Related papers: Residual Deep Gaussian Processes on Manifolds

Transformer models have consistently achieved remarkable results in various domains such as natural language processing and computer vision. However, despite ongoing research efforts to better understand these models, the field still lacks…

Computer models are used as a way to explore complex physical systems. Stationary Gaussian process emulators, with their accompanying uncertainty quantification, are popular surrogates for computer models. However, many computer models are…

Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…

A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…

Gaussian processes are a fully Bayesian smoothing technique that allows for the reconstruction of a function and its derivatives directly from observational data, without assuming a specific model or choosing a parameterization. This is…

Deep neural networks have reshaped modern machine learning by learning powerful latent representations that often align with the manifold hypothesis: high-dimensional data lie on lower-dimensional manifolds. In this paper, we establish a…

Due to its state-of-the-art estimation performance complemented by rigorous and non-conservative uncertainty bounds, Gaussian process regression is a popular tool for enhancing dynamical system models and coping with their inaccuracies.…

We introduce Deep Sigma Point Processes, a class of parametric models inspired by the compositional structure of Deep Gaussian Processes (DGPs). Deep Sigma Point Processes (DSPPs) retain many of the attractive features of (variational)…

We reframe linear dimensionality reduction as a problem of Bayesian inference on matrix manifolds. This natural paradigm extends the Bayesian framework to dimensionality reduction tasks in higher dimensions with simpler models at greater…

Many datasets are in the form of tables of binned data. Performing regression on these data usually involves either reading off bin heights, ignoring data from neighbouring bins or interpolating between bins thus over or underestimating the…

We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…

We develop a scalable deep non-parametric generative model by augmenting deep Gaussian processes with a recognition model. Inference is performed in a novel scalable variational framework where the variational posterior distributions are…

We propose deep convolutional Gaussian processes, a deep Gaussian process architecture with convolutional structure. The model is a principled Bayesian framework for detecting hierarchical combinations of local features for image…

Quantifying spatial and/or temporal associations in multivariate geolocated data of different types is achievable via spatial random effects in a Bayesian hierarchical model, but severe computational bottlenecks arise when spatial…

Deep Gaussian processes (DGPs) provide a Bayesian non-parametric alternative to standard parametric deep learning models. A DGP is formed by stacking multiple GPs resulting in a well-regularized composition of functions. The Bayesian…

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…

Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…

Gaussian processes are one of the dominant approaches in Bayesian learning. Although the approach has been applied to numerous problems with great success, it has a few fundamental limitations. Multiple methods in literature have addressed…

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…

As a means of improving analysis of biological shapes, we propose an algorithm for sampling a Riemannian manifold by sequentially selecting points with maximum uncertainty under a Gaussian process model. This greedy strategy is known to be…