Ens-CGP synthesizes ensemble-based inference with Gaussian processes.
problem Ensemble-based inference and Gaussian process modeling.
method Formulates Ens-CGP as a conditional Gaussian process for ensemble moments.
result Ens-CGP provides a unified probabilistic foundation for Kalman-type methods.
Study on Gaussian ensemble of matrix products with mixed moments computed.
problem Understanding the statistical properties of matrix products of Gaussian matrices.
method Analysis of a multi-Wishart ensemble and enumeration of non-crossing pairings.
result Mixed moments of the product matrix are computed and found to be weighted by Fuss-Catalan numbers at large N. This work preserves linear invariants in ensemble filters for non-Gaussian data assimilation.
problem Maintaining critical invariants like mass, stoichiometric balance, and charge in non-Gaussian data assimilation.
method Introducing a novel class of nonlinear ensemble filters using measure transport theory.
result Recovery of a constrained Kalman filter for Gaussian settings and combination with regularization techniques.
Ensembles dynamic models using random feature approximations.
problem Online scalable Bayesian learning with dynamic models and ensembling.
method Random feature approximations and dynamic models using random walks.
result Better performance with alternative basis expansions like Hilbert space Gaussian processes.
DGMEs use Gaussian mixtures to quantify uncertainty in deep learning.
problem Quantifying uncertainty in complex predictive densities.
method DGMEs use a Gaussian mixture model with an EM algorithm for parameter learning.
result DGMEs outperform state-of-the-art models in uncertainty quantification.
Extends spectral number variance convergence to random matrix ensembles for twisted Laplacians.
problem Spectral number variance convergence for twisted Laplacians and Dirac operators.
method Extends Rudnick's approach to Gaussian ensembles for twisted Laplacians and Dirac operators.
result Convergence to Gaussian ensembles for twisted Laplacians and Dirac operators.
GEnBP combines EnKF and GaBP for efficient high-dimensional inference.
problem Efficient inference in high-dimensional models.
method Gaussian Ensemble Belief Propagation algorithm combining EnKF and GaBP.
result GEnBP outperforms existing methods in accuracy and efficiency.
EnKF's update is shown to be similar to Matheron's method in Gaussian process regression.
problem Data assimilation in high-dimensional systems.
method Empirical Matheron update applied to EnKF.
result Ensemble Kalman Filter's update is equivalent to an empirical Matheron update.
Unified framework for ensemble transport-based smoothing of non-Gaussian time series.
problem Bayesian time series re-analysis with non-Gaussian distributions.
method Measure transport approach to derive consistent prior-to-posterior transformations.
result General ensemble framework for transport-based smoothing of state-space models.
A new method for uncertainty estimation in neural networks using Gaussian-softmax integration.
problem Quantifying uncertainty in neural network predictions.
method Proposes a single-model approach integrating Gaussian distribution with softmax outputs, using mean-field approximation.
result Competitive performance on uncertainty estimation tasks and outperforms many methods on out-of-distribution detection.
Decentralized Gaussian processes for multi-agent systems.
problem Scalable and flexible learning solutions for multi-agent systems.
method Asymptotically exact decentralized solution to Gaussian processes, with online Bayesian model averaging for hyperparameter selection.
result Asymptotically exact decentralized Gaussian process approximation and online Bayesian model averaging.
GPR ensemble method predicts stock returns efficiently.
problem Predicting stock returns using machine learning.
method Ensemble Gaussian Process Regression (GPR) for online learning.
result Method outperforms existing models in R-squared and Sharpe ratio. A new method detects outliers using ensembles of Dirichlet process mixtures.
problem Challenges in unsupervised outlier detection using Dirichlet process mixtures.
method Ensembles of Dirichlet process Gaussian mixtures with random subspace and subsampling.
result Empirically outperforms existing approaches in unsupervised outlier detection.
A new ensemble of Gaussian processes improves active learning efficiency.
problem Efficiently labeling data in high-cost domains like medical imaging.
method Adaptive weighted ensemble of Gaussian processes (EGP) for active learning.
result EGP-based approaches outperform single GP-based active learning methods.
Compact Gaussian model approximates deep ensemble predictions.
problem Efficiently approximating deep ensemble models for image prediction.
method Sparse-structured multivariate Gaussian with Cholesky parameterization trained to match pre-trained ensemble outputs.
result Compact representation captures uncertainty and structured correlations explicitly.
Real world systems typically feature a variety of different dependency types and topologies that complicate model selection for probabilistic graphical models. We introduce the ensemble-of-forests model, a generalization of the ensemble-of-trees model. Our model enables structure learning of Markov random fields (MRF) …
Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically with the number of observations. Several approaches based on inducing points were …
New nonlinear smoothers improve state estimation in chaotic systems.
problem Improving state estimation in chaotic dynamical systems with non-Gaussian behavior.
method Developed nonlinear backward ensemble transport smoothers with parameterization and regularization of transport maps.
result Nonlinear smoothers yield lower estimation error than conventional methods for comparable model evaluations.
This work evaluates uncertainty in deep Gaussian processes.
problem Uncertainty quantification in deep Gaussian processes.
method Hierarchical deep Gaussian processes (DGPs) and Deep Sigma Point Processes (DSPPs) evaluated on regression and classification tasks.
result DSPPs provide strong in-distribution calibration but are less robust under distribution shift compared to ensembles.
EnEMF uses Epanechnikov kernel for high-dimensional filtering, improving accuracy and robustness.
problem Suboptimal Gaussian mixture kernel density estimates in high-dimensional settings.
method Ensemble Epanechnikov mixture filter (EnEMF) using optimal Epanechnikov kernel.
result EnEMF reduces error per particle on high-dimensional systems like Lorenz '96.
Paper solves a key problem in learning from high-dimensional covariance matrices.
problem Computing normalizing factors for Riemannian Gaussian distributions on high-dimensional covariance matrices.
method Equivalence with random matrix theory and log-normal matrix ensembles to approximate normalizing factors.
result Efficient approximation of normalizing factors with decreasing error as dimension increases.
A new framework for recycling Gaussian process approximations.
problem Efficiently combining multiple Gaussian process approximations.
method Construct variational ensembles using a dictionary of fitted Gaussian processes.
result Framework allows for various tasks and scalability.
We examine a network of learners which address the same classification task but must learn from different data sets. The learners cannot share data but instead share their models. Models are shared only one time so as to preserve the network load. We introduce DELCO (standing for Decentralized Ensemble Learning with CO…
EGPR method forecasts power grid load and generation with high accuracy.
problem Accurate week-long forecasting of load demand and power generation for efficient power grid operation.
method Gaussian process regression with ensembles of preceding weeks' data.
result EGPR method outperforms traditional methods in forecasting weekly load and generation.
Study symmetry breaking in quantum mechanics to understand many-body physics.
problem Understanding many-body physics from quantum mechanics.
method Analyzing potentials with unstable critical points and local minima.
result Emergence of many-body physics from spontaneous symmetry breaking.
Enhanced ensemble filters use machine learning to improve accuracy in filtering models.
problem Accuracy limitations of traditional ensemble Kalman filters.
method Introduces a measure neural mapping (MNM) to map joint predicted state and observation to updated state estimates.
result Superior root-mean-square-error performance compared to leading methods in filtering models.
We prove that a Gaussian ensemble of smooth random sections of a real vector bundle over compact manifold canonically defines a metric on the bundle together with a connection compatible with it. Additionally, we prove a refined Gauss-Bonnet-Chern theorem stating that if the bundle and the manifold are oriented, then t…
The use of ensembles of neural networks (NNs) for the quantification of predictive uncertainty is widespread. However, the current justification is intuitive rather than analytical. This work proposes one minor modification to the normal ensembling methodology, which we prove allows the ensemble to perform Bayesian inf…
HD algorithm simulates dynamics on random matrix ensembles without generating full matrices.
problem Simulating dynamics on dense random matrix ensembles with high space and time complexity.
method Householder reflectors for adaptive and recursive construction, deferring decisions.
result Significant reductions in runtime and memory footprint for practical T≪n. Tree ensemble kernels improve Bayesian optimization for mixed features and constraints.
problem Optimizing over mixed-feature spaces with known constraints.
method Kernel interpretation of tree ensembles as Gaussian Process prior, compatible optimization formulation for acquisition function, integration of known constraints.
result Framework outperforms state-of-the-art methods for mixed-feature spaces and constraints.
The paper learns compact implicit surface maps from streaming data using an ensemble of sparse Gaussian processes.
problem Creating compact and accurate implicit surface maps from streaming range data.
method An ensemble of sparse Gaussian process experts, incrementally adjusted, trades-off between model complexity and prediction error.
result The approach learns compact and accurate implicit surface models comparable to or better than exact GP regression with subsampled data.
Study finds Calabi-Yau models' operator spectra match random matrix theory.
problem Understanding spectra of Calabi-Yau sigma models.
method Numerical methods for Ricci-flat metrics, averaging over complex structure moduli space.
result Spectrum matches Gaussian orthogonal ensemble of random matrix theory.
New samplers improve MCMC efficiency in high dimensions.
problem Efficient sampling in high-dimensional problems.
method Affine invariant ensemble samplers, including derivative-free and derivative-based HMC.
result Affine invariant ensemble HMC outperforms standard HMC in high dimensions.
Study develops ensemble machine learning framework for predicting groundwater heavy metal pollution.
problem Statistical complexity and spatial heterogeneity of heavy metal contamination in groundwater.
method Nested cross-validated ensemble machine learning with response transformations (raw, log, Gaussian copula).
result Copula-based models with DBSCAN clustering diagnostics provide the most reliable and interpretable assessments of groundwater contamination.
Bayesian deep ensembles improve prediction accuracy in various settings.
problem Improving prediction accuracy of deep ensembles in out-of-distribution settings.
method Introducing a randomised, untrainable function to each ensemble member, enabling a posterior predictive distribution interpretation.
result Bayesian deep ensembles make more conservative predictions and outperform standard ensembles in various tasks.
BI-EqNO improves Bayesian inference with flexible neural operators.
problem Inaccurate estimation of marginal likelihoods in approximate Bayesian methods.
method Equivariant neural operator framework for generalized approximate Bayesian inference.
result BI-EqNO enhances both deterministic and stochastic approaches to Bayesian inference.
Improved neural population modeling using shared features and ensemble detection.
problem Missing shared coding properties in neural latent variable models.
method Feature sharing across tuning curves and soft clustering of neurons.
result More interpretable and better-performing neural population models.
DVE uses GPs on DNN outputs to provide UQ without retraining.
problem Feature collapse in DNNs affects UQ methods.
method Deep Vecchia ensemble (DVE) of GPs on DNN hidden layers.
result Deterministic UQ possible in feature-collapsed DNNs.
We consider filtering in high-dimensional non-Gaussian state-space models with intractable transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in space and time. We propose a novel filtering methodology that harnesses transportation of measures, convex optimization, and ideas from proba…
A novel approach uses an ensemble of Gaussian processes for robust and adaptive reinforcement learning.
problem Adaptive reinforcement learning in large or continuous state spaces.
method Online scalable (OS) approach with a weighted ensemble of Gaussian processes.
result The ensemble approach improves performance in adversarial settings.
Ensemble of GANs improves performance on disconnected data.
problem Disconnected datasets in computer vision cannot be represented by continuous GANs.
method Construct an optimization problem to relate single GAN, ensemble of GANs, conditional GANs, and Gaussian Mixture GANs.
result Ensemble of GANs outperforms single GANs with fewer parameters.
Improving Bayesian filtering with strictly proper scoring rules
problem Bayesian filtering of partially and noisily observed dynamical systems
method Proper scoring ensemble filter (PSEF)
result Accurate approximation of challenging filtering distributions
We study dynamical behavior of the Chinese stock markets by investigating the statistical properties of daily ensemble returns and varieties defined respectively as the mean and the standard deviation of the ensemble daily price returns of a portfolio of stocks traded in China's stock markets on a given day. The distri…
Random matrix ensembles yield uniform distributions on manifolds.
problem Understanding distributions of vectors in random matrix ensembles.
method Analyzing eigenvalues, singular values, and Autonne-Takagi vectors of various random matrix ensembles.
result Uniform distributions on specific manifolds for different types of random matrix ensembles.
ATPF combines PF and EnKF for better inference in complex systems.
problem Weight degeneracy in PF and approximation errors in EnKF.
method Adversarial learning to improve posterior matching and incorporate kernel methods for optimization.
result ATPF provides theoretical guarantees and practical advantages over PF and EnKF.
Enhances optimization and sampling methods using ensemble-based gradient inference.
problem Improving ensemble-based methods for optimization and sampling.
method Ensemble-based gradient inference (EGI) to extract higher-order derivatives from particle ensembles.
result Augmented algorithms outperform gradient-free variants, especially in multimodal and non-Gaussian settings.
NN-GPR improves climate model predictions by preserving fine-scale spatial information.
problem Dilution of fine-scale spatial information and bias in model averaging.
method Gaussian process regression with an infinitely wide deep neural network.
result NN-GPR produces more accurate and detailed climate projections.
Proposes a new method for nonlinear Bayesian updates using ensemble kernel regression.
problem Nonlinear and non-Gaussian Bayesian updates for complex systems.
method Combines Kalman filtering for observed components and kernel density estimation for unobserved components, with subsampling and clustering.
result Reduces estimation errors in highly nonlinear scenarios compared to standard linear updates.