arXiv subjects

Antonio Galves

Publications and source records attributed to Antonio Galves.

At least 19 recordsLinked to original sources

arXiv2024

Fast Consensus and Metastability in a Highly Polarized Social Network

A polarized social network is modeled as a system of interacting marked point processes with memory of variable length. Each point process indicates the successive times in which a social actor expresses a "favorable" or "contrary" opinion. After expressing an opinion, the social pressure on the actor is reset to 0, waiting for the group's reaction. The orientation and the rate at which an actor expresses an opinion is influenced by the social pressure exerted on it, modulated by a polarization coefficient. We prove that the network reaches an instantaneous but metastable consensus, when the polarization coefficient diverges.

math.PR↗

arXiv2023

The brain uses renewal points to model random sequences of stimuli

It has been classically conjectured that the brain assigns probabilistic models to sequences of stimuli. An important issue associated with this conjecture is the identification of the classes of models used by the brain to perform this task. We address this issue by using a new clustering procedure for sets of electroencephalographic (EEG) data recorded from participants exposed to a sequence of auditory stimuli generated by a stochastic chain. This clustering procedure indicates that the brain uses renewal points in the stochastic sequence of auditory stimuli in order to build a model.

q-bio.NC↗

arXiv2023

Clustering Sets of Functional Data by Similarity in Law

We introduce a new clustering method for the classification of functional data sets by their probabilistic law, that is, a procedure that aims to assign data sets to the same cluster if and only if the data were generated with the same underlying distribution. This method has the nice virtue of being non-supervised and non-parametric, allowing for exploratory investigation with few assumptions about the data. Rigorous finite bounds on the classification error are given along with an objective heuristic that consistently selects the best partition in a data-driven manner. Simulated data has been clustered with this procedure to show the performance of the method with different parametric model classes of functional data.

stat.ME↗

arXiv2023

What comes next? response times are affected by mispredictions in a stochastic game

Acting as a goalkeeper in a video-game, a participant is asked to predict the successive choices of the penalty taker. The sequence of choices of the penalty taker is generated by a stochastic chain with memory of variable length. It has been conjectured that the probability distribution of the response times is a function of the specific sequence of past choices governing the algorithm used by the penalty taker to make his choice at each step. We found empirical evidence that besides this dependence, the distribution of the response times depends also on the success or failure of the previous prediction made by the participant. Moreover, we found statistical evidence that this dependence propagates up to two steps forward after the prediction failure.

q-bio.NC↗

arXiv2023

Probabilistic prediction and context tree identification in the Goalkeeper Game

In this article we address two related issues on the learning of probabilistic sequences of events. First, which features make the sequence of events generated by a stochastic chain more difficult to predict. Second, how to model the procedures employed by different learners to identify the structure of sequences of events. Playing the role of a goalkeeper in a video game, participants were told to predict step by step the successive directions -- left, center or right -- to which the penalty kicker would send the ball. The sequence of kicks was driven by a stochastic chain with memory of variable length. Results showed that at least three features play a role in the first issue: 1) the shape of the context tree summarizing the dependencies between present and past directions; 2) the entropy of the stochastic chain used to generate the sequences of events; 3) the existence or not of a deterministic periodic sequence underlying the sequences of events. Moreover, evidence suggests that best learners rely less on their own past choices to identify the structure of the sequences of events.

stat.AP↗

arXiv2021

Estimating the interaction graph of stochastic neuronal dynamics by observing only pairs of neurons

We address the questions of identifying pairs of interacting neurons from the observation of their spiking activity. The neuronal network is modeled by a system of interacting point processes with memory of variable length. The influence of a neuron on another can be either excitatory or inhibitory. To identify the existence and the nature of an interaction we propose an algorithm based only on the observation of joint activity of the two neurons in successive time slots. This reduces the amount of computation and storage required to run the algorithm, thereby making the algorithm suitable for the analysis of real neuronal data sets. We obtain computable upper bounds for the probabilities of false positive and false negative detection. As a corollary we prove the consistency of the identification algorithm.

math.ST↗

arXiv2020

Retrieving the structure of probabilistic sequences of auditory stimuli from EEG data

Using a new probabilistic approach we model the relationship between sequences of auditory stimuli generated by stochastic chains and the electroencephalographic (EEG) data acquired while 19 participants were exposed to those stimuli. The structure of the chains generating the stimuli are characterized by rooted and labeled trees whose leaves, henceforth called contexts, represent the sequences of past stimuli governing the choice of the next stimulus. A classical conjecture claims that the brain assigns probabilistic models to samples of stimuli. If this is true, then the context tree generating the sequence of stimuli should be encoded in the brain activity. Using an innovative statistical procedure we show that this context tree can effectively be extracted from the EEG data, thus giving support to the classical conjecture.

q-bio.NC↗

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

Information transmission and criticality in the contact process

In the present paper, we study the relation between criticality and information transmission in the one-dimensional contact process with infection parameter $λ.$ To do this we define the {\it sensitivity} of the process to its initial condition. This sensitivity increases for values of $λ< λ_c, $ the value of the critical parameter. The main point of the present paper is that we show that actually it continues increasing even after $ λ_c $ and only starts decreasing for sufficiently large values of $λ.$ This provides a counterexample to the common belief that associates maximal information transmission to criticality.

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↗

arXiv2016

Blurred stochastic chains

Assume we have two stochastic chains taking values in a finite alphabet. These chains may be of infinite order. Assume also that these chains are coupled in such a way that given the past of both chains they have a not too large probability of differing. This is the case when we observe a chain through a noisy channel. This situation presumably also occurs in models for the brain activity when a chain of stimuli is presented to a volunteer and we observe a corresponding chain of neurophysiological recordings. The question is how these two chains are quantitatively related. Under suitable conditions, we obtain upper-bounds for the differences between the marginal conditional distributions of the two chains and between the probability of the next symbol of each chain, given the past of the past of one of them.

math.PR↗

arXiv2014

Identifying interacting pairs of sites in Ising models on a countable set

This paper address the problem of identifying pairs of interacting sites from a finite sample of independent realizations of the Ising model. We consider Ising models in a infinite countable set of sites under Dobrushin uniqueness condition. The observed sample contains only the values assigned by the Ising model to a finite set of sites. Our main result is an upperbound for the probability of misidentification of the pairs of interacting sites in this finite set.

math.ST↗

arXiv2014

Hydrodynamic limit for interacting neurons

This paper studies the hydrodynamic limit of a stochastic process describing the time evolution of a system with N neurons with mean-field interactions produced both by chemical and by electrical synapses. This system can be informally described as follows. Each neuron spikes randomly following a point process with rate depending on its membrane potential. At its spiking time, the membrane potential of the spiking neuron is reset to the value 0 and, simultaneously, the membrane potentials of the other neurons are increased by an amount of potential 1/N . This mimics the effect of chemical synapses. Additionally, the effect of electrical synapses is represented by a deterministic drift of all the membrane potentials towards the average value of the system. We show that, as the system size N diverges, the distribution of membrane potentials becomes deterministic and is described by a limit density which obeys a non linear PDE which is a conservation law of hyperbolic type.

math.PR↗

arXiv2013

Infinite systems of interacting chains with memory of variable length - a stochastic model for biological neural nets

We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as follows. For each component, the probability of having a spike at the next time unit depends on the entire time evolution of the system after the last spike time of the component. This class of systems extends in a non trivial way both the interacting particle systems, which are Markovian, and the stochastic chains with memory of variable length which have finite state space. These features make it suitable to describe the time evolution of biological neural systems. We construct a stationary version of the process by using a probabilistic tool which is a Kalikow-type decomposition either in random environment or in space-time. This construction implies uniqueness of the stationary process. Finally we consider the case where the interactions between components are given by a critical directed Erdös-Rényi-type random graph with a large but finite number of components. In this framework we obtain an explicit upper-bound for the correlation between successive inter-spike intervals which is compatible with previous empirical findings.

math.PR↗

arXiv2012

Joint estimation of intersecting context tree models

We study a problem of model selection for data produced by two different context tree sources. Motivated by linguistic questions, we consider the case where the probabilistic context trees corresponding to the two sources are finite and share many of their contexts. In order to understand the differences between the two sources, it is important to identify which contexts and which transition probabilities are specific to each source. We consider a class of probabilistic context tree models with three types of contexts: those which appear in one, the other, or both sources. We use a BIC penalized maximum likelihood procedure that jointly estimates the two sources. We propose a new algorithm which efficiently computes the estimated context trees. We prove that the procedure is strongly consistent. We also present a simulation study showing the practical advantage of our procedure over a procedure that works separately on each dataset.

math.ST↗

arXiv2012

Chains of infinite order, chains with memory of variable length, and maps of the interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we caracterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.

math.PR↗

arXiv2012

Partially observed Markov random fields are variable neighborhood random fields

The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random field. The second goal is to establish sufficient conditions ensuring that the variable neighborhoods are almost surely finite. We discuss the relationship between the almost sure finiteness of the interaction neighborhoods and the presence/absence of phase transition of the underlying Markov random field. In the case where the underlying random field has no phase transition we show that the finiteness of neighborhoods depends on a specific relation between the noise level and the minimum values of the one-point specification of the Markov random field. The case in which there is phase transition is addressed in the frame of the ferromagnetic Ising model. We prove that the existence of infinite interaction neighborhoods depends on the phase.

math.PR↗

arXiv2012

Context tree selection and linguistic rhythm retrieval from written texts

The starting point of this article is the question "How to retrieve fingerprints of rhythm in written texts?" We address this problem in the case of Brazilian and European Portuguese. These two dialects of Modern Portuguese share the same lexicon and most of the sentences they produce are superficially identical. Yet they are conjectured, on linguistic grounds, to implement different rhythms. We show that this linguistic question can be formulated as a problem of model selection in the class of variable length Markov chains. To carry on this approach, we compare texts from European and Brazilian Portuguese. These texts are previously encoded according to some basic rhythmic features of the sentences which can be automatically retrieved. This is an entirely new approach from the linguistic point of view. Our statistical contribution is the introduction of the smallest maximizer criterion which is a constant free procedure for model selection. As a by-product, this provides a solution for the problem of optimal choice of the penalty constant when using the BIC to select a variable length Markov chain. Besides proving the consistency of the smallest maximizer criterion when the sample size diverges, we also make a simulation study comparing our approach with both the standard BIC selection and the Peres-Shields order estimation. Applied to the linguistic sample constituted for our case study, the smallest maximizer criterion assigns different context-tree models to the two dialects of Portuguese. The features of the selected models are compatible with current conjectures discussed in the linguistic literature.

stat.ML↗