Related papers: Frequency-domain Gaussian Process Models for $H_\i…
Gaussian processes are Bayesian non-parametric models used in many areas. In this work, we propose a Non-stationary Heteroscedastic Gaussian process model which can be learned with gradient-based techniques. We demonstrate the…
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…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
Covariate measurement error in nonparametric regression is a common problem in nutritional epidemiology and geostatistics, and other fields. Over the last two decades, this problem has received substantial attention in the frequentist…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
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,…
Nonparametric Bayesian approaches based on Gaussian processes have recently become popular in the empirical learning community. They encompass many classical methods of statistics, like Radial Basis Functions or various splines, and are…
This paper presents a hierarchical Bayesian modeling framework for the uncertainty quantification in modal identification of linear dynamical systems using multiple vibration data sets. This novel framework integrates the state-of-the-art…
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…
Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in…
Gaussian processes (GPs) are widely used metamodels for approximating expensive computer simulations, particularly in engineering design and spatial prediction. However, their performance can deteriorate significantly when covariance…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
Deep Learning Gaussian Processes (DL-GP) are proposed as a methodology for analyzing (approximating) computer models that produce heteroskedastic and high-dimensional output. Computer simulation models have many areas of applications,…
Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…
Leveraging autonomous systems in safety-critical scenarios requires verifying their behaviors in the presence of uncertainties and black-box components that influence the system dynamics. In this work, we develop a framework for verifying…
We propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is…
Gaussian Process (GP) models provide a flexible framework for prediction and uncertainty quantification. For most covariance functions, however, exact GP prediction with $n$ points scales as $\mathcal{O}(n^3)$, making it prohibitively…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
One major impediment to the wider use of deep learning for clinical decision making is the difficulty of assigning a level of confidence to model predictions. Currently, deep Bayesian neural networks and sparse Gaussian processes are the…
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…