New change surfaces for multidimensional changes and counterfactuals.
problem Limited expressiveness of standard changepoint models in multidimensional settings.
method Model-agnostic formalization of change surfaces, using Gaussian Process Change Surfaces (GPCS).
result Discovery of complex, heterogeneous changes in measles incidence and lead testing kit requests.
We present a scalable Gaussian process model for identifying and characterizing smooth multidimensional changepoints, and automatically learning changes in expressive covariance structure. We use Random Kitchen Sink features to flexibly define a change surface in combination with expressive spectral mixture kernels to …
Study on compact Kähler surfaces for sign-changing curvatures.
problem Prescribing sign-changing Chern scalar curvatures on compact Kähler surfaces.
method Established a Chen-Li type existence theorem and provided an alternative proof.
result Alternative proof of Ding-Liu's theorem on sign-changing Gaussian curvatures.
New algorithm detects changes in Gaussian Process covariance structures.
problem Detecting abrupt changes in Gaussian Process covariance structures.
method Statistical hypothesis tests and Bayesian Online Change Point Detection (BOCPD) with improved thresholds.
result CBOCPD finds multiple structural breaks in GPs even with imprecise hyperparameters.
Study on bounded Gaussian curvature in mixed type surfaces of Lorentzian manifolds.
problem Characterizing the behavior of Gaussian curvature at non-degenerate lightlike points of mixed type surfaces.
method Introducing invariants and using Gauss-Bonnet type formula results.
result Gauss-Bonnet type formula for mixed type surfaces with bounded Gaussian curvature.
Warped Gaussian process model for non-stationary time series forecasting.
problem Non-stationary time series with gradually varying volatility, change points, or both.
method Non-parametric warping of input distances with Gaussian process, gradient optimization for training.
result State-of-the-art forecasting performance at lower implementation and computation cost.
EVARS-GPR refines Gaussian Process Regression for seasonal data with sudden scale changes.
problem Challenges in forecasting with changing system behavior over time.
method Combines online change point detection with data augmentation for refitting.
result 20.8% lower RMSE on real-world datasets compared to similar methods.
Gaussian process improves nowcasting of COVID-19 deaths.
problem Correcting for delays in reporting daily deaths.
method Flexible Gaussian process model with latent variables.
result Gaussian process nowcasts outperform other methods.
New method detects changes without partitioning distributions.
problem Detects changes in unknown probability distributions without partitioning.
method Aggregates e-processes over possible changepoints and infimum over candidate no-change distributions.
result Achieves first-order asymptotically optimal detection delay.
In this paper we classify complete surfaces of constant mean curvature whose Gaussian curvature does not change sign in a simply connected homogeneous manifold with a 4-dimensional isometry group.
New model uses heteroscedastic Gaussian process for alkenone SST proxy.
problem Restoring historical sea surface temperatures using proxies.
method Heteroscedastic Gaussian process regression method.
result Nonparametric approach handles variable noise patterns and outliers.
A new model captures car-following and lane-changing behaviors in traffic.
problem Modeling stochastic microscopic traffic behaviors.
method Physics regularized Gaussian process (PRGP) approach.
result The proposed model outperforms previous methods in estimation precision.
The paper finds surfaces closest to being flat that span a given contour.
problem Finding surfaces in R3 that are as flat as possible while spanning a given contour. method The approach involves minimizing the total Gaussian curvature squared and solving a system of PDEs.
result The optimal surface is shown to be controlled by a biharmonic equation with specific boundary conditions.
We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation crucially depends on a set of points, called knots, at which the original proces…
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.
Single linear solve combines surface reconstruction and uncertainty quantification.
problem Reconstructing surfaces from partial point clouds with uncertainty.
method Geometric Gaussian processes for stochastic surface reconstruction.
result Single linear solve for surface reconstruction with probabilistic capabilities.
Consider an orientable compact surface in three dimensional Euclidean space with minimum total absolute curvature. If the Gaussian curvature changes sign to finite order and satisfies a nondegeneracy condition along closed asymptotic curves, we show that any other isometric surface differs by at most a Euclidean motion…
e-GGPs learn graph vertex transitions over time.
problem Static graph Gaussian Processes cannot handle dynamic graph structures.
method Proposes e-GGPs with a transition function and neighbourhood kernel.
result e-GGPs outperform static GGPs on time-series regression.
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function parameters are usually learned using maximum likelihood, which can lead to overfitt…
Study uses SABR model to create implied volatilities from sparse quotes.
problem Creating accurate implied volatility surfaces from limited market data.
method Multitask Gaussian process with SABR model embeddings and hierarchical regularization.
result Model produces more accurate volatilities than single-task methods.
Gaussian process regression loses locality in high dimensions, affecting molecular energy surface fitting.
problem Loss of locality in high-dimensional Gaussian process regression.
method Analysis of Matern family kernels and multi-zeta basis functions.
result The property of locality disappears in high dimensions, impacting regression quality.
We investigate the Student-t process as an alternative to the Gaussian process as a nonparametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the covariance kernel of a G…
New kernels on symmetric groups enable efficient Gaussian process sampling.
problem Efficiently modeling and sampling on symmetric groups.
method Introduced power sum kernels and methods for efficient calculation and sampling.
result Polynomial computational complexity for sampling Gaussian processes.
Enhances DGP surrogates for efficient active learning.
problem Efficiently learning from expensive simulations with abrupt changes.
method Novel elliptical slice sampling for uncertainty quantification and active learning.
result Smaller training sets lead to effective and computationally tractable models.
Finite-width neural networks are approximated by Gaussian processes with finite size corrections.
problem Understanding the behavior of finite-width neural networks as they approach infinite width.
method Analyzing the distribution of outputs at initialization for large, finite neural networks with a single hidden layer.
result The distribution of outputs at initialization is well described by a Gaussian perturbed by the fourth Hermite polynomial, with the perturbation scale inversely proportional to the number of network units.
Extends Gaussian process regression for non-Gaussian data.
problem Inadequate modeling of uncertainty and over-smoothing in non-Gaussian datasets.
method Time-changed Gaussian processes with Lévy processes.
result Improved modeling of heavy-tailed non-Gaussian behaviors.
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.
We propose a multiresolution Gaussian process to capture long-range, non-Markovian dependencies while allowing for abrupt changes. The multiresolution GP hierarchically couples a collection of smooth GPs, each defined over an element of a random nested partition. Long-range dependencies are captured by the top-level GP…
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 framework interprets machine learning models using Gaussian processes.
problem Interpreting complex machine learning models.
method Gaussian process metamodeling to capture response surfaces.
result Maximizing likelihood function for variable importance.
Personalized model improves ADAS-Cog13 cognitive score forecasting.
problem Improving accuracy in predicting cognitive changes in Alzheimer's Disease.
method Meta-Weighted Gaussian Process Experts (pGPE) model for personalized forecasting.
result Meta-weighting of expert models leads to significant improvements in forecasting accuracy.
This work improves adaptive sampling for multi-fidelity Gaussian processes by considering cost and uncertainty.
problem Adaptive sampling for multi-fidelity Gaussian processes is computationally demanding and complex.
method The authors extend the design of experiment framework by partitioning prediction uncertainty based on fidelity level and cost, and utilize the Believer concept.
result The proposed framework effectively reduces predictive uncertainty in multi-fidelity Gaussian processes.
Proposes a new method to extend Gaussian processes for non-Gaussian data.
problem Non-Gaussian data in real-world scenarios.
method Layer-based approach to construct non-Gaussian stochastic processes.
result Unified approach to construct various non-Gaussian processes.
New bounds on AE success probability in GP models.
problem Limiting the success of adversarial examples in probabilistic models.
method Investigated upper bounds on AE success probability using Gaussian Processes.
result Proved a new upper bound of AE success probability dependent on perturbation norm, kernel function, and training dataset distance.
A key drawback of the current generation of artificial decision-makers is that they do not adapt well to changes in unexpected situations. This paper addresses the situation in which an AI for aerial dog fighting, with tunable parameters that govern its behavior, will optimize behavior with respect to an objective func…
Optimizes parameter reconstruction for optical scatterometry using Gaussian process regression.
problem Efficiently reconstructing geometry parameters of micro/nanostructures from scatterometry measurements.
method Bayesian optimization with Gaussian-process regression to find optimal parameter values.
result Gaussian process regression accelerates the optimization process for numerical simulations.
Develops an algorithm to approximate non-Gaussian posterior distributions in Bayesian inference.
problem Sampling non-Gaussian posterior distributions in Bayesian inverse problems.
method Iterative construction of Gaussian Process (GP) augmented proposal distributions for MCMC sampling.
result Optimal selection of sampling points using maximum information gain from GP surface.
This work improves Gaussian process regression for large, non-stationary data.
problem Scalability issues and performance degradation for non-stationary data.
method Combines variational free energy approximations with online expectation propagation and local splitting steps.
result Incremental adaptation to locality, heterogeneity, and non-stationarity in training data.
Researchers solved a geometry paradox for creased tubes.
problem Resolving the paradox of Gaussian curvature in creased tubes.
method Calculated Gaussian curvature in terms of rate of change of solid angle, dependent on fold angle and curvature.
result Gaussian curvature is zero overall despite the surface being doubly-curved.
Framework for applying GPs to real-world data with scalability guidelines.
problem Deployment of Gaussian Processes (GPs) is hindered by computational costs and lack of guidelines.
method Proposed a framework for identifying GP suitability and setting up robust models, formalizing decisions of experienced practitioners.
result More accurate results at test time for glacier elevation change case study.
In machine learning (ML) security, attacks like evasion, model stealing or membership inference are generally studied in individually. Previous work has also shown a relationship between some attacks and decision function curvature of the targeted model. Consequently, we study an ML model allowing direct control over t…
Researchers use Gaussian Process Regression to improve accuracy of a low-cost hot-wire anemometer.
problem Improving accuracy of low-cost hot-wire anemometers in varying temperatures.
method Probabilistic calibration using Gaussian Process Regression.
result The method provides good performance in estimating actual wind speeds, including uncertainty.
A key requirement for the current generation of artificial decision-makers is that they should adapt well to changes in unexpected situations. This paper addresses the situation in which an AI for aerial dog fighting, with tunable parameters that govern its behavior, must optimize behavior with respect to an objective …
Motivated by a recent work of X. Chen and M. Zhu (Commun. Math. Stat., 1 (2013) 369-385), we establish a Trudinger-Moser inequality on compact Riemannian surface without boundary. The proof is based on blow-up analysis together with Carleson-Chang's result (Bull. Sci. Math. 110 (1986) 113-127). This inequality is diffe…
Local solubility of Bao--Ratiu equations proven for surfaces with specific curvature conditions.
problem Existence of asymptotic directions for volume-preserving diffeomorphisms on surfaces.
method Analysis of degenerate Monge--Ampère equation following Han's work.
result Asymptotic directions always exist locally about a point on surfaces with specific curvature conditions.
Novel Hilbert space Gaussian process improves sequential design accuracy and efficiency.
problem Efficiently implementing Gaussian process acquisition functions for expensive simulations.
method Proposed a truncated eigenbasis representation for closed-form evaluation of IMSE acquisition function.
result Significantly lower prediction error and reduced computation time compared to benchmarks.
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.
Model change points in time-series data with neural SDEs and variational autoencoders.
problem Modeling change points in time-series data with neural stochastic differential equations.
method Proposes a novel model formulation and training procedure based on the variational autoencoder framework, alternating between updating neural SDE parameters and change points.
result Demonstrates the expressive power of the proposed model in modeling both classical parametric SDEs and real datasets with distribution shifts.