Related papers: Computation-Aware Kalman Filtering and Smoothing
Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions…
We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…
In this work we study the non-parametric reconstruction of spatio-temporal dynamical Gaussian processes (GPs) via GP regression from sparse and noisy data. GPs have been mainly applied to spatial regression where they represent one of the…
Optimal decision-making under partial observability requires reasoning about the uncertainty of the environment's hidden state. However, most reinforcement learning architectures handle partial observability with sequence models that have…
We present a scalable and robust Bayesian inference method for linear state space models. The method is applied to demand forecasting in the context of a large e-commerce platform, paying special attention to intermittent and bursty target…
The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this…
We present a novel Kalman filter for spatiotemporal systems called the numerical Gaussian process Kalman filter (GPKF). Numerical Gaussian processes have recently been introduced as a physics informed machine learning method for simulating…
State-space models are used in a wide range of time series analysis formulations. Kalman filtering and smoothing are work-horse algorithms in these settings. While classic algorithms assume Gaussian errors to simplify estimation, recent…
This paper considers the problem of fitting the parameters of a Kalman smoother to data. We formulate the Kalman smoothing problem with missing measurements as a constrained least squares problem and provide an efficient method to solve it…
Gaussian-process state-space models (GP-SSMs) provide a flexible nonparametric alternative for modeling time-series dynamics that are nonlinear or difficult to specify parametrically. While the Kalman filter is effective for linear-Gaussian…
Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous application areas. It provides sequentially calculated estimates of the system…
This paper is considered with joint estimation of state and time-varying noise covariance matrices in non-linear stochastic state space models. We present a variational Bayes and Gaussian filtering based algorithm for efficient computation…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
The majority of research on efficient and scalable algorithms in computational science and engineering has focused on the forward problem: given parameter inputs, solve the governing equations to determine output quantities of interest. In…
In this paper is proposed a novel incremental iterative Gauss-Newton-Markov-Kalman filter method for state estimation of dynamic models given noisy measurements. The mathematical formulation of the proposed filter is based on the…
In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold…
Kalman filtering is a classic state estimation technique used in application areas such as signal processing and autonomous control of vehicles. It is now being used to solve problems in computer systems such as controlling the voltage and…
We formulate approximate Bayesian inference in non-conjugate temporal and spatio-temporal Gaussian process models as a simple parameter update rule applied during Kalman smoothing. This viewpoint encompasses most inference schemes,…