arXiv research

We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to depend on a set of globally relevant inducing variables which factorize the model …

Study entropic regularization of Gaussian measures and processes on Hilbert space.

It is shown that $3$ disjoint sets with fixed Gaussian volumes that partition $\mathbb{R}^{n}$ with nearly minimum total Gaussian surface area must be close to adjacent $120$ degree sectors, when $n\geq2$. These same results hold for any number $m\leq n+1$ of sets partitioning $\mathbb{R}^{n}$, conditional on the solut…

The paper extends consistency results for sequential design strategies to vector-valued Gaussian processes.

It is shown that $m$ disjoint sets with fixed Gaussian volumes that partition $\mathbb{R}^{n}$ with minimum Gaussian surface area must be $(m-1)$-dimensional. This follows from a second variation argument using infinitesimal translations. The special case $m=3$ proves the Double Bubble problem for the Gaussian measure,…

The paper analyzes uncertainty quantification in sparse Gaussian process regression with a Brownian motion prior.

We study the problem of estimating the parameters of a Gaussian distribution when samples are only shown if they fall in some (unknown) subset $S \subseteq \R^d$. This core problem in truncated statistics has long history going back to Galton, Lee, Pearson and Fisher. Recent work by Daskalakis et al. (FOCS'18), provide…

The paper develops divergences for Gaussian processes and RKHS settings.

Study convergence and approximations of entropic regularized Wasserstein distances for Gaussian and RKHS measures.

Wide deep neural networks with Gaussian weights approximate Gaussian processes closely.

This study describes the Fisher-Rao metric on Gaussian measures in infinite-dimensional spaces.

Vecchia approximations provide the best accuracy-runtime trade-off for Gaussian process approximations.

A $q$-Gaussian measure is a generalization of a Gaussian measure. This generalization is obtained by replacing the exponential function with the power function of exponent $1/(1-q)$ ($q\neq 1$). The limit case $q=1$ recovers a Gaussian measure. For $1\leq q <3$, the set of all $q$-Gaussian densities over the real line …

Study on geometric Jensen-Shannon divergence for Gaussian measures in Hilbert space.

Graph Gaussian processes use Matérn models for better function learning.

The paper proves that symmetric sets with minimal Gaussian surface area are nearly convex cylinders.

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

Bayesian inference for wide neural networks using Edgeworth expansion.

New findings show Gaussian universality breaks down in high-dimensional linear factor mixtures.

Dividing local Gaussian processes improve real-time prediction efficiency.

The paper improves Gaussian process regression by optimizing hyperparameters.

New algorithms estimate parameters of Gaussian and non-Gaussian distributions from truncated samples.

Lower bound shows super-polynomial gap for estimating truncated Gaussian means.

The paper examines how heavy-tailed risks behave under Gaussian copula models.

Proposes a new Gaussian factor for probabilistic inference with degenerate settings.

We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity of target data. The proposed model can effectively make use of auxiliary data set…

FPI methods compute barycenters of Gaussian sets for various dissimilarity measures.

GMVAE improves open-set classification by clustering latent representations.

A new method combines Gaussian Processes to optimize under uncertainty.

Study on predicting sequences with Gaussian constraints, linking to intrinsic volumes and metric complexity.

The Information Bottleneck (IB) is a conceptual method for extracting the most compact, yet informative, representation of a set of variables, with respect to the target. It generalizes the notion of minimal sufficient statistics from classical parametric statistics to a broader information-theoretic sense. The IB curv…

Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The functions to be compared do not just differ in their parametrization but in thei…

Proposes Gaussian process priors on graph sets with geometric structure.

Simplified DGPs training by fixing inducing inputs to subset of data.

Researchers use Gaussian processes to approximate Lagrange multipliers for Maximum-Entropy distributions.

New findings on maximizing noise stability in partitions of Gaussian space.

The paper identifies a 'small' set of functions containing Gaussian process samples.

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

New Gaussian processes for Riemannian manifolds enable uncertainty quantification.

Topic models are widely used to discover the latent representation of a set of documents. The two canonical models are latent Dirichlet allocation, and Gaussian latent Dirichlet allocation, where the former uses multinomial distributions over words, and the latter uses multivariate Gaussian distributions over pre-train…

How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also provide a good fit for the original data set. We show that, perhaps surprisingly…

We propose a practical and scalable Gaussian process model for large-scale nonlinear probabilistic regression. Our mixture-of-experts model is conceptually simple and hierarchically recombines computations for an overall approximation of a full Gaussian process. Closed-form and distributed computations allow for effici…

Sharp Gaussian isoperimetry proven along Ricci flow.

New method for robust linear regression in nearly linear time.

Gaussian processes adapted for non-Euclidean spaces enhance decision-making.

GGMPs improve non-Gaussian conditional density estimation.

Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the great flexibility of multilayer models. In DGPs, given the inputs, the outputs …

We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter optimization based upon marginal likelihood maximization.…