Bayesian nonparametric state and impulsive measurement noise density estimation in nonlinear dynamic systems

Jaoua, Nouha; Duflos, Emmanuel; Vanheeghe, Philippe; Septier, François

doi:10.1109/icassp.2013.6638767

Cited by 9 publications

(5 citation statements)

References 14 publications

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“…This is because the different noise sources are represented by the active components of an infinite random mixture. Some recent applications of Bayesian nonparametric methods in nonlinear dynamical systems include Dirichlet process (DP) based reconstruction [11] and joint state-measurement noise density estimation with non-Gaussian and Gaussian observational and dynamical noise components respectively [15]. In this work we aim to:…”

Section: Introductionmentioning

confidence: 99%

A Bayesian nonparametric approach to reconstruction and prediction of random dynamical systems

Merkatas

Kaloudis

Hatjispyros

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods. Our results can be used by researchers in physical modeling interested in a fast and accurate estimation of low dimensional stochastic models when the size of the observed time series is small and the noise process (perhaps) is non-Gaussian. The inference procedure is demonstrated specifically in the case of polynomial maps of an arbitrary degree and when a Geometric Stick Breaking mixture process prior over the space of densities, is applied to the additive errors. Our method is parsimonious compared to Bayesian nonparametric techniques based on Dirichlet process mixtures, flexible and general. Simulations based on synthetic time series are presented.

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Section: Introductionmentioning

confidence: 99%

A Bayesian nonparametric approach to reconstruction and prediction of random dynamical systems

Merkatas

Kaloudis

Hatjispyros

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Many of these time-dependent DPs also allow clusters to stay, re-emerge, and die out over time (Caron et al, 2017;Lin et al, 2010). These dynamics can be incorporated through a cluster removal step as in Caron et al (2017), Caron et al (2012), which has been used for time-varying density estimation (Jaoua et al, 2014;Rodriguez and Ter Horst, 2008).…”

Section: Standard Nonparameric Priors 21 Dirichlet Processes and Thei...mentioning

confidence: 99%

A survey on Bayesian nonparametric learning for time series analysis

Vélez-Cruz

2024

Front. Signal Process.

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Time series analysis aims to understand underlying patterns and relationships in data to inform decision-making. As time series data are becoming more widely available across a variety of academic disciplines, time series analysis has become a rapidly growing field. In particular, Bayesian nonparametric (BNP) methods are gaining traction for their power and flexibility in modeling, predicting, and extracting meaningful information from time series data. The utility of BNP methods lies in their ability to encode prior information and represent complex patterns in the data without imposing strong assumptions about the underlying distribution or functional form. BNP methods for time series analysis can be applied to a breadth of problems, including anomaly detection, noise density estimation, and time series clustering. This work presents a comprehensive survey of the existing literature on BNP methods for time series analysis. Various temporal BNP models are discussed along with notable applications and possible approaches for inference. This work also highlights current research trends in the field and potential avenues for further development and exploration.

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“…The method proposed by Jaoua et al [2013] can be viewed as a special case of NSMC when the nested procedure to generate samples is given by IS with the proposal being the transition probability. Independent resampling PF (IR-PF) introduced in Lamberti et al [2016] generates samples in the same way as NSMC with IS, instead of SMC, as the nested procedure.…”

Section: Related Workmentioning

confidence: 99%

High-Dimensional Filtering Using Nested Sequential Monte Carlo

Naesseth

Lindsten

Schön

2019

IEEE Trans. Signal Process.

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Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without good proposal distributions struggle in high dimensions. We propose nested sequential Monte Carlo (NSMC), a methodology that generalises the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correct SMC algorithm. This way we can exactly approximate the locally optimal proposal, and extend the class of models for which we can perform efficient inference using SMC. We show improved accuracy over other state-of-the-art methods on several spatio-temporal state space models.Inference in complex and high-dimensional statistical models is a very challenging problem that is ubiquitous in applications such as climate informatics [Monteleoni et al., 2013], bioinformatics [Cohen, 2004] and machine learning [Wainwright and Jordan, 2008], to mention a few.We are interested in sequential Bayesian inference in settings where we have a sequence of posterior distributions that we need to compute. To be specific, we are focusing on settings where the model (or state variable) is high-dimensional, but where there are local dependencies. One example of the type of models we consider are the so-called spatiotemporal models [Wikle, 2015, Cressie and Wikle, 2011, Rue and Held, 2005.Sequential Monte Carlo (SMC) methods comprise one of the most successful methodologies for sequential Bayesian inference. However, SMC struggles in high dimensions and these methods are rarely used for dimensions, say, higher than ten . The purpose of the NSMC methodology is to push this limit well beyond the single digits.The basic strategy is to mimic the behavior of a so-called fully adapted (or locally optimal) SMC algorithm. Full adaptation can drastically improve the efficiency of SMC in high dimensions [Snyder et al., 2015]. Unfortunately, it can rarely be implemented in practice since the fully adapted proposal distributions are typically intractable. NSMC addresses this difficulty by requiring only approximate, properly weighted, samples from the proposal distribution. This enables us to use a second layer of SMC to simulate approximately from the proposal. The proper weighting condition ensures the validity of NSMC, thus providing a generalisation of the family of SMC methods. This paper extends preliminary work [Naesseth et al., 2015a] with the ability to handle more expressive models, more informative 2 central limit theorems and convergence proofs, as well as new experiments.

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Bayesian nonparametric state and impulsive measurement noise density estimation in nonlinear dynamic systems

Cited by 9 publications

References 14 publications

A Bayesian nonparametric approach to reconstruction and prediction of random dynamical systems

A Bayesian nonparametric approach to reconstruction and prediction of random dynamical systems

A survey on Bayesian nonparametric learning for time series analysis

High-Dimensional Filtering Using Nested Sequential Monte Carlo

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