Searcharxiv⌕ Search

arXiv subjects

Bertrand Cloez

Publications and source records attributed to Bertrand Cloez.

At least 19 recordsLinked to original sources
arXiv2025

Model-free algorithms for fast node clustering in SBM type graphs and application to social role inference in animals

We propose a novel family of model-free algorithms for node clustering and parameter inference in graphs generated from the Stochastic Block Model (SBM), a fundamental framework in community detection. Drawing inspiration from the Lloyd algorithm for the $k$-means problem, our approach extends to SBMs with general edge weight distributions. We establish the consistency of our estimator under a natural identifiability condition. Through extensive numerical experiments, we benchmark our methods against state-of-the-art techniques, demonstrating significantly faster computation times with the lower order of estimation error. Finally, we validate the practical relevance of our algorithms by applying them to empirical network data from behavioral ecology.

stat.ML↗
arXiv2025

Approximate Bayesian Computation with Deep Learning and Conformal prediction

Approximate Bayesian Computation (ABC) methods are commonly used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Classical ABC methods are based on nearest neighbor type algorithms and rely on the choice of so-called summary statistics, distances between datasets and a tolerance threshold. Recently, methods combining ABC with more complex machine learning algorithms have been proposed to mitigate the impact of these ``user-choices''. In this paper, we propose the first, to our knowledge, ABC method completely free of summary statistics, distance, and tolerance threshold. Moreover, in contrast with usual generalizations of the ABC method, it associates a confidence interval (having a proper frequentist marginal coverage) with the posterior mean estimation (or other moment-type estimates). Our method, named ABCD-Conformal, uses a neural network with Monte Carlo Dropout to provide an estimation of the posterior mean (or other moment type functionals), and conformal theory to obtain associated confidence sets. Efficient for estimating multidimensional parameters and amortized, we test this new method on four different applications and compare it with other ABC methods in the literature.

stat.ME↗
arXiv2025

Strong law of large numbers and L log L condition for supercritical branching processes

We consider branching processes for structured populations: each individual is characterized by a type or trait which belongs to a general measurable state space. We focus on the supercritical recurrent case, where the population may survive and grow and the trait distribution converges. The branching process is then expected to be driven by the positive triplet of first eigenvalue problem of the first moment semigroup. Under the assumption of convergence of the renormalized semigroup in weighted total variation norm, we prove strong convergence of the normalized empirical measure and non-degeneracy of the limiting martingale. Convergence is obtained under an Llog L condition which provides a Kesten-Stigum result in infinite dimension and relaxes the uniform convergence assumption of the renormalized first moment semigroup required in the work of Asmussen and Hering in 1976. The techniques of proofs combine families of martingales and contraction of semigroups and the truncation procedure of Asmussen and Hering. We also obtain L^1 convergence of the renormalized empirical measure and contribute to unifying different results in the literature. These results greatly extend the class of examples where a law of large numbers applies, as we illustrate it with absorbed branching diffusion, the house of cards model and some growth-fragmentation processes.

math.PR↗
arXiv2025

Central limit theorems for branching processes under mild assumptions on the mean semigroup

We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment assumption and the exponential convergence of the mean semigroup in a weighted total variation norm. This latter assumption is pretty weak and does not necessitate symmetric properties or specific spectral knowledge on this semigroup. In particular, we recover two of the three known regimes (namely the small and critical branching processes) of convergence in known cases, and extend them to a wider family of processes. To prove our central limit theorems, we use the Stein's method, which in addition allows us to newly provide a rate of convergence to this type of convergence.

math.PR↗
arXiv2024

The principal eigenvalue problem for time-periodic nonlocal equations with drift

In this work, we consider a general time-periodic linear transport equation with integral source term. We prove the existence of a Floquet principal eigenvalue, namely a real number such that the equation rescaled by this number admits nonnegative periodic solutions. We also prove the exponential attractiveness of these solutions. The method relies on general spectral results about positive operators.

math.AP↗
arXiv2023

Recent advances in the long-time analysis of killed degenerate processes and their particle approximation

We review some recent results of quantitative long-time convergence for the law of a killed Markov process conditioned to survival toward a quasi-stationary distribution, and on the analogous question for the particle systems used in practice to sample these distributions. With respect to the existing literature, one of the novelties of these works is the degeneracy of the underlying process with respect to classical elliptic diffusion, namely it can be a non-elliptic hypoelliptic diffusion, a piecewise deterministic Markov process or an Euler numerical scheme.

math.PR↗
arXiv2022

Uniform in time propagation of chaos for a Moran model

The goal of this article is to study the limit of the empirical distribution induced by a mutation-selection multi-allelic Moran model, whose dynamic is given by a continuous-time irreducible Markov chain. The rate matrix driving the mutation is assumed irreducible and the selection rates are assumed uniformly bounded. The paper is divided into two parts. The first one deals with processes with general selection rates. For this case we are able to prove the propagation of chaos in $\mathbb{L}^p$ over the compacts, with speed of convergence of order $1/\sqrt{N}$. Further on, we consider a specific type of selection that we call additive selection. Essentially, we assume that the selection rate can be decomposed as the sum of three terms: a term depending on the allelic type of the parent (which can be understood as selection at death), another term depending on the allelic type of the descendant (which can be understood as selection at birth) and a third term which is symmetric. Under this setting, our results include a uniform in time bound for the propagation on chaos in $\mathbb{L}^p$ of order $1/\sqrt{N}$, and the proof of the asymptotic normality with zero mean and explicit variance, for the approximation error between the empirical distribution and its limit, when the number of individuals tend towards infinity. Additionally, we explore the interpretation of the Moran model with additive selection as a particle process whose empirical distribution approximates a quasi-stationary distribution, in the same spirit as the Fleming\,--\,Viot particle systems. We then address the problem of minimising the asymptotic quadratic error, when the time and the number of particles go to infinity.

math.PR↗
arXiv2022

Kalman filter with impulse noised outliers : A robust sequential algorithm to filter data with a large number of outliers

Impulsed noise outliers are data points that differs significantly from other observations.They are generally removed from the data set through local regression or Kalman filter algorithm.However, these methods, or their generalizations, are not well suited when the number of outliers is ofthe same order as the number of low-noise data. In this article, we propose a new model for impulsenoised outliers based on simple latent linear Gaussian processes as in the Kalman Filter. We present a fastforward-backward algorithm to filter and smooth sequential data and which also detect these outliers.We compare the robustness and efficiency of this algorithm with classical methods. Finally, we applythis method on a real data set from a Walk Over Weighing system admitting around 60% of outliers. Forthis application, we further develop an (explicit) EM algorithm to calibrate some algorithm parameters.

stat.ME↗
arXiv2022

A non-conservative Harris ergodic theorem

We consider non-conservative positive semigroups and obtain necessary and sufficient conditions for uniform exponential contraction in weighted total variation norm. This ensures the existence of Perron eigenelements and provides quantitative estimates of the spectral gap, complementing Krein-Rutman theorems and generalizing probabilistic approaches. The proof is based on a non-homogenous $h$-transform of the semigroup and the construction of Lyapunov functions for this latter. It exploits then the classical necessary and sufficient conditions of Harris's theorem for conservative semigroups and recent techniques developed for the study of absorbed Markov processes. We apply these results to population dynamics. We obtain exponential convergence of birth and death processes conditioned on survival to their quasi-stationary distribution, as well as estimates on exponential relaxation to stationary profiles in growth-fragmentation PDEs.

math.AP↗
arXiv2022

Quasi-stationary behavior for an hybrid model of chemostat: the Crump-Young model

The Crump-Young model consists of two fully coupled stochastic processes modeling the substrate and microorganisms dynamics in a chemostat. Substrate evolves following an ordinary differential equation whose coefficients depend of microorganisms number. Microorganisms are modeled though a pure jump process whose the jump rates depend on the substrate concentration. It goes to extinction almost-surely in the sense that microorganism population vanishes. In this work, we show that, conditionally on the non-extinction, its distribution converges exponentially fast to a quasi-stationary distribution. Due to the deterministic part, the dynamics of the Crump-Young model is highly degenerated. The proof is then original and consists of technical sharp estimates and new approaches for the quasi-stationary convergence.

math.PR↗
arXiv2020

On an irreducibility type condition for the ergodicity of nonconservative semigroups

We propose a simple criterion, inspired from the irreducible aperiodic Markov chains, to derive the exponential convergence of general positive semi-groups. When not checkable on the whole state space, it can be combined to the use of Lyapunov functions. It differs from the usual generalization of irreducibility and is based on the accessibility of the trajectories of the underlying dynamics. It allows to obtain new existence results of principal eigenelements, and their exponential attractiveness, for a nonlocal selection-mutation population dynamics model defined in a space-time varying environment.

math.PR↗
arXiv2020

Long-time behavior and darwinian optimality for an asymmetric size-structured branching process

We study the long time behavior of an asymmetric size-structured measure-valued growth-fragmentation branching process that models the dynamics of a population of cells taking into account physiological and morphological asymmetry at division. We show that the process exhibits a Malthusian behavior; that is that the global population size grows exponentially fast and that the trait distribution of individuals converges to some stable distribution. The proof is based on a generalization of Lyapunov function techniques for non-conservative semi-groups. We then investigate the fluctuations of the growth rate with respect to the parameters guiding asymmetry. In particular, we exhibit that, under some special assumptions, asymmetric division is optimal in a Darwinian sense.

math.PR↗
arXiv2019

Ergodic behavior of non-conservative semigroups via generalized Doeblin's conditions

We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and Doeblin's type conditions for coupling the associated process. Our aim is to provide quantitative estimates for linear partial differential equations and we develop several applications for population dynamics in varying environment. We start with the asymptotic profile for a growth diffusion model with time and space non-homogeneity. Moreover we provide general estimates for semigroups which become asymptotically homogeneous, which are applied to an age-structured population model. Finally, we obtain a speed of convergence for periodic semi-groups and new bounds in the homogeneous setting. They are are illustrated on the renewal equation.

math.AP↗
arXiv2019

Efficient Matrix Profile Computation Using Different Distance Functions

Matrix profile has been recently proposed as a promising technique to the problem of all-pairs-similarity search on time series. Efficient algorithms have been proposed for computing it, e.g., STAMP, STOMP and SCRIMP++. All these algorithms use the z-normalized Euclidean distance to measure the distance between subsequences. However, as we observed, for some datasets other Euclidean measurements are more useful for knowledge discovery from time series. In this paper, we propose efficient algorithms for computing matrix profile for a general class of Euclidean distances. We first propose a simple but efficient algorithm called AAMP for computing matrix profile with the "pure" (non-normalized) Euclidean distance. Then, we extend our algorithm for the p-norm distance. We also propose an algorithm, called ACAMP, that uses the same principle as AAMP, but for the case of z-normalized Euclidean distance. We implemented our algorithms, and evaluated their performance through experimentation. The experiments show excellent performance results. For example, they show that AAMP is very efficient for computing matrix profile for non-normalized Euclidean distances. The results also show that the ACAMP algorithm is significantly faster than SCRIMP++ (the state of the art matrix profile algorithm) for the case of z-normalized Euclidean distance.

cs.LG↗
arXiv2018

Optimal stopping for measure-valued piecewise deterministic Markov processes

This paper investigates the random horizon optimal stopping problem for measure-valued piecewise deterministic Markov processes (PDMPs). This is motivated by population dynamics applications, when one wants to monitor some characteristics of the individuals in a small population. The population and its individual characteristics can be represented by a point measure. We first define a PDMP on a space of locally finite measures. Then we define a sequence of random horizon optimal stopping problems for such processes. We prove that the value function of the problems can be obtained by iterating some dynamic programming operator. Finally we prove on a simple counter-example that controlling the whole population is not equivalent to controlling a random lineage.

math.PR↗
arXiv2018

Markovian tricks for non-Markovian trees: contour process, extinction and scaling limits

In this work, we study a family of non-Markovian trees modeling populations where individuals live and reproduce independently with possibly time-dependent birth-rate and lifetime distribution. To this end, we use the coding process introduced by Lambert. We show that, in our situation, this process is no longer a L{é}vy process but remains a Feller process and we give a complete characterization of its generator. This allows us to study the model through well-known Markov processes techniques. On one hand, introducing a scale function for such processes allows us to get necessary and sufficient conditions for extinction or non-extinction and to characterize the law of such trees conditioned on these events. On the other hand, using Lyapounov drift techniques , we get another set of, easily checkable, sufficient criteria for extinction or non-extinction and some tail estimates for the tree length. Finally, we also study scaling limits of such random trees and observe that the Bessel tree appears naturally.

math.PR↗
arXiv2017

Intertwinings and Stein's magic factors for birth-death processes

This article investigates second order intertwinings between semigroups of birth-death processes and discrete gradients on the space of natural integers N. It goes one step beyond a recent work of Chafa{ï} and Joulin which establishes and applies to the analysis of birth-death semigroups a first order intertwining. Similarly to the first order relation, the second order intertwining involves birth-death and Feynman-Kac semigroups and weighted gradients on N, and can be seen as a second derivative relation. As our main application, we provide new quantitative bounds on the Stein factors of discrete distributions. To illustrate the relevance of this approach, we also derive approximation results for the mixture of Poisson and geometric laws.

math.PR↗