimate, namely the posterior mean as opposed to the commonly used maximum a posteriori estimate. We systematically compare the different inference techniques on simulated as well as on multi-electrode recordings of retinal ganglion cells, and explore the effects of the chosen prior and the performance measure used. We find that good performance can be achieved by choosing an Laplace prior together with the posterior mean estimate