arXiv subjects

Pierre Gloaguen

Publications and source records attributed to Pierre Gloaguen.

10 recordsLinked to original sources

arXiv2026

Efficient Online Variational Estimation via Monte Carlo Sampling

This article addresses online variational estimation in parametric state-space models. We propose a new procedure for efficiently computing the evidence lower bound and its gradient in a streaming-data setting, where observations arrive sequentially. The algorithm allows for the simultaneous training of the model parameters and the distribution of the latent states given the observations. It is based on i.i.d. Monte Carlo sampling, coupled with a well-chosen deep architecture, enabling both computational efficiency and flexibility. The performance of the method is illustrated on both synthetic data and real-world air-quality data. The proposed approach is theoretically motivated by the existence of an asymptotic contrast function and the ergodicity of the underlying Markov chain, and applies more generally to the computation of additive expectations under posterior distributions in state-space models.

stat.ME↗

arXiv2025

HyperSBINN: A Hypernetwork-Enhanced Systems Biology-Informed Neural Network for Efficient Drug Cardiosafety Assessment

Mathematical modeling in systems toxicology enables a comprehensive understanding of the effects of pharmaceutical substances on cardiac health. However, the complexity of these models limits their widespread application in early drug discovery. In this paper, we introduce a novel approach to solving parameterized models of cardiac action potentials by combining meta-learning techniques with Systems Biology-Informed Neural Networks (SBINNs). The proposed method, hyperSBINN, effectively addresses the challenge of predicting the effects of various compounds at different concentrations on cardiac action potentials, outperforming traditional differential equation solvers in speed. Our model efficiently handles scenarios with limited data and complex parameterized differential equations. The hyperSBINN model demonstrates robust performance in predicting APD90 values, indicating its potential as a reliable tool for modeling cardiac electrophysiology and aiding in preclinical drug development. This framework represents an advancement in computational modeling, offering a scalable and efficient solution for simulating and understanding complex biological systems.

stat.ML↗

arXiv2024

Importance sampling for online variational learning

This article addresses online variational estimation in state-space models. We focus on learning the smoothing distribution, i.e. the joint distribution of the latent states given the observations, using a variational approach together with Monte Carlo importance sampling. We propose an efficient algorithm for computing the gradient of the evidence lower bound (ELBO) in the context of streaming data, where observations arrive sequentially. Our contributions include a computationally efficient online ELBO estimator, demonstrated performance in offline and true online settings, and adaptability for computing general expectations under joint smoothing distributions.

stat.AP↗

arXiv2023

Auto-encoding GPS data to reveal individual and collective behaviour

We propose an innovative and generic methodology to analyse individual and collective behaviour through individual trajectory data. The work is motivated by the analysis of GPS trajectories of fishing vessels collected from regulatory tracking data in the context of marine biodiversity conservation and ecosystem-based fisheries management. We build a low-dimensional latent representation of trajectories using convolutional neural networks as non-linear mapping. This is done by training a conditional variational auto-encoder taking into account covariates. The posterior distributions of the latent representations can be linked to the characteristics of the actual trajectories. The latent distributions of the trajectories are compared with the Bhattacharyya coefficient, which is well-suited for comparing distributions. Using this coefficient, we analyse the variation of the individual behaviour of each vessel during time. For collective behaviour analysis, we build proximity graphs and use an extension of the stochastic block model for multiple networks. This model results in a clustering of the individuals based on their set of trajectories. The application to French fishing vessels enables us to obtain groups of vessels whose individual and collective behaviours exhibit spatio-temporal patterns over the period 2014-2018.

stat.AP↗

arXiv2022

Amortized backward variational inference in nonlinear state-space models

We consider the problem of state estimation in general state-space models using variational inference. For a generic variational family defined using the same backward decomposition as the actual joint smoothing distribution, we establish for the first time that, under mixing assumptions, the variational approximation of expectations of additive state functionals induces an error which grows at most linearly in the number of observations. This guarantee is consistent with the known upper bounds for the approximation of smoothing distributions using standard Monte Carlo methods. Moreover, we propose an amortized inference framework where a neural network shared over all times steps outputs the parameters of the variational kernels. We also study empirically parametrizations which allow analytical marginalization of the variational distributions, and therefore lead to efficient smoothing algorithms. Significant improvements are made over state-of-the art variational solutions, especially when the generative model depends on a strongly nonlinear and noninjective mixing function.

stat.ME↗

arXiv2021

Backward importance sampling for online estimation of state space models

This paper proposes a new Sequential Monte Carlo algorithm to perform online estimation in the context of state space models when either the transition density of the latent state or the conditional likelihood of an observation given a state is intractable. In this setting, obtaining low variance estimators of expectations under the posterior distributions of the unobserved states given the observations is a challenging task. Following recent theoretical results for pseudo-marginal sequential Monte Carlo smoothers, a pseudo-marginal backward importance sampling step is introduced to estimate such expectations. This new step allows to reduce very significantly the computational time of the existing numerical solutions based on an acceptance-rejection procedure for similar performance, and to broaden the class of eligible models for such methods. For instance, in the context of multivariate stochastic differential equations, the proposed algorithm makes use of unbiased estimates of the unknown transition densities under much weaker assumptions than standard alternatives. The performance of this estimator is assessed for high-dimensional discrete-time latent data models, for recursive maximum likelihood estimation in the context of partially observed diffusion process, and in the case of a bidimensional partially observed stochastic Lotka-Volterra model.

stat.AP↗

arXiv2021

A pseudo-marginal sequential Monte Carlo online smoothing algorithm

We consider online computation of expectations of additive state functionals under general path probability measures proportional to products of unnormalised transition densities. These transition densities are assumed to be intractable but possible to estimate, with or without bias. Using pseudo-marginalisation techniques we are able to extend the particle-based, rapid incremental smoother (PaRIS) algorithm proposed in [J.Olsson and J.Westerborn. Efficient particle-based online smoothing in general hidden Markov models: The PaRIS algorithm. Bernoulli, 23(3):1951--1996, 2017] to this setting. The resulting algorithm, which has a linear complexity in the number of particles and constant memory requirements, applies to a wide range of challenging path-space Monte Carlo problems, including smoothing in partially observed diffusion processes and models with intractable likelihood. The algorithm is furnished with several theoretical results, including a central limit theorem, establishing its convergence and numerical stability. Moreover, under strong mixing assumptions we establish a novel $O(n \varepsilon)$ bound on the asymptotic bias of the algorithm, where $n$ is the path length and $\varepsilon$ controls the bias of the density estimators.

stat.CO↗

arXiv2018

The Langevin diffusion as a continuous-time model of animal movement and habitat selection

1. The utilisation distribution describes the relative probability of use of a spatial unit by an animal. It is natural to think of it as the long-term consequence of the animal's short-term movement decisions: it is the accumulation of small displacements which, over time, gives rise to global patterns of space use. However, most utilisation distribution models either ignore the underlying movement, assuming the independenceof observed locations, or are based on simplistic Brownian motion movement rules. 2. We introduce a new continuous-time model of animal movement, based on the Langevin diffusion. This stochastic process has an explicit stationary distribution, conceptually analogous to the idea of the utilisation distribution, and thus provides an intuitive framework to integrate movement and space use. We model the stationary (utilisation) distribution with a resource selection function to link the movement to spatial covariates, and allow inference into habitat selection. 3. Standard approximation techniques can be used to derive the pseudo-likelihood of the Langevin diffusion movement model, and to estimate habitat preference and movement parameters from tracking data. We investigate the performance of the method on simulated data, and discuss its sensitivity to the time scale of the sampling. We present an example of its application to tracking data of Stellar sea lions (Eumetopiasjubatus). 4. Due to its continuous-time formulation, this method can be applied to irregular telemetry data. It provides a rigorous framework to estimate long-term habitat selection from correlated movement data.

stat.AP↗

arXiv2017

Stochastic differential equation based on a multimodal potential to model movement data in ecology

This paper proposes a new model for individuals movement in ecology. The movement process is defined as a solution to a stochastic differential equation whose drift is the gradient of a multimodal potential surface. This offers a new flexible approach among the popular potential based movement models in ecology. To perform parameter inference, the widely used Euler method is compared with two other pseudo-likelihood procedures and with a Monte Carlo Expectation Maximization approach based on exact simulation of diffusions. Performances of all methods are assessed with simulated data and with a data set of fishing vessels trajectories. We show that the usual Euler method performs worse than the other procedures for all sampling schemes.

math.ST↗

arXiv2017

Online Sequential Monte Carlo smoother for partially observed stochastic differential equations

This paper introduces a new algorithm to approximate smoothed additive functionals for partially observed stochastic differential equations. This method relies on a recent procedure which allows to compute such approximations online, i.e. as the observations are received, and with a computational complexity growing linearly with the number of Monte Carlo samples. This online smoother cannot be used directly in the case of partially observed stochastic differential equations since the transition density of the latent data is usually unknown. We prove that a similar algorithm may still be defined for partially observed continuous processes by replacing this unknown quantity by an unbiased estimator obtained for instance using general Poisson estimators. We prove that this estimator is consistent and its performance are illustrated using data from two models.

stat.ME↗