Related papers: Implicit Maximum a Posteriori Filtering via Adapti…

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…

Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…

This paper proposes new methodology for sequential state and parameter estimation within the ensemble Kalman filter. The method is fully Bayesian and propagates the joint posterior density of states and parameters over time. In order to…

This paper presents an adaptive Kalman filter for a linear dynamic system perturbed by an additive disturbance. The objective is to estimate both of the state and the unknown disturbance concurrently, while learning the disturbance as a…

We derive a novel, provably robust, and closed-form Bayesian update rule for online filtering in state-space models in the presence of outliers and misspecified measurement models. Our method combines generalised Bayesian inference with…

A way of constructing a nonlinear filter close to the optimal Kolmogorov - Wiener filter is proposed within the framework of the statistical approach to inverse problems. Quasi-optimal filtering, which has no Bayesian assumptions, produces…

Bayesian optimization offers a flexible framework to optimize an objective function that is expensive to be evaluated. A Bayesian optimizer iteratively queries the function values on its carefully selected points. Subsequently, it makes a…

Kalman filters are routinely used for many data fusion applications including navigation, tracking, and simultaneous localization and mapping problems. However, significant time and effort is frequently required to tune various Kalman…

We propose a new recursive estimator for linear dynamical systems under Gaussian process noise and non-Gaussian measurement noise. Specifically, we develop an approximate maximum a posteriori (MAP) estimator using dynamic programming and…

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…

We propose a method for optimal Bayesian filtering with deterministic particles. In order to avoid particle degeneration, the filter step is not performed at once. Instead, the particles progressively flow from prior to posterior. This is…

Least squares support vector machines are a commonly used supervised learning method for nonlinear regression and classification. They can be implemented in either their primal or dual form. The latter requires solving a linear system,…

State-space models can be used to incorporate subject knowledge on the underlying dynamics of a time series by the introduction of a latent Markov state-process. A user can specify the dynamics of this process together with how the state…

Estimation of a dynamical system's latent state subject to sensor noise and model inaccuracies remains a critical yet difficult problem in robotics. While Kalman filters provide the optimal solution in the least squared sense for linear and…

Bayesian optimization is normally performed within fixed variable bounds. In cases like hyperparameter tuning for machine learning algorithms, setting the variable bounds is not trivial. It is hard to guarantee that any fixed bounds will…

We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary problems arise in each step of either filter. We give a new…

Bayesian optimization is a methodology to optimize black-box functions. Traditionally, it focuses on the setting where you can arbitrarily query the search space. However, many real-life problems do not offer this flexibility; in…

The robust estimation of dynamically changing features, such as the position of prey, is one of the hallmarks of perception. On an abstract, algorithmic level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing signals…