Related papers: Progressive Gaussian Filtering
In this letter, a new filtering technique to solve a nonlinear state estimation problem has been developed. It is well known that for a nonlinear system, the prior and posterior probability density functions (pdf) are non-Gaussian in…
We describe a set of Gaussian Process based approaches that can be used to solve non-linear Ordinary Differential Equations. We suggest an explicit probabilistic solver and two implicit methods, one analogous to Picard iteration and the…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an integral of Gaussian density functions weighted by a mixing…
Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…
Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…
We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…
Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically…
In this article, we propose and develop a novel Bayesian algorithm for optimization of functions whose first and second partial derivatives are known. The basic premise is the Gaussian process representation of the function which induces a…
In order to handle large data sets omnipresent in modern science, efficient compression algorithms are necessary. Here, a Bayesian data compression (BDC) algorithm that adapts to the specific measurement situation is derived in the context…
We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP)…
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 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…
Ordinary differential equations (ODE) have been widely used for modeling dynamical complex systems. For high-dimensional ODE models where the number of differential equations is large, it remains challenging to estimate the ODE parameters…
It has recently been established that the numerical solution of ordinary differential equations can be posed as a nonlinear Bayesian inference problem, which can be approximately solved via Gaussian filtering and smoothing, whenever a…
Marginalization techniques are presented for the Bayesian filtering problem under the assumption of Gaussian priors and posteriors and a set of sequentially more constraining state space model assumptions. The techniques provide the…
Given a sample from a discretely observed compound Poisson process, we consider non-parametric estimation of the density $f_0$ of its jump sizes, as well as of its intensity $\lambda_0.$ We take a Bayesian approach to the problem and…
We study a Bayesian approach to nonparametric estimation of the periodic drift function of a one-dimensional diffusion from continuous-time data. Rewriting the likelihood in terms of local time of the process, and specifying a Gaussian…
Non-Gaussian Bayesian filtering is a core problem in stochastic filtering. The difficulty of the problem lies in parameterizing the state estimates. However the existing methods are not able to treat it well. We propose to use power moments…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…