arXiv subjects

Christophe Pouzat

Publications and source records attributed to Christophe Pouzat.

10 recordsLinked to original sources

arXiv2026

Simulation Based Inference of a Simple Neural Network Structure

Neurophysiologists are nowadays able to record from a large number of extracellular electrodes and to extract, from the raw data, the sequences of action potentials or spikes generated by many neurons. Unfortunately these ''many neurons'' still represent only a tiny fraction of the neuronal population that constitutes the network. Using association statistics such as the estimation of the cross-correlation functions, they are trying to infer the structure of the network formed by the recorded neurons. But this inference is compromised by the tremendous under-sampling of the neuronal population. We propose to focus instead on simple spike train statistics, like the empirical spikes frequency, or the interspike interval distribution. Their sampling distributions can be estimated by simulations, and, given a few observed spike train statistics, they provide enough information to infer the structure of the underlying network. We show that, on a ''toy model'', our method gives significantly better results than the sub-network reconstruction method with regards to the inference of the connection probability of the original network.

stat.AP↗

arXiv2025

ToMATo: an efficient and robust clustering algorithm for high dimensional datasets. An illustration with spike sorting

Clustering algorithms became an essential part of the neurophysiological data analysis toolbox in the last twenty five years. Many problems, from the definition of cell types/groups based on morphological, molecular and physiological data to the identification of sub-networks in fMRI data, are now routinely tackled with clustering analysis. Since the datasets to which this type of analysis is applied tend to be defined in larger and larger dimensional spaces, there is a need for efficient and robust clustering methods in high dimension. There is also a need for methods that assume as little as possible about the clusters shape and size. We report here our experience with the ToMATo (Topological Mode Analysis Tool) algorithm. It is based on a definitely deep mathematical theory (algebraic topology), but its Python based open-source implementation is easily accessible to practitioners. We applied ToMATo to a problem we know well, spike sorting. Its capability to work in the ''native'' space of the data (no dimension reduction is required) is remarkable, as well as its robustness with respect to outliers (superposed spikes).

stat.AP↗

arXiv2024

A Quasi-Stationary Approach to Metastability in a System of Spiking Neurons with Synaptic Plasticity

After reviewing the behavioral studies of working memory and of the cellular substrate of the latter, we argue that metastable states constitute candidates for the type of transient information storage required by working memory. We then present a simple neural network model made of stochastic units whose synapses exhibit short-term facilitation. The Markov process dynamics of this model was specifically designed to be analytically tractable, simple to simulate numerically and to exhibit a quasi-stationary distribution (QSD). Since the state space is finite this QSD is also a Yaglom limit, which allows us to bridge the gap between quasi-stationarity and metastability by considering the relative orders of magnitude of the relaxation and absorption times. We present first analytical results: characterization of the absorbing region of the Markov process, irreducibility outside this absorbing region and consequently existence and uniqueness of a QSD. We then apply Perron-Frobenius spectral analysis to obtain any specific QSD, and design an approximate method for the first moments of this QSD when the exact method is intractable. Finally we use these methods to study the relaxation time toward the QSD and establish numerically the memorylessness of the time of extinction.

q-bio.NC↗

arXiv2021

Interacting Hawkes processes with multiplicative inhibition

In the present work, we introduce a general class of mean-field interacting nonlinear Hawkes processes modelling the reciprocal interactions between two neuronal populations, one excitatory and one inhibitory. The model incorporates two features: inhibition, which acts as a multiplicative factor onto the intensity of the excitatory population and additive retroaction from the excitatory neurons onto the inhibitory ones. We give first a detailed analysis of the well-posedness of this interacting system as well as its dynamics in large population. The second aim of the paper is to give a rigorous analysis of the longtime behavior of the mean-field limit process. We provide also numerical evidence that inhibition and retroaction may be responsible for the emergence of limit cycles in such system.

math.PR↗

arXiv2019

A system of interacting neurons with short term synaptic facilitation

In this paper we present a simple microscopic stochastic model describing short term plasticity within a large homogeneous network of interacting neurons. Each neuron is represented by its membrane potential and by the residual calcium concentration within the cell at a given time. Neurons spike at a rate depending on their membrane potential. When spiking, the residual calcium concentration of the spiking neuron increases by one unit. Moreover, an additional amount of potential is given to all other neurons in the system. This amount depends linearly on the current residual calcium concentration within the cell of the spiking neuron. In between successive spikes, the potentials and the residual calcium concentrations of each neuron decrease at a constant rate. We show that in this framework, short time memory can be described as the tendency of the system to keep track of an initial stimulus by staying within a certain region of the space of configurations during a short but macroscopic amount of time before finally being kicked out of this region and relaxing to equilibrium. The main technical tool is a rigorous justification of the passage to a large population limit system and a thorough study of the limit equation.

math.PR↗

arXiv2017

Estimation of neuronal interaction graph from spike train data

One of the main current issues in Neurobiology concerns the understanding of interrelated spiking activity among multineuronal ensembles and differences between stimulus-driven and spontaneous activity in neurophysiological experiments. Multi electrode array recordings that are now commonly used monitor neuronal activity in the form of spike trains from many well identified neurons. A basic question when analyzing such data is the identification of the directed graph describing "synaptic coupling" between neurons. In this article we deal with this matter working with a high quality multielectrode array recording dataset (Pouzat et al., 2015) from the first olfactory relay of the locust, $Schistocerca$ $americana$. From a mathematical point of view this paper presents two novelties. First we propose a procedure allowing to deal with the small sample sizes met in actual datasets. Moreover we address the sensitive case of partially observed networks. Our starting point is the procedure introduced in Duarte et al. (2016). We evaluate the performance of both original and improved procedures through simulation studies, which are also used for parameter tuning and for exploring the effect of recording only a small subset of the neurons of a network.

q-bio.NC↗

arXiv2014

SPySort: Neuronal Spike Sorting with Python

Extracellular recordings with multi-electrode arrays is one of the basic tools of contemporary neuroscience. These recordings are mostly used to monitor the activities, understood as sequences of emitted action potentials, of many individual neurons. But the raw data produced by extracellular recordings are most commonly a mixture of activities from several neurons. In order to get the activities of the individual contributing neurons, a pre-processing step called spike sorting is required. We present here a pure Python implementation of a well tested spike sorting procedure. The latter was designed in a modular way in order to favour a smooth transition from an interactive sorting, for instance with IPython, to an automatic one. Surprisingly enough - or sadly enough, depending on one's view point -, recoding our now 15 years old procedure into Python was the occasion of major methodological improvements.

cs.CE↗

arXiv2009

On Goodness of Fit Tests For Models of Neuronal Spike Trains Considered as Counting Processes

After an elementary derivation of the "time transformation", mapping a counting process onto a homogeneous Poisson process with rate one, a brief review of Ogata's goodness of fit tests is presented and a new test, the "Wiener process test", is proposed. This test is based on a straightforward application of Donsker's Theorem to the intervals of time transformed counting processes. The finite sample properties of the test are studied by Monte Carlo simulations. Performances on simulated as well as on real data are presented. It is argued that due to its good finite sample properties, the new test is both a simple and a useful complement to Ogata's tests. Warnings are moreover given against the use of a single goodness of fit test.

stat.AP↗

arXiv2005

Efficient spike-sorting of multi-state neurons using inter-spike intervals information

We demonstrate the efficacy of a new spike-sorting method based on a Markov Chain Monte Carlo (MCMC) algorithm by applying it to real data recorded from Purkinje cells (PCs) in young rat cerebellar slices. This algorithm is unique in its capability to estimate and make use of the firing statistics as well as the spike amplitude dynamics of the recorded neurons. PCs exhibit multiple discharge states, giving rise to multimodal interspike interval (ISI) histograms and to correlations between successive ISIs. The amplitude of the spikes generated by a PC in an "active" state decreases, a feature typical of many neurons from both vertebrates and invertebrates. These two features constitute a major and recurrent problem for all the presently available spike-sorting methods. We first show that a Hidden Markov Model with 3 log-Normal states provides a flexible and satisfying description of the complex firing of single PCs. We then incorporate this model into our previous MCMC based spike-sorting algorithm (Pouzat et al, 2004, J. Neurophys. 91, 2910-2928) and test this new algorithm on multi-unit recordings of bursting PCs. We show that our method successfully classifies the bursty spike trains fired by PCs by using an independent single unit recording from a patch-clamp pipette.

q-bio.QM↗

arXiv2004

Technique(s) for Spike - Sorting

Spike-sorting techniques attempt to classify a series of noisy electrical waveforms according to the identity of the neurons that generated them. Existing techniques perform this classification ignoring several properties of actual neurons that can ultimately improve classification performance. In this chapter, after illustrating the spike-sorting problem with real data, we propose a more realistic spike train generation model. It incorporates both a description of "non trivial" (ie, non Poisson) neuronal discharge statistics and a description of spike waveform dynamics (eg, the events amplitude decays for short inter-spike intervals). We show that this spike train generation model is analogous to a one-dimensional Potts spin glass model. We can therefore use the computational methods which have been developed in fields where Potts models are extensively used. These methods are based on the construction of a Markov Chain in the space of model parameters and spike train configurations, where a configuration is defined by specifying a neuron of origin for each spike. This Markov Chain is built such that its unique stationary density is the posterior density of model parameters and configurations given the observed data. A Monte Carlo simulation of the Markov Chain is then used to estimate the posterior density. The theoretical background on Markov chains is provided and the way to build the transition matrix of the Markov Chain is illustrated with a simple, but realistic, model for data generation . Simulated data are used to illustrate the performance of the method and to show that it can easily cope with neurons generating spikes with highly dynamic waveforms and/or generating strongly overlapping clusters on Wilson plots.

q-bio.QM↗