Related papers: Regression Analysis for Multivariate Dependent Cou…
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…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…
Multi-output Gaussian process (MGP) is commonly used as a transfer learning method to leverage information among multiple outputs. A key advantage of MGP is providing uncertainty quantification for prediction, which is highly important for…
We consider the problem of estimating the parameters of the covariance function of a Gaussian process by cross-validation. We suggest using new cross-validation criteria derived from the literature of scoring rules. We also provide an…
In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…
The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty. Existing…
We propose a scalable framework for inference in an inhomogeneous Poisson process modeled by a continuous sigmoidal Cox process that assumes the corresponding intensity function is given by a Gaussian process (GP) prior transformed with a…
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 occupy one of the leading places in modern statistics and probability theory due to their importance and a wealth of strong results. The common use of Gaussian processes is in connection with problems related to…
A key challenge in the practical application of Gaussian processes (GPs) is selecting a proper covariance function. The moving average, or process convolutions, construction of GPs allows some additional flexibility, but still requires…
A Gaussian process (GP) is a powerful and widely used regression technique. The main building block of a GP regression is the covariance kernel, which characterizes the relationship between pairs in the random field. The optimization to…
Generalized linear regressions, such as logistic regressions or Poisson regressions, are long-studied regression analysis approaches, and their applications are widely employed in various classification problems. Our study considers a…
We develop a Gaussian process ("GP") framework for modeling mortality rates and mortality improvement factors. GP regression is a nonparametric, data-driven approach for determining the spatial dependence in mortality rates and jointly…
This paper introduces warped Gaussian processes (WGP) regression in remote sensing applications. WGP models output observations as a parametric nonlinear transformation of a GP. The parameters of such prior model are then learned via…
Multivariate compositional count data arise in many applications including ecology, microbiology, genetics, and paleoclimate. A frequent question in the analysis of multivariate compositional count data is what values of a covariate(s) give…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for…
Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical…
We present a novel approach for explaining Gaussian processes (GPs) that can utilize the full analytical covariance structure present in GPs. Our method is based on the popular solution concept of Shapley values extended to stochastic…
Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice,…