New findings show Gaussian universality breaks down in high-dimensional linear factor mixtures.
problem The limitations of Gaussian universality in high-dimensional classification.
method Characterization of empirical risk minimization for classification under linear factor mixture models.
result Gaussian universality breaks down under high-dimensional linear factor mixtures.
This paper speeds up Gaussian process regression for autocorrelated data.
problem Temporal overfitting in Gaussian process models for autocorrelated data.
method Modifying existing Gaussian process approximations to handle blocked, de-correlated data.
result Proposed methods accelerate Gaussian process regression on autocorrelated data without sacrificing performance.
Improved VB algorithm for NIG mixtures outperforms Gaussian mixtures for non-Gaussian data.
problem Clustering non-Gaussian data, especially heavy-tailed and asymmetric.
method Proposed an improved VB algorithm for NIG mixture models and extended Dirichlet process mixture models.
result Outperforms Gaussian mixtures and existing NIG mixture models, especially for highly non-normative data.
Gaussian processes model geospatial trajectories with uncertainty.
problem Interpolating and predicting complex spatiotemporal data.
method Gaussian process models trajectories as multidimensional Gaussian distributions.
result Gaussian processes provide a flexible and probabilistic way to interpolate geospatial data.
Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it on the observed data. In system identification, Gaussian processes are used to …
A new algorithm splits Gaussian processes for efficient streaming data.
problem Poor scaling of Gaussian processes in streaming data.
method Sequential partitioning of input space and localized Gaussian process fitting.
result The algorithm achieves linear memory complexity and superior time and space complexity.
Develops a new method for functional regression that works with non-Gaussian data.
problem Limited models for regression in function spaces with Gaussian process priors.
method Introduces Neural Operator Flows (OpFlow) for non-Gaussian function spaces.
result OpFlow enables robust and accurate uncertainty quantification for functional regression.
The paper shows how to infer conditional independence from non-Gaussian data.
problem Inferring conditional independence from non-Gaussian distributions.
method Developed a method to recover conditional independence structure from the precision matrix of generalized nonparanormal data.
result The conditional independence structure can be inferred from the precision matrix of generalized nonparanormal data.
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 learns Gaussian mixtures from censored data.
problem Learning Gaussian mixtures with incomplete data.
method Proposes an algorithm to estimate weights and means with minimal samples.
result Achieves accurate estimation with very few samples.
Develops intrinsic Gaussian process regression for manifold-valued data.
problem Lack of intrinsic Gaussian process methods for manifold-valued response variables.
method Proposes an intrinsic covariance structure and a novel intrinsic Gaussian process regression model.
result Establishes asymptotic properties and shows posterior consistency.
Paper generalizes Gaussian universality and CGMT to dependent data, impacting data augmentation in high-dimensional logistic regression.
problem Limitation of Gaussian universality and CGMT in handling dependent data.
method Generalizes Gaussian universality and CGMT to dependent data (block dependence, m-dependence, mixing). Establishes a novel CGMT framework.
result Gaussian universality holds for high-dimensional logistic regression under various types of dependence.
The variational autoencoder (VAE) is a generative model with continuous latent variables where a pair of probabilistic encoder (bottom-up) and decoder (top-down) is jointly learned by stochastic gradient variational Bayes. We first elaborate Gaussian VAE, approximating the local covariance matrix of the decoder as an o…
This study tackles Gaussian process regression with summarized data.
problem Learning and inference with summarized data (summary statistics, counts) in spatial modeling.
method Sample quasi-likelihood approach to Gaussian process regression.
result Approximation performance of the method is influenced by data granularity and covariance function length scale.
GAGA accelerates 3D molecular generation by replacing long trajectories with Gaussian approximations.
problem High computational cost of long generative trajectories in 3D molecular generation.
method GAGA identifies a characteristic step where molecular data becomes sufficiently Gaussian, replacing the trajectory with a Gaussian approximation.
result Significant improvement in both generation quality and computational efficiency.
New method improves Gaussian kernel approximations for high-frequency data.
problem Limited scalability of kernel-based models to large data sets.
method Local random feature approximations using Maclaurin expansions and polynomial sketches.
result Significant improvement in kernel approximations and downstream performance for high-frequency data.
New method estimates Gaussian copulas with missing data using EM algorithm.
problem Estimating Gaussian copulas with missing data and prior assumptions.
method Rigorous application of the Expectation Maximization (EM) algorithm for marginal distributions and dependence structure.
result Joint distribution learned is closer to the underlying distribution.
Diffusion models generate data with Gaussian Universality, matching linear model test errors.
problem Analyzing the performance of models trained on synthetic data generated by diffusion models.
method Investigates Gaussian Universality for data distributions generated via diffusion models, matching test errors of linear models trained on synthetic data to Gaussian Mixture models.
result The test error of a linear model trained on diffusion-generated data matches the test error of a linear model trained on Gaussian Mixture data with matching means and covariances per class.
Combines boosting and latent Gaussian models for better predictions.
problem Boosting's assumptions and latent Gaussian models' limitations.
method Integrates tree-boosting and latent Gaussian models.
result Increased prediction accuracy in simulations and real-world data.
Proposes diffusion models using mixed Gaussian priors for better data representation.
problem Improving data representation in diffusion models.
method Structured diffusion models with a mixture of Gaussians as prior.
result Improved model performance compared to classical diffusion models.
Survey of Gaussian process constraints for modeling expensive data.
problem Modeling expensive data with physical constraints.
method Overview of various Gaussian process constraints and their implementation.
result Discussion of computational challenges introduced by constraints.
New algorithm converts data into sub-gaussian designs efficiently.
problem Efficiently converting large datasets into sub-gaussian random designs for robust performance.
method Algorithmic Gaussianization through sketching and averaging, using LESS embeddings.
result Efficient data sketches nearly indistinguishable from sub-gaussian designs.
The study uncovers the breakdown of Gaussian universality in high-dimensional empirical risk minimization.
problem Understanding the breakdown of Gaussian universality in high-dimensional empirical risk minimization.
method Extending the Convex Gaussian Min-Max Theorem to non-Gaussian settings, deriving asymptotic min-max characterizations, and proving asymptotic equivalence of regularizers.
result The projection of the ERM estimator onto a test covariate approximately follows a Gaussian convolution under certain conditions.
Study shows perceptrons with random labels perform similarly to Gaussian data.
problem The assumption of Gaussian input data is often seen as a limitation in machine learning.
method Analyzed generalized linear classification (perceptron model) with random labels.
result Minimum training loss is independent of data covariance for high-dimensional input data.
GP-ND avoids obstacles in trajectory planning using Gaussian Process regression.
problem Avoiding obstacles in trajectory planning for real-world systems.
method GP-ND models negative data pairs using Gaussian distributions and maximizes their KL divergence from the GP to avoid them.
result GP-ND outperforms traditional GP learning in obstacle-aware trajectory planning.
Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model identifiability. Linear non-Gaussian component analysis (LNGCA) generalizes the ICA model t…
A new Gaussian process regression method infers implicit manifold structure from data.
problem Scaling Gaussian process regression to high-dimensional data.
method Proposes a fully differentiable Gaussian process regression technique that infers implicit manifold structure from data.
result Improves predictive performance and calibration of standard Gaussian process regression in high-dimensional settings.
Fast approximate inference for non-Gaussian data.
problem Efficient inference for non-Gaussian data.
method Laplace Matching for fast approximate inference in latent Gaussian models.
result Achieves high approximation quality with low computational cost.
The paper finds non-Gaussian directions in high-dimensional data using Wasserstein distance.
problem Locating interesting non-Gaussian features in high-dimensional data.
method Projection pursuit using 2-Wasserstein distance to maximize the difference from Gaussian.
result Statistical guarantees for accurately approximating an unknown low-dimensional non-Gaussian subspace.
A scalable Gaussian process clustering method for large datasets.
problem Infeasibility of Gaussian process clustering on large grids.
method Embedding Vecchia approximation in EM algorithm for scalability.
result Efficient Gaussian process clustering for large environmental applications.
Paper extends multi-task Gaussian Cox processes for heterogeneous tasks.
problem Modeling multiple heterogeneous correlated tasks jointly.
method Data augmentation and mean-field approximation for non-conjugate Bayesian inference.
result Demonstrates improved performance and inference on synthetic and real data.
Proposes GPLFR for predicting high-dimensional outputs with few data.
problem Predicting high-dimensional outputs from limited data.
method GPLFR combines Gaussian process and linear-Gaussian decoding for high-dimensional prediction.
result GPLFR outperforms existing methods in predicting high-dimensional outputs.
Develops a new method to discover stochastic systems with non-Gaussian noise.
problem Discovering governing laws from complex systems with non-Gaussian noise.
method Theoretical framework and numerical algorithm to extract stochastic differential equations with Gaussian and non-Gaussian noise.
result Demonstrated the efficacy and accuracy of the approach on various systems.
Unified bounds for iterative algorithms with Gaussian data matrices.
problem Establishing non-asymptotic bounds for iterative algorithms with Gaussian data.
method Explicit coupling between iterates and Gaussian process with deterministic covariance.
result Tight, dimension-free bounds for generalized first-order methods.
This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to operate in "big data" regimes where one is interested in quantifying the uncertaint…
Dividing local Gaussian processes improve real-time prediction efficiency.
problem Efficient online prediction for large data sets.
method Iterative data-driven division of input space for sublinear computational complexity.
result Sublinear computational complexity in real-time prediction.
Vecchia approximations provide the best accuracy-runtime trade-off for Gaussian process approximations.
problem High computational cost of Gaussian processes for large data sets.
method Systematic comparison of different Gaussian process approximations.
result Vecchia approximations consistently provide the best accuracy-runtime trade-off.
Method extracts governing laws from non-Gaussian stochastic systems data.
problem Modeling complex dynamics with non-Gaussian Lévy noise.
method Data-driven method to extract stochastic dynamical systems from noisy data.
result Established a theoretical framework and numerical algorithm to compute Lévy jump measure, drift, and diffusion.
This work explores variably scaled kernels to improve non-stationary Gaussian processes.
problem Limited ability of stationary kernels to represent heterogeneous correlation structures.
method Introduces variably scaled kernels to modify correlation structures explicitly.
result Improved reconstruction accuracy and better uncertainty estimates for non-stationary data.
New method splits unknown covariance Gaussians into independent parts.
problem Splitting multivariate Gaussian data with unknown covariance.
method Developed a general algorithm for decomposing unknown covariance Gaussians.
result Demonstrated decomposition for single multivariate Gaussian with unknown covariance.
Simplified DGPs training by fixing inducing inputs to subset of data.
problem Challenging training of deep Gaussian processes.
method Fixed subset of data for inducing inputs, variational sampling.
result Significant reduction in trainable parameters and computation cost without performance degradation.
We introduce a wrapped Gaussian for SPD matrices, enhancing data analysis.
problem Handling circular and non-flat data distributions on SPD manifolds.
method Introduced a non-isotropic wrapped Gaussian using the exponential map, derived theoretical properties, and proposed a maximum likelihood framework.
result Demonstrated the robustness and flexibility of the wrapped Gaussian model on synthetic and real-world datasets.
The study examines the universality of Gaussian data in high-dimensional generalized linear estimation.
problem Understanding when Gaussian data suffices for high-dimensional generalized linear estimation.
method Sharp asymptotic expressions for test and training errors in high-dimensional Gaussian mixture data with labels from a single-index model.
result The universality of Gaussian data in error estimation depends on the alignment between target weights and mixture cluster means and covariances.
Dynamic Boltzmann Machine (DyBM) has been shown highly efficient to predict time-series data. Gaussian DyBM is a DyBM that assumes the predicted data is generated by a Gaussian distribution whose first-order moment (mean) dynamically changes over time but its second-order moment (variance) is fixed. However, in many fi…
New EM algorithm for mixtures of elliptical distributions handles missing data and outliers.
problem Missing data imputation for noisy and non-Gaussian data.
method Investigation of a new EM algorithm for mixtures of elliptical distributions.
result The proposed algorithm is robust to outliers and competitive with other methods.
Inter-domain Deep Gaussian Processes improve inference for non-stationary data.
problem Inference limitations in Gaussian processes for non-stationary data.
method Combines inter-domain and deep Gaussian processes for scalable approximate inference.
result Outperforms inter-domain shallow GPs and conventional DGPs on non-stationary data.
This paper proposes a method to approximate non-Gaussian likelihoods in Gaussian Processes.
problem Approximating non-Gaussian likelihoods in Gaussian Processes.
method Proposes a piece-wise constant approximation for the inverse-link function.
result Yields a closed form solution for the SVGP lower bound.
The paper examines how kernel approximations affect Gaussian process regression in large data applications.
problem Effect of kernel approximations on Gaussian process regression in large data applications.
method Unified framework to analyze Gaussian process regression under computational and epistemic misspecification.
result Theoretical analysis of Gaussian process regression under various misspecifications.