arXiv research

Smooth Schrödinger Bridges improve trajectory inference by smoothing Gaussian processes.

The paper establishes bounds on the smoothness parameter in Gaussian process interpolation.

GPCDL uses Gaussian Processes to learn smooth templates from data.

Improved model for non-smooth signals with complex spectra.

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning,…

Bayesian optimization tackles non-smooth tuning problems.

Develops state-space deep Gaussian processes for irregular signals.

Unified framework for efficient Gaussian process inference.

The paper proposes a method to model non-smooth functions using clustering, classification, and Gaussian process modeling.

Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true when the model is well-specified, which is often not the case in practice. In thi…

This work investigates the properties of Gaussian-smoothed sliced divergences for comparing distributions.

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral dens…

Bayesian optimization on networks using Gaussian process models.

New Gaussian min-max theorem extends classical results to non-i.i.d. Gaussian matrices.

Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too restrictive. One way to alleviate this limitation is to find a different representation of …

Accelerates GPR with localized kernels for faster performance.

Wide neural networks can be closely approximated by Gaussian processes, with rates depending on the activation function's properties.

Extends Gaussian process regression for non-Gaussian data.

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gauss…

RAMBO optimizes multi-regime problems by discovering and modeling distinct energy basins.

Improved kernel ridge regression for large datasets using weighted random binning.

Gaussian processes are typically used for smoothing and interpolation on small datasets. We introduce a new Bayesian nonparametric framework -- GPatt -- enabling automatic pattern extrapolation with Gaussian processes on large multidimensional datasets. GPatt unifies and extends highly expressive kernels and fast exact…

The paper considers the problem of global optimization in the setup of stochastic process bandits. We introduce an UCB algorithm which builds a cascade of discretization trees based on generic chaining in order to render possible his operability over a continuous domain. The theoretical framework applies to functions u…

Paper improves regret bounds for Gaussian process upper confidence bound in Bayesian optimization.

The paper explores the identifiability and interpretability of Gaussian process models using different kernel structures.

This study examines Gaussian processes on Riemannian manifolds and proves contraction rates.

Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently, probabilistic graphical models for reciprocal processes have been provided. This …

This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing algorithms. We show that many sigma-point methods can be interpreted as Gaussia…

It is now known that an extended Gaussian process model equipped with rescaling can adapt to different smoothness levels of a function valued parameter in many nonparametric Bayesian analyses, offering a posterior convergence rate that is optimal (up to logarithmic factors) for the smoothness class the true function be…

Improved sample efficiency in reinforcement learning with deep Gaussian processes.

Paper speeds up Gaussian process inference using Matérn kernels.

VMGP extends Gaussian processes for Bayesian meta-learning, improving uncertainty prediction.

Bounds on Gaussian approximation for neural networks with novel smoothing techniques.

Deep-HGP uses Bayesian nonparametric approach for complex data regression.

Introduces a new theoretical framework for exponential smoothing.

Generative Bayesian Computation improves surrogates for expensive simulations.

Improves Gaussian process models for large datasets.

We derive expressions for the predicitive information rate (PIR) for the class of autoregressive Gaussian processes AR(N), both in terms of the prediction coefficients and in terms of the power spectral density. The latter result suggests a duality between the PIR and the multi-information rate for processes with mutua…

The paper develops a state-space approach to deep Gaussian processes for efficient state estimation.

Novel method uses Gaussian process to estimate particle sizes from scattering data.

Neural-net-induced Gaussian process (NNGP) regression inherits both the high expressivity of deep neural networks (deep NNs) as well as the uncertainty quantification property of Gaussian processes (GPs). We generalize the current NNGP to first include a larger number of hyperparameters and subsequently train the model…

Reinforcement learning algorithms rely on exploration to discover new behaviors, which is typically achieved by following a stochastic policy. In continuous control tasks, policies with a Gaussian distribution have been widely adopted. Gaussian exploration however does not result in smooth trajectories that generally c…

Quantum-assisted Gaussian process speeds up data regression.

GP-BART improves BART's predictive performance by incorporating Gaussian process priors.

Enhances Gaussian process models for handling variable error variances and multiple responses.

A new method scales Gaussian process variational autoencoders to handle high-dimensional time series.

Two methods improve Gaussian process predictive distributions' calibration.

Efficient spatio-temporal Gaussian process inference method.