Surveying joint Gaussian graphical models to identify shared structures across domains.
problem Estimating shared structures across different data sources.
method Statistical inference of joint Gaussian graphical models.
result Improved estimation power for high-dimensional data.
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.
A novel extrapolation method is proposed for longitudinal forecasting. A hierarchical Gaussian process model is used to combine nonlinear population change and individual memory of the past to make prediction. The prediction error is minimized through the hierarchical design. The method is further extended to joint mod…
Adaptive Gaussian process approximates Bayesian inference for costly likelihoods.
problem Bayesian inference with computationally expensive likelihood functions.
method Gaussian process approximation with active learning design points.
result Competitive performance compared to existing methods for Bayesian computation.
Paper introduces non-linear process convolutions for multi-output Gaussian processes.
problem Building accurate covariance functions for multi-output Gaussian processes.
method Volterra series for non-linearity, closed-form expressions for mean and covariance.
result Non-linear model outperforms classical process convolution in synthetic and real datasets.
A new method combines Gaussian graphical models for better distributed Gaussian process predictions.
problem Poor results from traditional DGP due to violated conditional independence assumption.
method Proposes using Gaussian graphical models to aggregate local predictions from subsets of data.
result Our method outperforms other state-of-the-art DGP approaches on both synthetic and real datasets.
Flexible joint model predicts events from noisy multivariate data.
problem Predicting events from noisy multivariate time series data with missing values.
method Sparse multiple-output Gaussian processes for scalable joint modeling, optimal event prediction policy.
result Significantly outperforms state-of-the-art techniques in event prediction.
A novel method uses GPLFMs for joint input-state estimation in linear structural systems.
problem Combined state and input estimation of linear structural systems.
method Gaussian process latent force models (GPLFMs) combined with Kalman filters.
result GPLFMs outperform conventional Kalman filters in state and input estimation.
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.
Maximizing high-dimensional, non-convex functions through noisy observations is a notoriously hard problem, but one that arises in many applications. In this paper, we tackle this challenge by modeling the unknown function as a sample from a high-dimensional Gaussian process (GP) distribution. Assuming that the unknown…
Joint Gaussian Processes combine real and simulated data for better biophysical parameter retrieval.
problem Inverting radiative transfer models for accurate biophysical parameter estimation.
method Joint Gaussian Process (JGP) that combines real and simulated data for regression.
result JGP outperforms traditional methods in leaf area index retrieval from Landsat data.
Framework for imputing missing heart data to simulate brain-heart interactions.
problem Lack of multi-modal patient data representing heart and brain processes.
method Probabilistic framework for joint cardiac data imputation and mechanistic model personalization.
result Accurate imputation of missing cardiac features in incomplete datasets.
Novel approach for estimating joint probability densities using tensor decompositions and dictionaries.
problem Estimating joint probability densities of mixed discrete and continuous variables.
method Low-rank tensor decomposition combined with dictionary learning.
result Better classification and lower error rates compared to existing methods.
GPAR model uses Gaussian processes to efficiently model dependencies between multiple outputs.
problem Efficiently modeling dependencies between multiple outputs in a scalable manner.
method GPAR model decomposes the joint distribution over outputs using the product rule, each conditional modeled by a standard GP.
result GPAR outperforms existing GP models and achieves state-of-the-art performance on benchmarks.
Develops an online learning framework for Bayesian joint filtering.
problem Streaming inference of nonlinear state-space models.
method Variational inference and sequential Monte Carlo.
result Efficient approximation of filtering posterior for a wide class of models.
New GP-VAE model improves scalability and performance.
problem Inability of conventional VAEs to model correlations between data points.
method Principled sparse inference approaches to improve scalability of GP-VAEs.
result New model outperforms existing approaches in runtime and memory usage.
Deep Transformed Gaussian Processes extend TGPs with variational inference for scalable multi-layer modeling.
problem Flexible modeling of complex data distributions.
method DTGPs are a multi-layer model of TGPs using variational inference for scalability.
result DTGPs achieve good scalability and performance in multiple regression datasets.
This paper proposes a method to safely adjust exploration in RL to satisfy constraints.
problem Unsafe exploration in reinforcement learning violates constraints on controlled object states.
method Automatic adjustment of exploration inputs and variance-covariance matrix for safety.
result The method guarantees satisfaction of joint chance constraints with specified probability.
A new method uses Gaussian processes to efficiently model and compute counterparty credit valuation adjustments (CVA).
problem Efficiently modeling and computing CVA for large OTC derivative portfolios.
method Multi-Gaussian process regression approach to learn a metamodel for the mark-to-market cube of a derivative portfolio.
result The method accurately and efficiently computes CVA for interest rate swap portfolios.
Researchers derive an analytic expression for Gaussian stochastic volatility models.
problem Analyzing rich autocorrelation structures and persistence in financial markets.
method Two different analytic derivations of the joint characteristic function.
result First analytic formulae for option pricing in rough volatility models.
Wide deep neural networks with Gaussian weights approximate Gaussian processes closely.
problem Understanding the approximation of deep neural networks with Gaussian weights to Gaussian processes.
method Established novel rates for the Gaussian approximation of random deep neural networks with Gaussian parameters and Lipschitz activation functions in the wide limit.
result The distance between the network output and the Gaussian approximation scales inversely with the width of the network.
Bayesian method learns network structure from Gaussian process priors.
problem Computational infeasibility of Bayesian structure learning in GPNs.
method Monte Carlo and MCMC methods for sampling network structures.
result Method outperforms state-of-the-art algorithms in recovering network structure.
Real music signals are highly variable, yet they have strong statistical structure. Prior information about the underlying physical mechanisms by which sounds are generated and rules by which complex sound structure is constructed (notes, chords, a complete musical score), can be naturally unified using Bayesian modell…
Study entropic regularization of Gaussian measures and processes on Hilbert space.
problem Regularizing 2-Wasserstein distance for infinite-dimensional Gaussian measures and processes.
method Minimum Mutual Information property, closed form formulas, Fréchet differentiability, Sinkhorn barycenter equation.
result Entropic 2-Wasserstein distance and Sinkhorn divergence are Fréchet differentiable in Hilbert space.
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.
ARCNPs improve CNPs by autoregressively modeling dependencies.
problem CNPs struggle with modeling dependencies in predictions.
method Autoregressive deployment of factorized Gaussian CNPs.
result ARCNPs significantly outperform non-AR CNPs in various tasks.
Paper proposes no-regret algorithms for private GP bandit optimization.
problem Private Gaussian process bandit optimization.
method Combines uniform kernel approximator with random perturbations for differentially private GP bandit algorithms.
result Provable no-regret algorithms for stationary kernel functions in two DP settings.
Model infers utility from lion GPS data using Gaussian processes.
problem Understanding lion decision-making based on GPS data.
method Gaussian processes, vector calculus, Kullback-Leibler divergence.
result Identifies significant landmarks influencing lion trajectories.
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a novel construction of Gaussian process as a projection from fixed discrete frequen…
Develops a multi-resolution multi-task framework for integrating noisy, varying data.
problem Integrating evidence from multiple observation processes with varying resolutions and noise levels.
method Multi-resolution Multi-task Gaussian Processes (MRGP) framework, shallow and deep Gaussian Process mixtures.
result Generalizes and outperforms state-of-the-art GP compositions, offering efficient corrections and approximations.
A new model combines Gaussian processes with collaborative filtering for uncertainty-aware recommendations.
problem Uncertainty in recommendation systems.
method Combining Gaussian process multi-output models with collaborative filtering.
result Generates uncertainty estimates for predictions.
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gauss…
Paper presents a multi-task learning model for aggregated data using Gaussian processes.
problem Learning from aggregated data at different scales.
method Gaussian processes for joint learning of variables aggregated at different scales.
result Model can compute cross-covariance between tasks at different scales.
A novel kernel models latent variable couplings across multiple processes.
problem Modeling latent variable couplings across multiple processes.
method Mutually-dependent Hadamard kernel and latent correlation Gaussian process (LCGP) model.
result The LCGP model recovers latent signal correlations and achieves state-of-the-art performance.
Adaptive BO improves solder joint reliability by 3% with half the computational cost.
problem Improving solder joint reliability under thermomechanical loading.
method Adaptive Bayesian optimization with Gaussian process regression.
result Adaptive BO outperforms regular BO by 3% on average at any given computational budget.
This paper improves gradient matching for ODEs using Gaussian processes and mean-field approximations.
problem Learning parameters of ODEs with Gaussian processes and gradient matching.
method Mean-field variational inference for gradient matching with Gaussian processes.
result Established tight variational lower bounds that facilitate maximum a posteriori estimation of ODE parameters.
This paper analyzes deep Stable neural networks, showing convergence rates under different growth settings.
problem Analyzing the behavior of deep Stable neural networks as width increases.
method Large-width asymptotic analysis and convergence rates for fully connected feed-forward deep Stable NNs.
result The rescaled deep Stable NN converges weakly to a Stable SP under joint growth, with sup-norm convergence rates established.
Method simulates drawdown and duration in Lévy models using Gaussian approximation.
problem Simulating drawdown and duration in Lévy models with high jump activity.
method Stick-breaking Gaussian approximation for simulation, bounds on Wasserstein distances.
result Good agreement between theoretical bounds and numerical performance.
A new model fits SPX and VIX volatility surfaces and term structures efficiently.
problem Calibrating SPX and VIX volatility models to market data.
method Gaussian polynomial volatility models, joint calibration, functional quantization, Neural Networks.
result A conventional one-factor Markovian model outperforms rough and non-rough models.
A new model for Gaussian process experts tackles scalability and uncertainty issues.
problem Scalability and excessive number of experts degrade predictive performance and increase uncertainty.
method Nested partitioning scheme infers the number of components, a generalised GP framework accommodates multiple response types, and a factorised exponential family structure handles multiple input types.
result Effectiveness demonstrated on synthetic data and an Alzheimer's challenge dataset.
Gaussian BP algorithm converges exponentially under walk summability for cyclic graphs.
problem Convergence rate of Gaussian BP for cyclic graphs.
method Extending known results on walk summability, proving exponential convergence rate.
result Gaussian BP converges exponentially under walk summability for cyclic graphs.
Researchers use Gaussian processes with non-stationary kernels to model precipitation patterns in the Upper Indus Basin.
problem Uncertainty in precipitation patterns in the Upper Indus Basin, Himalayas.
method Proposes Gaussian processes with structured non-stationary kernels to model precipitation patterns, accounting for spatial variation with a latent Gaussian process.
result The proposed model adapts to varying precipitation patterns across distinct topography and outperforms stationary models in ablation experiments.
Efficiently models learning curves using Gaussian processes with latent Kronecker structure.
problem Joint modeling of machine learning model performance across hyper-parameters and training progress.
method Imposes latent Kronecker structure to leverage efficient product kernels and handle missing values.
result Matches the performance of a Transformer on a learning curve prediction task.
Paper establishes lower bounds for Gaussian process bandit optimization under various perturbation models.
problem Lower bounds for Gaussian process bandit optimization in noisy and robust settings.
method Novel proof techniques for standard and robust settings, including deterministic strategies.
result Demonstrates inevitable joint dependence of cumulative regret on corruption level and time horizon in robust settings.
This work extends stochastic localization to joint probability measures for data analysis.
problem Data distributional analysis in high-dimensional probability.
method Unified stochastic localization under Eldan's α-scheme, coupled probability measures via shared Brownian motion.
result Eldan's α-distance as a scalable surrogate for Wasserstein distance.
Paper uses PCE to quantify ML model and input uncertainties.
problem Accurately quantify and propagate combined uncertainties in ML predictions.
method Polynomial Chaos Expansion (PCE) for joint input and model uncertainty.
result Efficient and accurate calculation of output variability and sensitivity.
ConvGNP improves sensor placement for climate monitoring.
problem Maximizing informativeness of environmental sensor placements in remote regions.
method Convolutional Gaussian neural processes (ConvGNP) for non-stationary spatial predictions.
result ConvGNP outperforms traditional GP models in predicting sensor performance and reducing uncertainty.