Convergence of a Particle-based Approximation of the Block Online Expectation Maximization Algorithm

Online variants of the Expectation Maximization (EM) algorithm have recently been proposed to perform parameter inference with large data sets or data streams, in independent latent models and in hidden Markov models. Nevertheless, the convergence properties of these algorithms remain an open problem at least in the hidden Markov case. This contribution deals with a new online EM algorithm which updates the parameter at some deterministic times. Some convergence results have been derived even in general latent models such as hidden Markov models. These properties rely on the assumption that some intermediate quantities are available in closed form or can be approximated by Monte Carlo methods when the Monte Carlo error vanishes rapidly enough. In this paper, we propose an algorithm which approximates these quantities using Sequential Monte Carlo methods. The convergence of this algorithm and of an averaged version is established and their performance is illustrated through Monte Carlo experiments

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

Parameter estimation for stochastic hybrid model applied to urban traffic flow estimation

This study proposes a novel data-based approach for estimating the parameters of a stochastic hybrid model describing the traffic flow in an urban traffic network with signalized intersections. The model represents the evolution of the traffic flow rate, measuring the number of vehicles passing a given location per time unit. This traffic flow rate is described using a mode-dependent first-order autoregressive (AR) stochastic process. The parameters of the AR process take different values depending on the mode of traffic operation – free flowing, congested or faulty – making this a hybrid stochastic process. Mode switching occurs according to a first-order Markov chain. This study proposes an expectation-maximization (EM) technique for estimating the transition matrix of this Markovian mode process and the parameters of the AR models for each mode. The technique is applied to actual traffic flow data from the city of Jakarta, Indonesia. The model thus obtained is validated by using the smoothed inference algorithms and an online particle filter. The authors also develop an EM parameter estimation that, in combination with a time-window shift technique, can be useful and practical for periodically updating the parameters of hybrid model leading to an adaptive traffic flow state estimator

Simultaneous localization and mapping in wireless sensor networks

AbstractMobile device localization in wireless sensor networks is a challenging task. It has already been addressed when the WiFi propagation maps of the access points are modeled deterministically or estimated using an offline human training calibration. However, these techniques do not take into account the environmental dynamics. In this paper, the maps are assumed to be made of an average indoor propagation model combined with a perturbation field which represents the influence of the environment. This perturbation field is embedded with a distribution describing the prior knowledge about the environmental influence. The device is localized with Sequential Monte Carlo methods and relies on the estimation of the propagation maps. This inference task is performed online, using the observations sequentially, with a new online Expectation Maximization based algorithm. The performance of the algorithm is illustrated with Monte Carlo experiments using both simulated data and a true data set

Online but Accurate Inference for Latent Variable Models with Local Gibbs Sampling

We study parameter inference in large-scale latent variable models. We first propose an unified treatment of online inference for latent variable models from a non-canonical exponential family, and draw explicit links between several previously proposed frequentist or Bayesian methods. We then propose a novel inference method for the frequentist estimation of parameters, that adapts MCMC methods to online inference of latent variable models with the proper use of local Gibbs sampling. Then, for latent Dirich-let allocation,we provide an extensive set of experiments and comparisons with existing work, where our new approach outperforms all previously proposed methods. In particular, using Gibbs sampling for latent variable inference is superior to variational inference in terms of test log-likelihoods. Moreover, Bayesian inference through variational methods perform poorly, sometimes leading to worse fits with latent variables of higher dimensionality