Related papers: Gaussian Process Quantile Regression using Expecta…

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a…

Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…

The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…

Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…

This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…

Neural processes are a family of probabilistic models that inherit the flexibility of neural networks to parameterize stochastic processes. Despite providing well-calibrated predictions, especially in regression problems, and quick…

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

In this paper, a functional partial quantile regression approach, a quantile regression analog of the functional partial least squares regression, is proposed to estimate the function-on-function linear quantile regression model. A partial…

Recent advances in learning techniques have enabled the modelling of dynamical systems for scientific and engineering applications directly from data. However, in many contexts explicit data collection is expensive and learning algorithms…

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…

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with…

In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and…

Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian processes but their training remains challenging. Sparse approximations simplify the training but often require optimization over a large number of inducing…

A general information transmission model, under independent and identically distributed Gaussian codebook and nearest neighbor decoding rule with processed channel output, is investigated using the performance metric of generalized mutual…

This paper introduces an innovative approach to enhance distributed cooperative learning using Gaussian process (GP) regression in multi-agent systems (MASs). The key contribution of this work is the development of an elective learning…

In this paper, we develop a quantile functional regression modeling framework that models the distribution of a set of common repeated observations from a subject through the quantile function, which is regressed on a set of covariates to…

Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…

Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as…