Related papers: Gaussian process classification using posterior li…
We present a novel Bayesian framework for inverse problems in which the pos terior distribution is interpreted as the intensity measure of a Poisson point process (PPP). The posterior density is approximated using kernel density estimation,…
In recent years, inconsistency in Bayesian deep learning has attracted significant attention. Tempered or generalized posterior distributions are frequently employed as direct and effective solutions. Nonetheless, the underlying mechanisms…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
In many clinical trials treatments need to be repeatedly applied as diseases relapse frequently after remission over a long period of time (e.g., 35 weeks). Most research in statistics focuses on the overall trial design, such as sample…
Conditional density estimation (density regression) estimates the distribution of a response variable y conditional on covariates x. Utilizing a partition model framework, a conditional density estimation method is proposed using logistic…
Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…
Recently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution, and a number of particle filters based on this principle have been proposed. Samples are drawn…
This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…
Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…
In applications of Gaussian processes where quantification of uncertainty is of primary interest, it is necessary to accurately characterize the posterior distribution over covariance parameters. This paper proposes an adaptation of the…
A multi-output Gaussian process (GP) is introduced as a model for the joint posterior distribution of the local predictive ability of set of models and/or experts, conditional on a vector of covariates, from historical predictions in the…
This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and…
This paper presents a new Expectation Propagation (EP) framework for image restoration using patch-based prior distributions. While Monte Carlo techniques are classically used to sample from intractable posterior distributions, they can…
In this article, we evaluate the performance of a data-driven background estimate method based on Gaussian Process Regression (GPR). A realistic background spectrum from a search conducted by CMS is considered, where a large sub-region…
As a powerful Bayesian non-parameterized algorithm, the Gaussian process (GP) has performed a significant role in Bayesian optimization and signal processing. GPs have also advanced online decision-making systems because their posterior…
This research note presents a derivation and implementation of efficient and scalable gradient computations using the celerite algorithm for Gaussian Process (GP) modeling. The algorithms are derived in a "reverse accumulation" or…
The performance of Gaussian Process (GP) regression is often hampered by the curse of dimensionality, which inflates computational cost and reduces predictive power in high-dimensional problems. Variable selection is thus crucial for…
We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the…
Motivated by deep neural networks, the deep Gaussian process (DGP) generalizes the standard GP by stacking multiple layers of GPs. Despite the enhanced expressiveness, GP, as an $L_2$ regularization prior, tends to be over-smooth and…
We propose a scalable stochastic variational approach to GP classification building on Polya-Gamma data augmentation and inducing points. Unlike former approaches, we obtain closed-form updates based on natural gradients that lead to…