Efficient GP framework for scalable non-stationary processes.
problem Heavy memory and computational requirements in Gaussian process regression for large data sets.
method Exploits structure in the kernel matrix, uses multiple sets of non-equidistant inducing points, and employs Toeplitz and Kronecker structure for efficient inference.
result Demonstrated scalability on numerical examples and large biomedical datasets.
Improved GP models for fast training and good performance.
problem Training scalable Gaussian process models efficiently.
method Cross-validation and nearest neighbor truncation for scalable GP training.
result Our method offers fast training and excellent predictive performance.
Paper analyzes GPS data to identify POIs and user similarities.
problem Analyzing GPS data for meaningful places and user profiles.
method Data mining algorithms applied to raw GPS data.
result Steps to identify POIs and user similarities are satisfactory.
The paper reviews trajectory data applications for road transportation agencies.
problem Lack of understanding of trajectory data value for transportation agencies.
method Literature review and case study in Maryland.
result Illustrates applications of trajectory data in six areas of road transportation.
SHMM models human mobility from GPS and text data, overcoming text sparsity.
problem Modeling human mobility from semantic trace data, especially addressing text sparsity.
method SHMM is a multi-modal spherical hidden Markov model that jointly models location, time, and text embeddings on a unit sphere using vMF distribution.
result SHMM outperforms state-of-the-art models in next location prediction and has lower training cost.
Case vs control comparisons have been the classical approach to the study of neurological diseases. However, most patients will not fall cleanly into either group. Instead, clinicians will typically find patients that cannot be classified as having clearly progressed into the disease state. For those subjects, very lit…
Symplectic GP regression models Hamiltonian systems for particle tracing.
problem Efficiently modeling long-term Hamiltonian flow maps for charged particles.
method Multi-output Gaussian process regression with symplectic matrix-valued covariance function.
result Symplectic methods outperform existing approaches in learning Hamiltonian functions.
Extends GP regression to complex Helmholtz problems, improving wavefield inference in brain elastography.
problem Infer complex Helmholtz wavefields from sparse, noisy data.
method Operator-informed Gaussian processes, realifying complex operator into real blocks, using PDE residuals and boundary traces.
result Competitive with finite-difference and neural-network methods, reconstructs brain shear curl field with high correlation.
Post-process Bayesian inference speeds up posterior approximation.
problem Leveraging pre-existing model evaluations for quick posterior approximation.
method Variational Sparse Bayesian Quadrature (VSBQ) using sparse Gaussian process (GP) surrogate model.
result VSBQ builds high-quality posterior approximations from existing optimization traces.
Study privacy-utility trade-off in IoT time-series data sharing with RL.
problem Privacy concerns in IoT time-series data sharing with temporal correlations.
method Reformulated as MDP, solved with asynchronous actor-critic deep RL.
result Validated solution on synthetic and real GPS datasets.
We describe a collection of computer scripts written in PARI/GP to compute, for reflection groups determined by finite-volume polyhedra in H3, the commensurability invariants known as the invariant trace field and invariant quaternion algebra. Our scripts also allow one to determine arithmeticity of such gr…
This paper tackles efficient testing strategies for COVID-19 by using a partially observable MDP approach.
problem Greedy testing strategies miss dormant virus areas, leading to inefficient use of testing resources.
method Develops efficient learning strategies based on policy iteration and look-ahead rules for a sequential learning-based resource allocation problem.
result Shows that the testing problem can be effectively managed using a partially observable MDP approach.
GP-PCA reduces infinite-dimensional GP posteriors to a finite space for meta-learning.
problem How to define a structure for a set of Gaussian process posteriors.
method Information geometric framework and variational inference.
result GP-PCA improves meta-learning performance through reduced GP posteriors.
GP-CATE calibrates CATE intervals in few-placebo trials with Gaussian processes.
problem Calibrating uncertainty intervals for CATE in small-arm trials.
method GP-CATE uses Gaussian processes to model each arm's outcome surface directly.
result GP-CATE achieves calibrated coverage where other methods fail.
Two algorithms improve GP bandits by selecting priors and minimizing regret.
problem Selecting appropriate GP priors for unknown functions.
method Developed two algorithms: Prior-Elimination GP-TS and HyperPrior GP-TS.
result Established sublinear regret bound for HyperPrior GP-TS.
We introduce a framework for analyzing transductive combination of Gaussian process (GP) experts, where independently trained GP experts are combined in a way that depends on test point location, in order to scale GPs to big data. The framework provides some theoretical justification for the generalized product of GP e…
Efficiently optimize GPs by reusing candidate solutions multiple times.
problem High computational cost of Gaussian process optimization due to unique historical points.
method Sticking to a candidate solution for multiple evaluation steps and limiting switches.
result Improved efficiency and practicality of Gaussian process optimization algorithms.
GP+ is a Python library for Gaussian process learning.
problem Probabilistic learning and inference for complex models.
method Integration of nonlinear manifold learning with Gaussian processes.
result GP+ enables probabilistic data fusion and inverse parameter estimation.
Adaptive Nyström method improves Gaussian Process Regression scalability.
problem Scalability issue in Gaussian Process Regression due to cubic complexity.
method Adaptive Nyström approach that greedily selects landmarks to minimize kernel approximation error.
result Significantly outperforms random landmark selection in accuracy and stability.
HIP-GP improves GP inference for inter-domain observations with millions of inducing points.
problem Inference for Gaussian Processes across different domains.
method Hierarchical inducing point Gaussian process with grid structure and stationary kernel assumption.
result Improved approximation accuracy through increased number of inducing points.
Central to robot exploration and mapping is the task of persistent localization in environmental fields characterized by spatially correlated measurements. This paper presents a Gaussian process localization (GP-Localize) algorithm that, in contrast to existing works, can exploit the spatially correlated field measurem…
This paper improves GP for learning complex data distributions.
problem Vanilla Gaussian processes struggle with complex data distributions.
method Introduces scalable GP paradigms with latent variables and variational inference.
result Scalable modulated GPs, especially latent GPs, learn diverse data distributions better.
Efficiently trains GPs with billions of inducing inputs using Tensor Train decomposition.
problem Training GPs with large numbers of inducing inputs.
method Tensor Train decomposition for variational parameters in stochastic variational inference.
result Achieves state-of-the-art results on several benchmarks.
Develops SGP-VAE for efficient sparse GP inference in multi-dimensional datasets.
problem Sparse GP approximations and missing data in multi-dimensional spatio-temporal datasets.
method Leverages partial inference networks for sparse GP approximations and amortized variational inference.
result Outperforms multi-output GPs and structured VAEs in various experiments.
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.
Efficient sparse GP model improves audio source separation.
problem Sparse Gaussian Process (GP) inference is computationally expensive for long audio frames.
method Used GP regression, spectral mixture kernels, and variational sparse GPs.
result Proposed method outperforms LD-PSDTF, KL-NMF, and IS-NMF.
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…
The paper defines conditions for Gaussian process sample path regularity.
problem Lack of understanding of Gaussian process sample path regularity.
method Analyzes covariance kernels to determine sample path regularity.
result Necessary and sufficient conditions for Hölder regularity are provided.
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.
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size. This paper presents two parallel GP regression methods that exploit low-rank co…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size. This paper presents two parallel GP regression methods that exploit low-rank co…
GP-DRF model handles variable-sized input and learns deep features.
problem Scaling deep Gaussian processes for variable-sized data.
method GP-DRF model combining GPs and DRF layers for efficient inference.
result GP-DRF outperforms standard GP and DRF models across various datasets.
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.
GP-KAN uses Gaussian Processes in KANs for robust, parameter-efficient non-linear modeling.
problem Non-linear modeling with limited parameters and uncertainty estimates.
method Integrates Gaussian Processes into Kolmogorov Arnold Networks (KANs) for robust non-linear modeling.
result GP-KAN achieves 98.5% accuracy on MNIST with 80k parameters compared to 1.5M for state-of-the-art models.
This is a continuation of our previous work arXiv:1601.05617 on trace and inverse trace of Steklov eigenvalues. More new inequalities for the trace and inverse trace of Steklov eigenvalues are obtained.
Deep neural networks are shown to be equivalent to Gaussian processes in the limit of infinite width.
problem Bayesian inference for deep neural networks.
method Deriving the equivalence between deep neural networks and Gaussian processes, developing a computationally efficient pipeline for covariance function computation.
result Bayesian inference for deep neural networks can be performed using Gaussian processes, improving accuracy and uncertainty estimation.
This paper analyzes regret bounds for Gaussian process Thompson sampling.
problem Analyzing the performance of Gaussian process Thompson sampling (GP-TS) in Bayesian optimization.
method The paper derives several regret bounds for GP-TS, including a lower bound, upper bounds on the second moment of cumulative regret, expected lenient regret, and improved cumulative regret.
result The paper provides improved regret upper bounds for GP-TS, showing that it suffers from a polynomial dependence on 1/δ with probability δ. GP-SUM filters complex non-Gaussian states using Gaussian Processes.
problem Stochastic dynamic filtering and state propagation with complex beliefs.
method GP-SUM combines sampling and probabilistic Bayes filters, using Gaussian Processes for dynamic and observation models.
result GP-SUM outperforms other filters on benchmarks and predicts non-Gaussian states accurately.
GP-ALPS automatically selects latent processes for multi-output GPs.
problem Manual selection of latent processes in multi-output GPs is time-consuming and prone to biases.
method Developed a variational inference scheme to automatically choose latent processes.
result Demonstrated suitability of GP-ALPS in preliminary experiments.
We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point a…
In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then governed by another GP. A single layer model is equivalent to a standard GP or the GP …
GP-CNAS uses genetic programming to automatically design CNN architectures.
problem Designing optimal CNN architectures is laborious and error-prone.
method GP-CNAS uses a tree-based representation of CNNs and dynamic crossover operators to search for optimal architectures.
result GP-CNAS finds optimal CNN architectures with balanced depth and width in limited trials.
IE-GP framework learns sequentially arriving data with adaptive kernels.
problem Sequential data adaptation in Gaussian process models.
method Incremental ensemble of Gaussian process learners with adaptive weights.
result IE-GP framework effectively learns and adapts to sequential data.
Smooths GPS data with splines for noisy, irregularly sampled data.
problem Noisy, irregularly sampled GPS data with non-Gaussian noise.
method Smoothing splines with chosen spline order and tension parameter, allowing for non-Gaussian noise and outliers.
result Effective smoothing and interpolation of GPS data.
Unified view of GP approximations improves efficiency.
problem Disparate variational features limit GP efficiency.
method View GP as a Banach space to unify feature selection.
result Unified understanding of existing and new features.
We consider the sequential Bayesian optimization problem with bandit feedback, adopting a formulation that allows for the reward function to vary with time. We model the reward function using a Gaussian process whose evolution obeys a simple Markov model. We introduce two natural extensions of the classical Gaussian pr…
Enforces physical constraints in GP regression models.
problem Unbounded GP models can produce infeasible values.
method Enforces nonnegativity constraints probabilistically.
result Reduces model variance and enforces physical bounds.
Two methods improve Gaussian process predictive distributions' calibration.
problem Improving the reliability of Gaussian process predictive intervals.
method Introduces two methods: cps-gp and bcr-gp, both adapting conformal predictive systems to GP interpolation.
result Both methods provide finite-sample marginal calibration and smooth predictive distributions.