This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process, the mixture model has the advantages of modeling multimodal data and alleviating…
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48 results for “multivariate Gaussian process”
Bayesian model learns complex multivariate dependencies.
problem Learning dependency structures across multiple dimensions.
method Flexible Gaussian process priors and Dirichlet process for structure learning.
result Efficient variational inference for model parameters.
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…
Modeling massive highly-multivariate nonstationary spatial data with the basis graphical lassostat.ME
New framework models complex spatial data with basis functions and graphical vectors.
problem Modeling highly-multivariate spatial processes with varying resolutions.
method Extends graphical lasso to multivariate Gaussian processes with independent graphical vectors at different resolutions, using an orthogonal basis and fusion penalty.
result Linear complexity and parsimonious conditional independence structure in multilevel graphical model.
This tutorial simplifies Gaussian process regression for beginners.
problem Understanding Gaussian process regression for machine learning.
method Explains basic concepts, provides a concise GPR description, and reviews implementation packages.
result Clear understanding of Gaussian process regression fundamentals.
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,…
Large deviation principles for multivariate stochastic volatility models.
problem Understanding the behavior of log-processes in multivariate stochastic volatility models.
method Establishing a comprehensive sample path large deviation principle for log-processes.
result Asymptotic formulas for first exit times and barrier option prices derived from the LDP.
Elliptical slice samplingstat.CO
Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with multivariate Gaussian priors. Its key properties are: 1) it has simple, generic c…
Efficiently models multiple correlated point data using generalized LGCPs.
problem Joint modeling of multiple correlated point data.
method Generalized LGCP framework with Gaussian process priors and variational inference.
result Orders of magnitude faster inference compared to existing methods.
Gaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to re-formulate the matrix-variate Gaussian distribution as a multivariate normal distribution. Although it is effective in many cases, re-formulation is not always workable a…
A scalable and regularized approach to minimize negative transfer in multivariate Gaussian processes.
problem Challenges in constructing multivariate Gaussian processes, especially with a large number of outputs.
method Regularized pairwise modeling approach using bivariate Gaussian processes.
result Minimizes negative transfer of knowledge between uncorrelated outputs in large multivariate models.
Proposes a new model for EHR data using time-dependent Gaussian processes.
problem Joint modeling of multiple clinical variables over time.
method Multivariate nonstationary Gaussian processes with time-varying parameters and posterior inference via HMC.
result The proposed model outperforms stationary models and reveals latent correlations predictive of patient risk.
Framework predicts events from longitudinal and time-to-event data using MGCP and Cox model.
problem Predicting events from mixed longitudinal and time-to-event data.
method Uses multivariate Gaussian convolution process (MGCP) and Cox model for joint modeling. Implements variational inference to estimate parameters.
result Framework outperforms state-of-the-art approaches in synthetic and real-world data.
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…
We tackle the problem of multi-task learning with copula process. Multivariable prediction in spatial and spatial-temporal processes such as natural resource estimation and pollution monitoring have been typically addressed using techniques based on Gaussian processes and co-Kriging. While the Gaussian prior assumption…
Study improves tourism demand forecasting using a Gaussian process regression model.
problem Improving accuracy of regional tourism demand forecasts.
method Extension of Gaussian process regression model for multi-input multi-output forecasting.
result Gaussian process regression model outperforms neural network in multivariate forecasting.
Model for inferring multivariate functions from areal data.
problem Inferring multivariate functions from areal data with varying granularities.
method Probabilistic model using Gaussian processes with spatial aggregation.
result Model effectively estimates spatial correlations and dependencies between areal data sets.
New method for estimating functional Gaussian graphical models for multivariate data.
problem Challenges in extending Gaussian graphical models to multivariate functional data due to compact covariance operators.
method Introducing partial separability for multivariate functional data, leading to a novel Karhunen-Loève expansion and efficient estimation through the joint graphical lasso.
result A well-defined functional Gaussian graphical model that can be identified with a sequence of finite-dimensional graphical models, each of identical fixed dimension.
We derive Gaussian approximations for random forest predictions using region-based stabilization.
problem Improving the accuracy of random forest predictions for Poisson process data.
method Region-based stabilization and Malliavin-Stein method for multivariate Gaussian approximation.
result Established Gaussian approximation bounds for random forest predictions under Poisson process.
Develops a new MCMC-based Wishart prior for Gaussian Process covariance matrix.
problem Difficult inference for multivariate Gaussian Processes with multiple lengthscale parameters.
method Introduces a self-assembled Wishart prior and uses MCMC for Bayesian inference on kernel hyperparameters.
result Demonstrates the effectiveness of the new prior in GP-based learning with empirical results.
Multivariate categorical data occur in many applications of machine learning. One of the main difficulties with these vectors of categorical variables is sparsity. The number of possible observations grows exponentially with vector length, but dataset diversity might be poor in comparison. Recent models have gained sig…
Paper examines Gaussian process perspective of CNNs.
problem Understanding when and why CNNs perform well.
method Casts CNNs in a Gaussian process framework.
result Gains insights into CNN performance and assumptions.
Enhances Gaussian process models for handling variable error variances and multiple responses.
problem Limited ability of Gaussian process models to capture abrupt changes and heteroscedastic errors.
method Introduces a novel heteroscedastic Gaussian process (HeGP) framework coupled with variational inference and EM algorithm.
result Effective modeling of multivariate responses with varying error variances.
Scalable Bayesian dynamic covariance modeling with variational Wishart and inverse Wishart processesstat.ML
The paper develops scalable Bayesian models for dynamic covariance matrices using Gaussian processes.
problem Modeling dynamic and heteroskedastic covariance matrices for multivariate time series.
method Gradient-based variational inference for Wishart and inverse Wishart processes, with modifications for scalability and factoring.
result The modified models can scale to high-dimensional covariance matrices and outperform multivariate GARCH in covariance forecasting.
This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding literature. The method can be performed in operations, where…
A new imputation model for clinical data captures both cross-sectional and temporal correlations.
problem Missing values in multivariable time series clinical data.
method Integrates Gaussian processes with mixture models and individualized mixing weights.
result The proposed model provides more accurate imputation than benchmarks on real-world and synthetic datasets.
Researchers disrupt Gaussian model inference to test adversarial attacks.
problem Disrupting conditional inference in multivariate Gaussian models under adversarial conditions.
method Considered white- and grey-box settings with complete and incomplete knowledge of the Gaussian distribution, respectively. Reduced to quadratic and stochastic quadratic programs. Derived structural properties for solution methods.
result Demonstrated the impact and efficacy of attacks in various applications, including real estate evaluation, interest rate estimation, and signals processing.
Study approximates multivariate risk measures for Gaussian risks.
problem Complex approximations of multivariate risk measures for Gaussian risks.
method Derived precise approximations of marginal mean excess, marginal expected shortfall, and multivariate conditional tail expectation.
result Similar results hold for elliptical and Gaussian-like multivariate risks.
Bayesian model selection improves multivariate causal discovery without restrictive assumptions.
problem Real-world causal discovery requires flexible assumptions to avoid restrictive model assumptions.
method Continuous relaxation of discrete model selection problem, using Causal Gaussian Process Conditional Density Estimator (CGP-CDE).
result Bayesian approach outperforms traditional methods in multivariate causal discovery.
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.
Proposes a deep generative model for robust forecasting on sparse multivariate time series.
problem Forecasting on sparse multivariate time series with suboptimal results when sparsity is high.
method Dynamic Gaussian Mixture distribution for modeling latent clusters, using neural networks and gating mechanism.
result Demonstrates robust modeling of sparse multivariate time series with improved accuracy.
New spectral mixture kernels improve MOGP cross-covariance interpretation.
problem Limited parametric interpretation of cross-covariances in MOGPs.
method Complex-valued cross-spectral densities, Cramér's Theorem, phase shifts, delays.
result Improved expressive and interpretable multivariate covariance functions.
Quanto Option Pricing on a Multivariate Levy Process Model with a Generative Artificial Intelligenceq-fin.MF
Study uses AI to price exotic options with a new Levy process model.
problem Pricing exotic options with a non-Gaussian Levy process model.
method Introduced a new multivariate Levy process model and used a generative AI model to estimate the probability density function.
result Developed a method to price quanto options using a trained generative AI model.
Copulas allow to learn marginal distributions separately from the multivariate dependence structure (copula) that links them together into a density function. Vine factorizations ease the learning of high-dimensional copulas by constructing a hierarchy of conditional bivariate copulas. However, to simplify inference, i…
New kernel handles irregularly-spaced multivariate time series.
problem No kernel exists for irregularly-spaced multivariate time series.
method Built a series kernel from vector kernels, ensuring it's PSD.
result Validated the series kernel on multiple datasets and time series classification.
Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by extending some standard probabilistic modelling tools to the circular domain. First w…
Proposes a method to forecast dependencies between thousands of time series.
problem Computational and numerical difficulties in estimating high-dimensional covariance matrices.
method Combines RNN and Gaussian copula process with low-rank covariance structure.
result Significant accuracy improvements over state-of-the-art baselines.
Proposes a method to decompose multivariate signals into Gaussian components.
problem Decomposing multivariate signals into Gaussian components.
method Greedy variational method for non-negative multivariate signals as a weighted sum of Gaussians.
result Upper bound for the distance from any mode of a Gaussian mixture model to the set of corresponding means.
Chained Gaussian Processesstat.ML
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…
Bayesian inference with finitely wide neural networkscond-mat.dis-nn
Bayesian inference for wide neural networks using Edgeworth expansion.
problem Analyzing the non-Gaussian behavior of wide neural networks in Bayesian inference.
method Proposed a non-Gaussian distribution using multivariate Edgeworth expansion for finite-width neural networks.
result Derived non-Gaussian posterior distribution in Bayesian regression tasks.
Efficient modeling of sub-kilometer surface wind with Gaussian processes and neural networksphysics.ao-ph
Paper uses Gaussian processes and neural nets to model sub-km wind accurately.
problem Accurately modeling sub-kilometer surface wind for optimal decision-making.
method Integrates Gaussian processes and neural networks to model wind gusts at sub-kilometer resolution.
result Modeling covariance structure improves prediction quality and calibration.
Paper speeds up Gaussian process inference using Matérn kernels.
problem Efficiently performing Gaussian process inference for large datasets.
method Exact Matérn kernel decomposition into empirical cumulative distribution functions, combined with divide-and-conquer approach.
result The proposed algorithm significantly speeds up Gaussian process inference for low-dimensional problems with hundreds of thousands of data points.
Bayesian learning from variable-length sequences using Gaussian processes with signature covariances.
problem Learning from sequences of varying lengths and complex sequential structures.
method Gaussian processes with signature kernels, sparse variational approach, combining with LSTM/GRU models.
result Effective learning from sequences of different lengths and complex structures.
Study invariant connections on multivariate Gaussian distributions.
problem Understanding statistical connections on multivariate Gaussian distributions.
method Investigate invariant connections on with the Fisher metric.
result Explicitly determined invariant connections and their moduli spaces.
In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If such time-varying smoothness is not accounted for, one can obtain misleading inf…
A new model detects anomalies in time series data efficiently.
problem Detect anomalies in high-dimensional time series data.
method r-ssGPFA, an unsupervised online anomaly detection model using state space Gaussian processes.
result The model detects anomalies efficiently and is computationally cheaper.
Unified Skew-Gaussian process framework for various regression and classification tasks.
problem Handling multiple types of regression and classification problems.
method Generalization of Skew-Gaussian processes to handle various types of data and likelihoods.
result Closed-form posterior distributions for multiple tasks.
VIPs use IPs for efficient inference in flexible models.
problem Efficient inference in flexible models like Bayesian neural networks and Gaussian processes.
method Variational Implicit Processes (VIPs) using generalised wake-sleep updates.
result VIPs provide better uncertainty estimates and lower errors compared to existing methods.