Exactly sparse Gaussian variational inference with application to derivative-free batch nonlinear state estimation

Barfoot, Timothy D.; Forbes, James Richard; Yoon, David J.

doi:10.1177/0278364920937608

Cited by 18 publications

(26 citation statements)

References 55 publications

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“…Our approach is based on the Exactly Sparse Gaussian Variational Inference (ESGVI) parameter learning framework of Barfoot et al [8], a nonlinear batch state estimation framework that provides a family of scalable estimators from a variational objective. Model parameters can be optimized jointly with the state using a data likelihood objective.…”

Section: Gps Cameramentioning

confidence: 99%

“…Barfoot et al [8] presented the ESGVI framework and showed that model parameters can be jointly optimized along with the state using an Expectation-Maximization (EM) iterative optimization scheme on a data likelihood objective. In the E-step, model parameters are held fixed, and the state is optimized.…”

Section: Related Workmentioning

confidence: 99%

“…INFERENCE PARAMETER LEARNING This section summarizes parameter learning in the ESGVI framework as presented in prior work [8,50,51]. The loss function is the negative log-likelihood of the observed data,…”

Section: Exactly Sparse Gaussian Variationalmentioning

confidence: 99%

“…In the M-step, we hold q(x) fixed and optimize V (q|θ) for θ. When the expectation over the posterior, q(x), is approximated at the mean of the Gaussian, the E-step is the familiar Maximum A Posteriori (MAP) estimator [8].…”

Section: Exactly Sparse Gaussian Variationalmentioning

confidence: 99%

“…where e k is as defined in (8). We do not backpropagate keypoint matches that are greater than α = 16.…”

Section: Outlier Rejectionmentioning

confidence: 99%

See 4 more Smart Citations

Radar Odometry Combining Probabilistic Estimation and Unsupervised Feature Learning

Burnett

Yoon

Schoellig

et al. 2021

Robotics: Science and Systems XVII

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This paper presents a radar odometry method that combines probabilistic trajectory estimation and deep learned features without needing groundtruth pose information. The feature network is trained unsupervised, using only the on-board radar data. With its theoretical foundation based on a data likelihood objective, our method leverages a deep network for processing rich radar data, and a non-differentiable classic estimator for probabilistic inference. We provide extensive experimental results on both the publicly available Oxford Radar RobotCar Dataset and an additional 100 km of driving collected in an urban setting. Our sliding-window implementation of radar odometry outperforms most hand-crafted methods and approaches the current state of the art without requiring a groundtruth trajectory for training. We also demonstrate the effectiveness of radar odometry under adverse weather conditions. Code for this project can be found at: https://github.com/utiasASRL/hero radar odometry

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Section: Gps Cameramentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Exactly Sparse Gaussian Variationalmentioning

confidence: 99%

Section: Exactly Sparse Gaussian Variationalmentioning

confidence: 99%

“…where e k is as defined in (8). We do not backpropagate keypoint matches that are greater than α = 16.…”

Section: Outlier Rejectionmentioning

confidence: 99%

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Radar Odometry Combining Probabilistic Estimation and Unsupervised Feature Learning

Burnett

Yoon

Schoellig

et al. 2021

Robotics: Science and Systems XVII

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The recursive variational Gaussian approximation (R-VGA)

2021

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We consider the problem of computing a Gaussian approximation to the posterior distribution of a parameter given N observations and a Gaussian prior. Owing to the need of processing large sample sizes N, a variety of approximate tractable methods revolving around online learning have flourished over the past decades. In the present work, we propose to use variational inference (VI) to compute a Gaussian approximation to the posterior through a single pass over the data. Our algorithm is a recursive version of variational Gaussian approximation we have called recursive variational Gaussian approximation (R-VGA). We start from the prior, and for each observation we compute the nearest Gaussian approximation in the sense of Kullback-Leibler divergence to the posterior given this observation. In turn, this approximation is considered as the new prior when incorporating the next observation. This recursive version based on a sequence of optimal Gaussian approximations leads to a novel implicit update scheme which resembles the online Newton algorithm, and which is shown to boil down to the Kalman filter for Bayesian linear regression. In the context of Bayesian logistic regression the implicit scheme may be solved, and the algorithm is shown to perform better than the extended Kalman filter, while being less computationally demanding than its sampling counterparts.

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Variational inference as iterative projection in a Bayesian Hilbert space with application to robotic state estimation

Barfoot

D’Eleuterio²

2022

Robotica

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Variational Bayesian inference is an important machine learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense “closest” to the full Bayesian posterior. Closeness is typically defined through the selection of an appropriate loss functional such as the Kullback-Leibler (KL) divergence. In this paper, we explore a new formulation of variational inference by exploiting the fact that (most) PDFs are members of a Bayesian Hilbert space under careful definitions of vector addition, scalar multiplication, and an inner product. We show that, under the right conditions, variational inference based on KL divergence can amount to iterative projection, in the Euclidean sense, of the Bayesian posterior onto a subspace corresponding to the selected approximation family. We work through the details of this general framework for the specific case of the Gaussian approximation family and show the equivalence to another Gaussian variational inference approach. We furthermore discuss the implications for systems that exhibit sparsity, which is handled naturally in Bayesian space, and give an example of a high-dimensional robotic state estimation problem that can be handled as a result. We provide some preliminary examples of how the approach could be applied to non-Gaussian inference and discuss the limitations of the approach in detail to encourage follow-on work along these lines.

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Exactly sparse Gaussian variational inference with application to derivative-free batch nonlinear state estimation

Cited by 18 publications

References 55 publications

Radar Odometry Combining Probabilistic Estimation and Unsupervised Feature Learning

Radar Odometry Combining Probabilistic Estimation and Unsupervised Feature Learning

The recursive variational Gaussian approximation (R-VGA)

Variational inference as iterative projection in a Bayesian Hilbert space with application to robotic state estimation

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