Related papers: Estimation error for blind Gaussian time series pr…

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…

We study the well known difficult problem of prediction in measurement error models. By targeting directly at the prediction interval instead of the point prediction, we construct a prediction interval by providing estimators of both the…

Machine learning models play a vital role in time series forecasting. These models, however, often overlook an important element: point uncertainty estimates. Incorporating these estimates is crucial for effective risk management, informed…

We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we…

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…

We develop an automated variational inference method for Bayesian structured prediction problems with Gaussian process (GP) priors and linear-chain likelihoods. Our approach does not need to know the details of the structured likelihood…

Probabilistic models are often used to make predictions in regions of the data space where no observations are available, but it is not always clear whether such predictions are well-informed by previously seen data. In this paper, we…

We consider the estimation of a sparse parameter vector from measurements corrupted by white Gaussian noise. Our focus is on unbiased estimation as a setting under which the difficulty of the problem can be quantified analytically. We show…

We consider the problem of approximating sums of high-dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size $n$,…

In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent…

We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian…

Uncertainty is an inherent characteristic of biological and geospatial data which is almost made by measurement error in the observed values of the quantity of interest. Ignoring measurement error can lead to biased estimates and inflated…

Time series forecasting is a challenging task due to the existence of complex and dynamic temporal dependencies. This can lead to incorrect predictions by even the best forecasting models. Using more training data is one way to improve the…

This paper deals with the evaluation of double line integrals of the squared exponential covariance function. We propose a new approach in which the double integral is reduced to a single integral using the error function. This single…

We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…

We consider convergence of alternating projections between non-convex sets and obtain applications to convergence of the Gerchberg-Saxton error reduction method, of the Gaussian expectation-maximization algorithm, and of Cadzow's algorithm.

Variable projection methods prove highly efficient in solving separable nonlinear least squares problems by transforming them into a reduced nonlinear least squares problem, typically solvable via the Gauss-Newton method. When solving…

We study a statistical model for infinite dimensional Gaussian random variables with unknown parameters. For this model we derive linear estimators for the mean and the variance of the Gaussian distribution. Furthermore, we construct…

In this paper we address the statistical problem of testing if a stationary process is Gaussian. The observation consists in a finite sample path of the process. Using a random projection technique introduced and studied in Cuesta-Albertos…

Fitting a polynomial to observed data is an ubiquitous task in many signal processing and machine learning tasks, such as interpolation and prediction. In that context, input and output pairs are available and the goal is to find the…