Related papers: Prediction performance after learning in Gaussian …
In this paper, we study the prediction of a circularly symmetric zero-mean stationary Gaussian process from a window of observations consisting of finitely many samples. This is a prevalent problem in a wide range of applications in…
The Cram\'er-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the…
When fitting Bayesian machine learning models on scarce data, the main challenge is to obtain suitable prior knowledge and encode it into the model. Recent advances in meta-learning offer powerful methods for extracting such prior knowledge…
We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
Gaussian process regression underpins countless academic and industrial applications of machine learning and statistics, with maximum likelihood estimation routinely used to select appropriate parameters for the covariance kernel. However,…
Consider the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signal-to-noise ratio (SNR) as well as a functional…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
We rigorously prove that deep Gaussian process priors can outperform Gaussian process priors if the target function has a compositional structure. To this end, we study information-theoretic lower bounds for posterior contraction rates for…
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…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
Machine learning-based reliability analysis methods have shown great advancements for their computational efficiency and accuracy. Recently, many efficient learning strategies have been proposed to enhance the computational performance.…
The minimum mean-square error (MMSE) achievable by optimal estimation of a random variable $Y\in\mathbb{R}$ given another random variable $X\in\mathbb{R}^{d}$ is of much interest in a variety of statistical settings. In the context of…
Kriging and Gaussian Process Regression are statistical methods that allow predicting the outcome of a random process or a random field by using a sample of correlated observations. In other words, the random process or random field is…
This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…
This paper investigates the minimum mean square error (MMSE) estimation of x, given the observation y = Hx+n, when x and n are independent and Gaussian Mixture (GM) distributed. The introduction of GM distributions, represents a…
Gaussian process regression (GPR) or kernel ridge regression is a widely used and powerful tool for nonlinear prediction. Therefore, active learning (AL) for GPR, which actively collects data labels to achieve an accurate prediction with…
Robust estimation is an important and timely research subject. In this paper, we investigate performance lower bounds on the mean-square-error (MSE) of any estimator for the Bayesian linear model, corrupted by a noise distributed according…
Gaussian process regression (GPR) is a non-parametric Bayesian technique for interpolating or fitting data. The main barrier to further uptake of this powerful tool rests in the computational costs associated with the matrices which arise…
Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…