Related papers: Warped Input Gaussian Processes for Time Series Fo…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
Adaptive time series forecasting is essential for prediction under regime changes. Several classical methods assume linear Gaussian state space model (LGSSM) with variances constant in time. However, there are many real-world processes that…
We consider the problem of estimating a signal from its warped observations. Such estimation is commonly performed by altering the observations through some inverse-warping, or solving a computationally demanding optimization formulation.…
The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…
We present an adaptive approach to the construction of Gaussian process surrogates for Bayesian inference with expensive-to-evaluate forward models. Our method relies on the fully Bayesian approach to training Gaussian process models and…
In a broad and fundamental type of ''inverse problems'' in science, one infers a spatially distributed physical attribute based on observations of processes that are controlled by the spatial attribute in question. The data-generating field…
Generative probabilistic forecasting produces future time series samples according to the conditional probability distribution given past time series observations. Such techniques are essential in risk-based decision-making and planning…
We propose a pointwise inference algorithm for high-dimensional linear models with time-varying coefficients. The method is based on a novel combination of the nonparametric kernel smoothing technique and a Lasso bias-corrected ridge…
Markov chain Monte Carlo methods for exponential family models with intractable normalizing constant, such as the exchange algorithm, require simulations of the sufficient statistics at every iteration of the Markov chain, which often…
We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…
The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose…
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…
Gaussian processes are a versatile framework for learning unknown functions in a manner that permits one to utilize prior information about their properties. Although many different Gaussian process models are readily available when the…
Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…
Covariance tapering is a popular approach for reducing the computational cost of spatial prediction and parameter estimation for Gaussian process models. However, tapering can have poor performance when the process is sampled at spatially…
A novel extrapolation method is proposed for longitudinal forecasting. A hierarchical Gaussian process model is used to combine nonlinear population change and individual memory of the past to make prediction. The prediction error is…
In this article, we show that a general class of weakly stationary time series can be modeled applying Gaussian subordinated processes. We show that, for any given weakly stationary time series $(z_t)_{z\in\mathbb{N}}$ with given equal…
In this work, we address time-series forecasting as a computer vision task. We capture input data as an image and train a model to produce the subsequent image. This approach results in predicting distributions as opposed to pointwise…
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…
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…