Hierarchical Bayesian ARX models for robust inference

Dahlin, Johan; Lindsten, Fredrik; Schön, Thomas B.; Wills, Adrian

doi:10.3182/20120711-3-be-2027.00318

Cited by 9 publications

(12 citation statements)

References 9 publications

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“…Figure 4 presents the results obtained by using BARX. The one-step-ahead predictors seem to perform well and this is reflected in a high model fit of 92.3% on validation data for the BARX model, which is a substantial increase from the model fit of 85.6% obtained in Dahlin et al [2012].…”

Section: Real-world Eeg Datamentioning

confidence: 84%

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Sparse Bayesian ARX models with flexible noise distributions

Dahlin¹,

Wills²,

Ninness

2018

IFAC-PapersOnLine

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This paper considers the problem of estimating linear dynamic system models when the observations are corrupted by random disturbances with nonstandard distributions. The paper is particularly motivated by applications where sensor imperfections involve significant contribution of outliers or wrap-around issues resulting in multi-modal distributions such as commonly encountered in robotics applications. As will be illustrated, these nonstandard measurement errors can dramatically compromise the effectiveness of standard estimation methods, while a computational Bayesian approach developed here is demonstrated to be equally effective as standard methods in standard measurement noise scenarios, but dramatically more effective in nonstandard measurement noise distribution scenarios.

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Section: Real-world Eeg Datamentioning

confidence: 84%

“…Finally, we revisit a real-world EEG data set analysed in Dahlin et al [2012], where the authors assume an ARX model with Student's t-distributed noise. We apply the same procedure as before to estimate the BARX model.…”

Section: Real-world Eeg Datamentioning

confidence: 99%

Sparse Bayesian ARX models with flexible noise distributions

Dahlin¹,

Wills²,

Ninness

2018

IFAC-PapersOnLine

Self Cite

View full text Add to dashboard Cite

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“…, results in (8). Defining the likelihood in this way encourages soft competition such that only one expert is dominant in a certain region of the input space [14].…”

Section: Mixture Of Experts Modelmentioning

confidence: 99%

“…This distribution has been used for robust estimation with outliers or atypical observations for many decades, see for example [4,5]. However, it is still a topic of ongoing research and has recently been employed for robust estimation in various fields: Gaussian processes [6], time series analysis using variational Bayes [7] and reversible jump Markov chain Monte Carlo [8], mixture models [9], mixture of regression models [10], mixture of autoregressive series [11] and mixture of experts using the expectation conditional maximisation [12]. In this paper the Student-t distribution is incorporated into a mixture of experts (MoE) Bayesian modelling framework so as to provide a novel approach to robustness to outlier data in piece-wise continuous data and bifurcating processes.…”

Section: Introductionmentioning

confidence: 99%

Robust nonlinear system identification: Bayesian mixture of experts using the t-distribution

Baldacchino

Worden

Rowson

2017

Mechanical Systems and Signal Processing

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A novel variational Bayesian mixture of experts model for robust regression of bifurcating and piece-wise continuous processes is introduced. The mixture of experts model is a powerful model which probabilistically splits the input space allowing different models to operate in the separate regions. However, current methods have no fail-safe against outliers. In this paper, a robust mixture of experts model is proposed which consists of Student-t mixture models at the gates and Student-t distributed experts, trained via Bayesian inference. The Student-t distribution has heavier tails than the Gaussian distribution, and so it is more robust to outliers, noise and non-normality in the data. Using both simulated data and real data obtained from the Z24 bridge this robust mixture of experts performs better than its Gaussian counterpart when outliers are present. In particular, it provides robustness to outliers in two forms: unbiased parameter regression models, and robustness to overfitting/complex models.

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“…For instance Student-t distributions [12] or Laplace distributions [13]. The problem has been studied using time domain [14], [15], frequency domain [16], and subspace approaches [17]. Bayesian approaches for impulseresponse estimation in the presence of outliers have also been proposed [7], [8].…”

Section: Introductionmentioning

confidence: 99%

Outlier-Robust Estimation of Uncertain-Input Systems With Applications to Nonparametric FIR and Hammerstein Models

Risuleo

Hjalmarsson

2018

IEEE Control Syst. Lett.

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In this paper, we present an extension of the class of uncertain-input models to handle cases of measurements with outliers. The general uncertain-input model framework allows us to treat system identification problems in which a linear system, represented by its impulse response, is subject to an input about which we have partial information. Both the impulse response and the input are modeled as Gaussian processes and the kernels are used to encode the information available. The whole model is then estimated using an approximate empirical Bayes approach. We extend the uncertain-input model framework to non-Gaussian measurement models by considering the noise precisions as realizations of a Gamma prior. We validate the approach on a dataset of linear systems and on a dataset of Hammerstein systems where the measurements are corrupted by outliers.

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Hierarchical Bayesian ARX models for robust inference

Cited by 9 publications

References 9 publications

Sparse Bayesian ARX models with flexible noise distributions

Sparse Bayesian ARX models with flexible noise distributions

Robust nonlinear system identification: Bayesian mixture of experts using the t-distribution

Outlier-Robust Estimation of Uncertain-Input Systems With Applications to Nonparametric FIR and Hammerstein Models

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