arXiv research

Improved Gaussian process models for interpretable predictions.

Combines additivity and active subspaces for high-dimensional Gaussian process modeling.

Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel …

Projection pursuit model improves Gaussian process regression for high-dimensional data.

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

We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-expo…

Generalized additive models (GAMs) are a widely used class of models of interest to statisticians as they provide a flexible way to design interpretable models of data beyond linear models. We here propose a scalable and well-calibrated Bayesian treatment of GAMs using Gaussian processes (GPs) and leveraging recent adv…

Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables to the model. Previous work on DGP models has introduced noise additively and use…

Gaussian process models -also called Kriging models- are often used as mathematical approximations of expensive experiments. However, the number of observation required for building an emulator becomes unrealistic when using classical covariance kernels when the dimension of input increases. In oder to get round the cu…

Scalable algorithm for sampling Gaussian processes using sparse grids and preconditioners.

We propose a partially linear additive Gaussian graphical model (PLA-GGM) for the estimation of associations between random variables distorted by observed confounders. Model parameters are estimated using an $L_1$-regularized maximal pseudo-profile likelihood estimator (MaPPLE) for which we prove $\sqrt{n}$-sparsisten…

Bayesian optimization tackles non-smooth tuning problems.

The paper forecasts joint electricity demand across 14 British regions using additive models.

A scalable Bayesian additive model for stellar flare detection using Gaussian process inference and hidden Markov models.

Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice, as do applications in which the residuals do not have a Gaussian distribution. …

This study converts BART to Gaussian process regression, revealing its limitations and potential improvements.

Optimized Franz-Parisi criterion matches SQ lower bounds for various statistical models.

Much recent work has concerned sparse approximations to speed up the Gaussian process regression from the unfavorable O(n3) scaling in computational time to O(nm2). Thus far, work has concentrated on models with one covariance function. However, in many practical situations additive models with multiple covariance func…

Paper introduces a nonparametric functional graphical model for random functions.

New algorithm for estimating MLR parameters with non-Gaussian noise.

Kernel Multigrid accelerates Back-fitting for additive Gaussian Processes.

Combines BART and Gaussian process for spatial covariate prediction with uncertainty.

New algorithm for collective Gaussian hidden Markov models inference.

Additive Gaussian process framework handles monotonicity constraints in high dimensions.

The paper analyzes and mitigates biases in scalable Gaussian Process methods.

In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the implied volatility. In addition, we prove that if the volatility function in an uncor…

Method estimates bivariate causal models using normalising flows and variational Gaussian process regression.

Proposes DAK model for improved GP computations.

The authors aim to develop numerical schemes of the two representative quadratic hedging strategies: locally risk minimizing and mean-variance hedging strategies, for models whose asset price process is given by the exponential of a normal inverse Gaussian process, using the results of Arai et al. \cite{AIS}, and Arai …

Gaussian processes struggle with compositional functions, but deep Gaussian processes can outperform.

New method distinguishes data noise from GP uncertainty.

Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator, a GP model can beneficially be used for tasks such as prediction, optimization, …

Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language, information retrieval and others. Gaussian graphical model selection is a statist…

Proposes I-prior extension for additive interaction models.

Enforces physical constraints in GP regression models.

BARK optimizes black-box functions using Bayesian Additive Regression Trees.

Paper presents characteristic function of Tsallis q-Gaussian and its applications.

A scalable factorized Gaussian process VAE for faster inference.

Sparse matrices simplify computation of GP variances and likelihoods.

We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the functional relationship between the task variables and the parameters of this con…

This tutorial simplifies Gaussian process regression for beginners.

In this paper, we prove that some Gaussian structural equation models with dependent errors having equal variances are identifiable from their corresponding Gaussian distributions. Specifically, we prove identifiability for the Gaussian structural equation models that can be represented as Andersson-Madigan-Perlman cha…

A model learns causal representations from high-dimensional data.

Bayesian inference for wide neural networks using Edgeworth expansion.

Combines boosting with Gaussian process and mixed effects models.

Paper uses variational inference to estimate nonlinear models.

Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formal…

New model improves QGP simulation efficiency and accuracy.