Enhances robustness of MOGP regression for multiple correlated outputs.
problem Model misspecification and outliers in MOGP regression.
method Extends RCGP framework to multi-output setting.
result Provable robust MOGP with joint correlation capture.
GNP models predictive correlations and outperforms NPs.
problem Training and understanding of Neural Processes.
method Proposed a new model, Gaussian Neural Process (GNP), which incorporates translation equivariance and provides universal approximation guarantees.
result Demonstrates encouraging performance and provides universal approximation guarantees.
tvGP-VAE models tensor-valued latent variables with Gaussian processes for better data structure representation.
problem Agnostic latent variables in VAEs ignore data structure correlations.
method Proposes tensor-variate Gaussian process prior for variational autoencoder.
result Explicitly modeling correlation structures improves model performance in reconstruction.
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.
A new method for Gaussian Processes handles mixed continuous and categorical inputs.
problem Modeling cross-correlations between continuous and categorical data.
method Low-Rank Correlation (LRC) method for Gaussian Processes with flexible rank approximation.
result LRC outperforms existing methods in estimating cross-correlations and predicting response surfaces.
Real-world measurement noise in applications like robotics is often correlated in time, but we typically assume i.i.d. Gaussian noise for filtering. We propose general Gaussian Processes as a non-parametric model for correlated measurement noise that is flexible enough to accurately reflect correlation in time, yet sim…
The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically d…
Exact and scalable algorithm for Gaussian process regression with Matérn correlations.
problem Efficient Gaussian process regression with Matérn correlations.
method Novel kernel packet theory and sparse representation of covariance matrix.
result Significantly superior to existing alternatives in computational time and predictive accuracy.
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.
A new method for faster prediction in distributed Gaussian processes.
problem Inefficient aggregation of distributed Gaussian processes with correlations.
method Proposes a novel approach for aggregated prediction in distributed GPs that incorporates correlations among experts.
result Results in more stable predictions in less time compared to state-of-the-art methods.
Study on MC dropout in wide neural networks and its convergence to Gaussian processes.
problem Understanding the behavior of Monte Carlo dropout in wide neural networks.
method Rigorously studied the limiting distribution of wide untrained NNs under dropout, proving convergence to Gaussian processes. Investigated correlations and non-Gaussian behavior in finite width NNs.
result Wide untrained neural networks under dropout converge to Gaussian processes for fixed sets of weights and biases.
We introduce Gaussian Process Topic Models (GPTMs), a new family of topic models which can leverage a kernel among documents while extracting correlated topics. GPTMs can be considered a systematic generalization of the Correlated Topic Models (CTMs) using ideas from Gaussian Process (GP) based embedding. Since GPTMs w…
We propose a family of multivariate Gaussian process models for correlated outputs, based on assuming that the likelihood function takes the generic form of the multivariate exponential family distribution (EFD). We denote this model as a multivariate generalized Gaussian process model, and derive Taylor and Laplace al…
A new method for sparse Gaussian process regression using correlated experts.
problem Sparse Gaussian process regression for large datasets with cubic computational complexity.
method Aggregating predictions from correlated experts to improve scalability and accuracy.
result Superior performance compared to state-of-the-art methods for synthetic and real-world datasets.
Proposes a Bayesian Autoencoder with sparse Gaussian process priors to capture data correlations.
problem Autoencoders' i.i.d. assumption of latent representations fails to capture data correlations.
method Imposes fully Bayesian sparse Gaussian Process priors on the latent space of a Bayesian Autoencoder and uses stochastic gradient Hamiltonian Monte Carlo for posterior estimation.
result Consistently outperforms alternatives relying on Variational Autoencoders on various tasks.
Proposes a flexible MGP model for dynamic, sparse correlations.
problem Handling dynamic and sparse correlations in multivariate data.
method Non-stationary MGP with dynamic spike-and-slab prior and EM algorithm.
result Captures dynamic and sparse correlations effectively.
We propose a correlated stochastic process of which the novel non-Gaussian probability mass function is constructed by exactly solving moment generating function. The calculation of cumulants and auto-correlation shows that the process is convergent and scale invariant in the large but finite number limit. We demonstra…
New kernel models multi-output Gaussian processes accurately.
problem Challenges in modelling cross-covariances for multiple-output Gaussian processes.
method Replaced Gaussian components with block components of finite bandwidth in spectral mixture kernel.
result First multi-output generalization of spectral mixture kernel that can approximate any stationary multi-output kernel to arbitrary precision.
Automates kernel discovery for longitudinal data analysis.
problem Handling irregularly sampled, sparse longitudinal data with multilevel correlation.
method Combines deep neural networks and non-parametric kernel methods to discover complex multilevel correlation structure.
result Significantly outperforms state-of-the-art methods on benchmark data sets.
Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, espe…
Batch Active Learning uses derivative information for Gaussian Process regression.
problem Efficiently selecting data batches in Gaussian Process regression models.
method Proposes using the predictive covariance matrix to select data batches, exploiting full correlation.
result Demonstrates the effectiveness of incorporating derivative information across diverse applications.
Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.
problem Modeling non-Gaussian time-series with stationary increments.
method Complex wavelet transform for scale variations, joint correlation matrix for scale dependencies, second wavelet transform for diagonalization, maximum entropy models conditioned by scattering spectra coefficients.
result Scattering spectra of self-similar processes are scale invariant, allowing statistical testing and generation of new time-series.
Study of deep linear neural networks with proportional width and depth.
problem Lack of descriptive power in Gaussian limit of deep linear neural networks.
method Proportional infinite-width infinite-depth limit for deep linear neural networks.
result Characterization of limiting distribution as a nontrivial mixture of Gaussians.
This paper evaluates heterogeneous information fusion using multi-task Gaussian processes in the context of geological resource modeling. Specifically, it empirically demonstrates that information integration across heterogeneous information sources leads to superior estimates of all the quantities being modeled, compa…
The paper develops a Gaussian process model for predicting chemical efficacy.
problem Statistical methodologies for analyzing chemical databases are limited.
method Conditional Gaussian process models with Tanimoto distance and a scaling parameter.
result Predictive performance improves when accounting for chemical space correlation.
Enhances multi-fidelity modeling with DGPs for different input domains.
problem Improving prediction accuracy with multi-fidelity models using different input domains.
method Extends Deep Gaussian Processes (DGPs) to handle different input domains for high and low-fidelity models.
result Demonstrates improved performance on real-world physical problems.
A new learning scheme improves model efficiency and performance.
problem Characterizing correlation between batch-level and global data distributions.
method Epoch-evolving Gaussian Process Guided Learning (GPGL) scheme with context labels and triangle consistency loss.
result Significantly outperforms existing models on mainstream datasets.
We propose multivariate nonstationary Gaussian processes for jointly modeling multiple clinical variables, where the key parameters, length-scales, standard deviations and the correlations between the observed output, are all time dependent. We perform posterior inference via Hamiltonian Monte Carlo (HMC). We also prov…
This paper introduces a multi-output Gaussian process for censored data.
problem Modeling bias in censored data using correlations between multiple outputs.
method Heteroscedastic multi-output Gaussian process with input-dependent noise and variational inference.
result The model better estimates the true process under complex censoring dynamics.
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.
We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates input dependent signal and noise correlations between multiple response variables,…
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated Lévy distribution. For both (i) and (ii), we find that due to the correlations in the variance,…
Similarity measure for Gaussian process predictive distributions.
problem Comparing predictive distributions of Gaussian processes for correlated functions.
method Developed a similarity metric to compare predictive distributions of Gaussian processes.
result Gaussian process predictive distributions can be compared and one is enough to model two correlated functions.
Unified model improves multi-task learning by accounting for temporal misalignment.
problem Poor predictive performance and uncertainty quantification due to temporal misalignment in multi-task learning.
method Uses Gaussian processes to model correlations and includes a monotonic warp of the input data to account for temporal misalignment.
result Improves predictive performance and uncertainty quantification in multi-task learning.
Improved Gaussian Process model for predicting trajectories without independence assumption errors.
problem Incorrect independence assumption in previous work on Gaussian Process uncertainty propagation.
method Proposed a novel piecewise linear approximation to correct the independence assumption in continuous models.
result Corrected the independence assumption in Gaussian Process models for predicting trajectories.
Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical copulas with the same unconditional correlation. Furthermore, for Gaussian and Stude…
New non-separable covariance kernels for spatiotemporal data derived from harmonic oscillator physics.
problem Capturing complex spatiotemporal dependencies in Gaussian processes.
method Hybrid spectral method based on the harmonic oscillator, deriving explicit covariance kernels.
result Explicit non-separable covariance kernels with space-time interactions.
Proposes GPCA module for channel attention in CNNs using Gaussian processes.
problem Improving performance in visual tasks through effective channel selection.
method Integrates Gaussian processes into channel attention mechanisms for probabilistic modeling of channel correlations.
result Demonstrates improved performance of GPCA module in end-to-end CNN training.
This paper simplifies MTGP derivations for Gaussian processes.
problem Understanding the derivations of Multi-task Gaussian Process formulations and their gradients.
method Friendly derivations of Multi-task Gaussian Process formulations and their gradients.
result Simplified derivations of Multi-task Gaussian Process formulations and gradients.
Projection pursuit model improves Gaussian process regression for high-dimensional data.
problem Scalability issues with traditional Gaussian process models in high dimensions.
method Additive Gaussian process regression with dimension expansion and gradient descent.
result The proposed method approximates more complex functions and outperforms traditional models.
Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only estimate states that are correlated with the observation. Therefore, sequential esti…
Empirical Bayes method improves Gaussian sequence model inference.
problem Estimating parameters in correlated Gaussian sequence models.
method Maximum Composite Marginal Likelihood (CML) estimator, leveraging geometric Brascamp-Lieb inequality.
result CML estimator converges at rate \( n_*^{-1/2} \) in weighted Hellinger distance.
We generalize the log Gaussian Cox process (LGCP) framework to model multiple correlated point data jointly. The observations are treated as realizations of multiple LGCPs, whose log intensities are given by linear combinations of latent functions drawn from Gaussian process priors. The combination coefficients are als…
Global inducing points improve Bayesian neural network performance.
problem Improving Bayesian neural network performance.
method Adapting correlated approximate posterior to all layers in a Bayesian neural network and deep Gaussian processes using learned global inducing points.
result State-of-the-art performance on CIFAR-10 (86.7%) without data augmentation or tempering.
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…
The paper presents a novel approach to multi-output regression using probabilistic circuits.
problem Capturing correlations between multiple output dimensions in large-scale regression problems.
method Employing a mixture of single-output Gaussian process experts encoded via a probabilistic circuit.
result The method can capture correlations between output dimensions and often outperforms other approaches.
Efficiently price VIX options using multilevel Monte Carlo in rough Bergomi model.
problem Pricing VIX options in a rough Bergomi model with high computational complexity.
method Combining rectangle discretization, Cholesky sampling, and multilevel Monte Carlo.
result Reduced computational complexity to O(ε−2log2(ε)) and asymptotically optimal O(ε−2). New GP kernel handles mixed-categorical data, improving model accuracy.
problem Improving Gaussian process models for mixed-categorical data.
method Extends continuous exponential kernels to handle mixed-categorical variables.
result The proposed GP model gives higher likelihood and smaller residual error.