Related papers: Approximate Bayes learning of stochastic different…
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,…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…
In stochastic variational inference, the variational Bayes objective function is optimized using stochastic gradient approximation, where gradients computed on small random subsets of data are used to approximate the true gradient over the…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
We introduce a new variational characterization of Gaussian diffusion processes as minimum uncertainty states. We then define a variational method constrained by kinematics of diffusions and Schr\"{o}dinger dynamics to seek states of local…
This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…
Stochastic variational Bayes algorithms have become very popular in the machine learning literature, particularly in the context of nonparametric Bayesian inference. These algorithms replace the true but intractable posterior distribution…
We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…
We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…
Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been…
This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential,…
Sparse pseudo-point approximations for Gaussian process (GP) models provide a suite of methods that support deployment of GPs in the large data regime and enable analytic intractabilities to be sidestepped. However, the field lacks a…
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…
Gaussian processes are powerful non-parametric probabilistic models for stochastic functions. However, the direct implementation entails a complexity that is computationally intractable when the number of observations is large, especially…
This work is concerned with model reduction of stochastic differential equations and builds on the idea of replacing drift and noise coefficients of preselected relevant, e.g. slow variables by their conditional expectations. We extend…
A linear Gaussian state-space smoothing algorithm is presented for estimation of derivatives from a sequence of noisy measurements. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements…
The aim of this paper is twofold. Firstly, we derive upper and lower non-Gaussian bounds for the densities of the marginal laws of the solutions to backward stochastic differential equations (BSDEs) driven by fractional Brownian motions.…