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We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…
Gaussian processes (GPs) are sophisticated distributions to model functional data. Whilst theoretically appealing, they are computationally cumbersome except for small datasets. We implement two methods for scaling GP inference in Stan:…
While Bayesian inference is the gold standard for uncertainty quantification and propagation, its use within physical chemistry encounters formidable computational barriers. These bottlenecks are magnified for modeling data with many…
Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed…
Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…
In applied Bayesian inference scenarios, users may have access to a large number of pre-existing model evaluations, for example from maximum-a-posteriori (MAP) optimization runs. However, traditional approximate inference techniques make…
Gaussian processes (GPs) are powerful but computationally expensive machine learning models, requiring an estimate of the kernel covariance matrix for every prediction. In large and complex domains, such as graphs, sets, or images, the…
Recently, particle-based variational inference (ParVI) methods have gained interest because they can avoid arbitrary parametric assumptions that are common in variational inference. However, many ParVI approaches do not allow arbitrary…
Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data…
Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention. We develop SigGPDE, a new scalable sparse variational inference framework…
Gaussian process (GP) surrogates are the default tool for emulating expensive computer experiments, but cubic cost, stationarity assumptions, and Gaussian predictive distributions limit their reach. We propose Generative Bayesian…
Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot…
Gaussian process (GP) regression is a flexible, nonparametric approach to regression that naturally quantifies uncertainty. In many applications, the number of responses and covariates are both large, and a goal is to select covariates that…
Deep Gaussian Processes (DGPs) are powerful surrogate models known for their flexibility and ability to capture complex functions. However, extending them to multi-output settings remains challenging due to the need for efficient dependency…
Multivariate time series with missing values are common in areas such as healthcare and finance, and have grown in number and complexity over the years. This raises the question whether deep learning methodologies can outperform classical…
A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…
We propose a novel online Gaussian process (GP) model that is capable of capturing long-term memory in sequential data in an online learning setting. Our model, Online HiPPO Sparse Variational Gaussian Process (OHSVGP), leverages the HiPPO…
Gaussian processes (GP) are powerful tools for probabilistic modeling purposes. They can be used to define prior distributions over latent functions in hierarchical Bayesian models. The prior over functions is defined implicitly by the mean…
Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for…
Dealing with missing values and incomplete time series is a labor-intensive, tedious, inevitable task when handling data coming from real-world applications. Effective spatio-temporal representations would allow imputation methods to…