Related papers: Gaussian Variational State Estimation for Nonlinea…
In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are…
This article studies the problem of estimating the state variable of non-smooth subdifferential dynamics constrained in a bounded convex domain given some real-time observation. On the one hand, we show that the value function of the…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…
This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian…
Gaussian process state-space models (GPSSMs) offer a principled framework for learning and inference in nonlinear dynamical systems with uncertainty quantification. However, existing GPSSMs are limited by the use of multiple independent…
We propose a novel method for maximum likelihood-based parameter inference in nonlinear and/or non-Gaussian state space models. The method is an iterative procedure with three steps. At each iteration a particle filter is used to estimate…
We consider the problem of state estimation in dynamical systems and propose a different mechanism for handling unmodeled system uncertainties. Instead of injecting random process noise, we assign different weights to measurements so that…
For linear and Gaussian state space models parametrized by $\theta_0 \in \Theta \subset \mathbb{R}^r, r \geq 1$ corresponding to the vector of parameters of the model, the Kalman filter gives exactly the solution for the optimal filtering…
Gaussian Process State Space Models (GP-SSMs) are a non-parametric model class suitable to represent nonlinear dynamics. They become increasingly popular in data-driven modeling approaches, i.e. when no first-order physics-based models are…
Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation approaches based on Gaussian mixture density approximations…
Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on…
We present an optimal control-based strategy to enhance the estimation of impulse-like disturbances in continuously monitored linear classical and quantum systems by exploiting non-equilibrium states. Using optimal estimation techniques for…
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…
This paper considers the problem of steering the state distribution of a nonlinear stochastic system from an initial Gaussian to a terminal distribution with a specified mean and covariance, subject to probabilistic path constraints. An…
Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters…
This paper deals with the problem of state estimation for a class of linear time-invariant systems with quadratic output measurements. An immersion-type approach is presented that transforms the system into a state-affine system by adding a…
An important task of uncertainty quantification is to identify {the probability of} undesired events, in particular, system failures, caused by various sources of uncertainties. In this work we consider the construction of Gaussian…
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
We study the class of state-space models and perform maximum likelihood estimation for the model parameters. We consider a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function with the…
Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…