Related papers: Variable selection for Gaussian process regression…
A key challenge with controlling complex dynamical systems is to accurately model them. However, this requirement is very hard to satisfy in practice. Data-driven approaches such as Gaussian processes (GPs) have proved quite effective by…
Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…
Sparse Bayesian learning is a state-of-the-art supervised learning algorithm that can choose a subset of relevant samples from the input data and make reliable probabilistic predictions. However, in the presence of high-dimensional data…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
We apply Gaussian process (GP) regression, which provides a powerful non-parametric probabilistic method of relating inputs to outputs, to survival data consisting of time-to-event and covariate measurements. In this context, the covariates…
This paper proposes an efficient general alternating-direction implicit (GADI) framework for solving large sparse linear systems. The convergence property of the GADI framework is discussed. Most of the existing ADI methods can be viewed as…
Recent work on simultaneous trajectory estimation and mapping (STEAM) for mobile robots has found success by representing the trajectory as a Gaussian process. Gaussian processes can represent a continuous-time trajectory, elegantly handle…
Missing values are common in many real-life datasets. However, most of the current machine learning methods can not handle missing values. This means that they should be imputed beforehand. Gaussian Processes (GPs) are non-parametric models…
Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…
This paper presents Sparse Gradient Descent as a solution for variable selection in convex piecewise linear regression, where the model is given as the maximum of $k$-affine functions $ x \mapsto \max_{j \in [k]} \langle a_j^\star, x…
Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot…
The Gaussian process (GP) is a popular way to specify dependencies between random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these…
We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any…
This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over…
Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…
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…
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic…
Gaussian processes (GPs) are typically criticised for their unfavourable scaling in both computational and memory requirements. For large datasets, sparse GPs reduce these demands by conditioning on a small set of inducing variables…
Large, multi-dimensional spatio-temporal datasets are omnipresent in modern science and engineering. An effective framework for handling such data are Gaussian process deep generative models (GP-DGMs), which employ GP priors over the latent…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…