Related papers: How Deep Are Deep Gaussian Processes?
Accurate assessment of systematic uncertainties is an increasingly vital task in physics studies, where large, high-dimensional datasets, like those collected at the Large Hadron Collider, hold the key to new discoveries. Common approaches…
Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…
We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution…
Gaussian processes (GPs) are very widely used for modeling of unknown functions or surfaces in applications ranging from regression to classification to spatial processes. Although there is an increasingly vast literature on applications,…
Deep learning is a hierarchical inference method formed by subsequent multiple layers of learning able to more efficiently describe complex relationships. In this work, Deep Gaussian Mixture Models are introduced and discussed. A Deep…
We introduce a class of scalable Bayesian hierarchical models for the analysis of massive geostatistical datasets. The underlying idea combines ideas on high-dimensional geostatistics by partitioning the spatial domain and modeling the…
Training energy-based probabilistic models is confronted with apparently intractable sums, whose Monte Carlo estimation requires sampling from the estimated probability distribution in the inner loop of training. This can be approximately…
Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates,…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
Gaussian processes are ubiquitous in nature and engineering. A case in point is a class of neural networks in the infinite-width limit, whose priors correspond to Gaussian processes. Here we perturbatively extend this correspondence to…
We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…
We present a unified view of likelihood based Gaussian progress regression for simulation experiments exhibiting input-dependent noise. Replication plays an important role in that context, however previous methods leveraging replicates have…
Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…
Understanding the impact of data structure on the computational tractability of learning is a key challenge for the theory of neural networks. Many theoretical works do not explicitly model training data, or assume that inputs are drawn…
Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the…
One obstacle to the use of Gaussian processes (GPs) in large-scale problems, and as a component in deep learning system, is the need for bespoke derivations and implementations for small variations in the model or inference. In order to…
Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…
Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this…