Related papers: Parameter estimation for fractional autoregressive…

Constructing accurate and computationally efficient surrogate models (or emulators) for predicting dynamical system responses is critical in many engineering domains, yet remains challenging due to the strongly nonlinear and…

In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it…

This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…

Multi-output regression models must exploit dependencies between outputs to maximise predictive performance. The application of Gaussian processes (GPs) to this setting typically yields models that are computationally demanding and have…

The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…

A recursive least squares algorithm with variable rate forgetting (VRF) is derived by minimizing a quadratic cost function.Under persistent excitation and boundedness of the forgetting factor, the minimizer given by VRF is shown to converge…

Many numerical algorithms have been established to reconstruct pressure fields from measured kinematic data with noise by Particle Image Velocimetry (PIV), such as the Pressure Poisson solver and the Omni-Directional Integration (ODI)…

In this paper, we unify popular non-rigid registration methods for point sets and surfaces under our general framework, GiNGR. GiNGR builds upon Gaussian Process Morphable Models (GPMM) and hence separates modeling the deformation prior…

Sparse variational approximations are popular methods for scaling up inference and learning in Gaussian processes to larger datasets. For $N$ training points, exact inference has $O(N^3)$ cost; with $M \ll N$ features, state of the art…

In this paper, we introduce a novel theoretical framework for Gaussian process regression error analysis, leveraging a function-space decomposition. Based on this framework, we develop a weighted Jacobi iterative method that utilizes…

This paper introduces a novel scheme to progressively estimate interferometric phases from a stack of synthetic aperture radar (SAR) images. The scheme is shown to yield comparable performance to full-covariance algorithms for a realistic…

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…

In this paper, we present a new statistical approach to the problem of incorporating experimental observations into a mathematical model described by linear partial differential equations (PDEs) to improve the prediction of the state of a…

Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…

Visual autoregressive models achieve remarkable generation quality through next-scale predictions across multi-scale token pyramids. However, the conventional method uses uniform scale downsampling to build these pyramids, leading to…

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…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Much recent work has concerned sparse approximations to speed up the Gaussian process regression from the unfavorable O(n3) scaling in computational time to O(nm2). Thus far, work has concentrated on models with one covariance function.…

We consider the problem of estimating the sparse time-varying parameter vectors of a point process model in an online fashion, where the observations and inputs respectively consist of binary and continuous time series. We construct a novel…

We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…