Related papers: Bayesian Manifold Regression
Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…
Shape constrained regression analysis has applications in dose-response modeling, environmental risk assessment, disease screening and many other areas. Incorporating the shape constraints can improve estimation efficiency and avoid…
Bayesian optimisation is a popular technique for hyperparameter learning but typically requires initial exploration even in cases where similar prior tasks have been solved. We propose to transfer information across tasks using learnt…
Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point…
Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist…
We develop Bayesian machine learning methods for mixed data sampling (MIDAS) regressions. This involves handling frequency mismatches and specifying functional relationships between many predictors and the dependent variable. We use…
The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…
Accurate tuning of hyperparameters is crucial to ensure that models can generalise effectively across different settings. In this paper, we present theoretical guarantees for hyperparameter selection using variational Bayes in the…
This article presents a novel approach to construct Intrinsic Gaussian Processes for regression on unknown manifolds with probabilistic metrics (GPUM) in point clouds. In many real world applications, one often encounters high dimensional…
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…
This paper develops a class of Bayesian non- and semiparametric methods for estimating regression curves and surfaces. The main idea is to model the regression as locally linear, and then place suitable local priors on the local parameters.…
A primary goal of computer experiments is to reconstruct the function given by the computer code via scattered evaluations. Traditional isotropic Gaussian process models suffer from the curse of dimensionality, when the input dimension is…
In many applications, such as economics, operations research and reinforcement learning, one often needs to estimate a multivariate regression function f subject to a convexity constraint. For example, in sequential decision processes the…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on…
Detecting boundary of an image based on noisy observations is a fundamental problem of image processing and image segmentation. For a $d$-dimensional image ($d = 2, 3, \ldots$), the boundary can often be described by a closed smooth $(d -…
Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of…
Existing high-dimensional Bayesian optimization (BO) methods aim to overcome the curse of dimensionality by carefully encoding structural assumptions, from locality to sparsity to smoothness, into the optimization procedure. Surprisingly,…
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.…