Related papers: Approximate Bayes learning of stochastic different…
In this paper, we consider the nonparametric estimation problem of the drift function of stochastic differential equations driven by $\alpha$-stable L\'{e}vy motion. First, the Kullback-Leibler divergence between the path probabilities of…
This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…
In this paper, we address high-dimensional parametric estimation of the drift function in diffusion models, specifically focusing on a $d$-dimensional ergodic diffusion process observed at discrete time points. We consider both a general…
Accurate assessment of systematic uncertainties is an increasingly vital task in physics studies, where large, high-dimensional datasets, like those collected at the Large Hadron Collider, hold the key to new discoveries. Common approaches…
Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling high-dimensional stochastic systems. In this work, we introduce an adaptive…
Of stochastic differential equations, diffusion processes have been adopted in numerous applications, as more relevant and flexible models. This paper studies diffusion processes in a different setting, where for a given stationary…
This paper provides a semiparametric model of estimating states of the volatility defined as the squared diffusion coefficient of a stochastic differential equation. Without assuming any functional form of the volatility function, we…
We present a novel approach to approximate Gaussian and mixture-of-Gaussians filtering. Our method relies on a variational approximation via a gradient-flow representation. The gradient flow is derived from a Kullback--Leibler discrepancy…
Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
This letter presents a non-parametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. The key idea is to represent the discrete shift maps on a smooth basis which can be obtained by the diffusion…
We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic…
The recently proposed non-Gaussian Mat\'{e}rn random field models, generated through Stochastic Partial differential equations (SPDEs), are extended by considering the class of Generalized Hyperbolic processes as noise forcings. The models…
An assumed density approximate likelihood is derived for a class of partially observed stochastic compartmental models which permit observational over-dispersion. This is achieved by treating time-varying reporting probabilities as latent…
We study a new parametric approach for hidden discrete-time diffusion models. This method is based on contrast minimization and deconvolution and leads to estimate a large class of stochastic models with nonlinear drift and nonlinear…
We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an…
This paper proposes a new class of real-time optimization schemes to overcome system-model mismatch of uncertain processes. This work's novelty lies in integrating derivative-free optimization schemes and multi-fidelity Gaussian processes…
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…
In this paper, enlightened by the asymptotic expansion methodology developed by Li(2013b) and Li and Chen (2016), we propose a Taylor-type approximation for the transition densities of the stochastic differential equations (SDEs) driven by…
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…