• Corpus ID: 239016048

Multi-group Gaussian Processes

  title={Multi-group Gaussian Processes},
  author={Didong Li and Andrew Jones and Sudipto Banerjee and Barbara E. Engelhardt},
Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known discrete subgroups of samples. For example, in genomics applications samples may be grouped according to tissue type or drug exposure. In the modeling process it is desirable to leverage the similarity among groups while accounting for differences between them… 


Hierarchical Bayesian modelling of gene expression time series across irregularly sampled replicates and clusters
The hierarchical Gaussian process model provides an excellent statistical basis for several gene-expression time-series tasks, and has only a few additional parameters over a regular GP, has negligible additional complexity, is easily implemented and can be integrated into several existing algorithms.
Diffusion Based Gaussian Processes on Restricted Domains
This article proposes a new class of diffusion-based GPs (DB-GPs), which learn a covariance that respects the geometry of the input domain, and approximate the covariance using finitely-many eigenpairs of the Graph Laplacian.
Regression and Classification Using Gaussian Process Priors
Gaussian processes are in my view the simplest and most obvious way of defining flexible Bayesian regression and classification models, but despite some past usage, they appear to have been rather neglected as a general-purpose technique.
High-Dimensional Bayesian Geostatistics.
Two approaches can be described as model-based solutions for big spatiotemporal datasets that ensure that the algorithmic complexity has ~ n floating point operations (flops), where n the number of spatial locations (per iteration).
Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets
A class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets are developed and it is established that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices.
Identifying latent groups in spatial panel data using a Markov random field constrained product partition model
Understanding the heterogeneity over spatial locations is an important problem that has been widely studied in many applications such as economics and environmental science. In this paper, we focus
Gaussian Processes for Machine Learning
The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics, and deals with the supervised learning problem for both regression and classification.
Cross-Covariance Functions for Multivariate Geostatistics
The main approaches to building cross-covariance models are reviewed, including the linear model of coregionalization, convolution methods, the multivariate Mat\'{e}rn and nonstationary and space-time extensions of these among others, and specialized constructions, including those designed for asymmetry, compact support and spherical domains, are covered.
Intrinsic Gaussian processes on complex constrained domains
The key novelty of the proposed approach is to utilise the relationship between heat kernels and the transition density of Brownian motion on manifolds for constructing and approximating valid and computationally feasible covariance kernels.
A General Framework for Vecchia Approximations of Gaussian Processes
Gaussian processes (GPs) are commonly used as models for functions, time series, and spatial fields, but they are computationally infeasible for large datasets. Focusing on the typical setting of