Robust spatio-temporal GP framework for outlier-resilient predictions.
problem Outliers in spatio-temporal data degrade GP performance.
method Adapted and specialised RCGP framework for spatio-temporal settings.
result RCGP provides reliable spatio-temporal predictions with outliers.
Paper introduces a new framework for spatio-temporal structured sparse regression.
problem Reconstructing spatio-temporal evolving patterns with high accuracy.
method Hierarchical Gaussian process with expectation propagation for online and offline Bayesian inference.
result 15% improvement in F-measure compared to existing methods.
Efficient spatio-temporal Gaussian process inference method.
problem Scalable Gaussian process inference for multivariate, spatio-temporal data.
method Combines spatio-temporal filtering with natural gradient variational inference, resulting in a scalable non-conjugate GP method.
result Linear scaling with respect to time and logarithmic scaling with respect to time steps.
STACI uses neural nets to estimate spatio-temporal fields with valid uncertainty quantification.
problem Scalable spatio-temporal deep learning models fail to capture underlying correlation structure.
method Variational Bayesian neural network approximation of non-stationary spatio-temporal Gaussian Process (GP) with conformal inference.
result STACI provides accurate prediction intervals for spatio-temporal processes, outperforming competing methods.
Gaussian processes model protein and mRNA dynamics in systems biology.
problem Quantitative modeling of post-transcriptional regulation in systems biology.
method Gaussian process as a prior distribution, hybrid Monte Carlo methods for inference.
result Reconstructed spatio-temporal fields of protein and mRNA expression without solving PDEs.
Modeling disease progression in brain images using monotonic Gaussian Processes.
problem Disentangling spatio-temporal disease trajectories from brain imaging data.
method Spatio-temporal matrix factorization with anatomically plausible priors, monotonic Gaussian Processes, and sparse codes.
result Monotonic Gaussian Processes model realistic disease trajectories in brain imaging data.
Improved Gaussian process inference for spatio-temporal data.
problem Cubic computational costs in Gaussian process inference, especially in spatio-temporal settings.
method Proposes the Vanilla-SPDE Exchange, leveraging an equivalence between standard and SPDE formulations to achieve improved computational cost.
result Demonstrates improved computational efficiency through complexity analysis and numerical experiments.
New graph kernels capture spatio-temporal interactions.
problem Lack of justified spatio-temporal graph kernels for graph problems.
method Derive graph kernels via SPDEs for spatio-temporal modelling.
result Non-separable spatio-temporal graph kernels outperform existing ones.
Efficiently reconstructs spatio-temporal Gaussian processes using Kalman filtering.
problem Non-parametric reconstruction of spatio-temporal Gaussian processes from sparse and noisy data.
method Coupling GP regression and Kalman filtering for a finite-dimensional state-space representation.
result Kalman filter state at instant tk represents a sufficient statistic for estimating the process at any t≥tk. Bayesian model for sparse regression with spatial-temporal structure.
problem Sparse linear regression with spatio-temporal constraints.
method Hierarchical Gaussian process prior and Expectation Propagation algorithm.
result Model successfully applied to real data.
Develops a new model for spatio-temporal data using imitation learning.
problem Capturing complex spatio-temporal dependence in discrete event data.
method NEST point process model with imitation learning for efficient model fitting.
result The imitation learning approach leads to more robust and interpretable results.
Model improves mortgage credit risk prediction with spatio-temporal machine learning.
problem Improving accuracy of default probabilities and loan portfolio loss distributions in mortgage credit risk.
method Combines tree-boosting with a latent spatio-temporal Gaussian process model.
result Predictive models outperform conventional methods due to non-linear and spatio-temporal effects.
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.
DeepKriging uses neural networks for spatio-temporal interpolation and forecasting.
problem Non-Gaussianity and nonstationarity in real-world data.
method Two-stage model: DNN for interpolation, LSTM for forecasting.
result DeepKriging provides probabilistic forecasts without stationarity assumptions.
Study sharp convergence rates of empirical UOT for spatio-temporal point processes.
problem Statistical analysis of UOT for spatio-temporal point processes.
method Empirical plug-in estimators for Kantorovich-Rubinstein distance between intensity measures.
result Sharp convergence rates of empirical UOT in terms of intrinsic dimensions of measures.
FNOs improve spatio-temporal forecasting without needing PDE details.
problem Complex spatio-temporal dynamics in physical and biological phenomena.
method Fourier Neural Operators (FNOs) for dynamic spatio-temporal modeling.
result FNO forecasts are accurate and capture complex real-world dependencies.
Deep ESN models forecast spatio-temporal data with uncertainty quantification.
problem Complex nonlinear dynamics in spatio-temporal systems are hard to model.
method Deep ensemble ESN models using bootstrap and hierarchical Bayesian frameworks.
result Models produce forecasts and uncertainty measures for spatio-temporal data.
Paper presents a spatio-temporal Bayesian model for early detection of COVID-19 hotspots.
problem Understanding spatio-temporal dynamics of COVID-19 hotspots to prevent outbreaks.
method Spatio-temporal Bayesian framework with a zero-mean Gaussian process and non-stationary kernel function enhanced by deep neural networks.
result Model demonstrates superior hotspot-detection performance compared to baseline methods.
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.
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.
Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling generally required and the analytically intractable likelihood function. Here, we expl…
Generative model for high-dimensional categorical data using Gaussian-Dirichlet fields.
problem Efficiently modeling and predicting high-dimensional categorical data.
method Combines Dirichlet and Gaussian processes for spatio-temporal modeling.
result Model accurately approximates categorical data in unobserved locations.
Gaussian processes improve system identification models.
problem Improving system identification models for non-linear dynamics.
method Using Gaussian processes to create time series prediction models.
result Gaussian processes enhance model accuracy in system identification.
Deep models improve spatial and spatio-temporal data analysis.
problem Improving analysis of spatial and spatio-temporal data.
method Hybrid models combining statistical and deep learning approaches.
result Deep models enhance traditional statistical methods for complex data.
Combines pseudo-point and state space approximations for scalable GPs.
problem Handling large numbers of off-the-grid spatial data-points and long time-series.
method Combines pseudo-point approximations for spatial data with state space GP approximations for temporal data.
result Combined approach is more scalable and applicable to a greater range of spatio-temporal problems.
Proposes a transformer model with geostatistical inductive bias for spatio-temporal forecasting.
problem Combining probabilistic rigor of geostatistics with flexible deep learning representations.
method Spatially-informed transformer with learnable covariance kernel.
result Successfully recovers spatial decay parameters end-to-end via backpropagation.
New method uses MMAF-guided learning for spatio-temporal probabilistic forecasts.
problem Probabilistic forecasting of spatio-temporal data with causal structure.
method Generalized Bayesian methodology, MMAF-guided learning, ensemble of stochastic feed-forward neural networks.
result Forecast performance comparable to, and sometimes better than, deep learning architectures.
Combines neural networks and Gaussian processes for better uncertainty estimation and generalization.
problem Improving output uncertainty estimation and generalization in deep learning.
method Combines neural networks and Gaussian processes with a scalable stochastic inference procedure.
result Achieves better uncertainty estimation and generalization performance than neural networks and Gaussian processes.
Bayesian model tackles spatio-temporal underdetermined problems.
problem Solving underdetermined linear inverse problems with spatial and temporal sparsity constraints.
method Generalized spike-and-slab prior with transformed Gaussian process, expectation propagation algorithm, and approximations for scalability.
result Demonstrated effectiveness on synthetic and real data sets.
Nonlocal Bayesian modeling for continuous spatio-temporal dynamics
problem Handling irregular time points, sparse observations, and nonlocal interactions in spatio-temporal forecasting
method Hierarchical Bayesian framework with coordinate-based spatial basis expansion and continuous-time ODE
result Strong forecasting and uncertainty calibration
New method uses neural networks to forecast spatial-temporal data.
problem Probabilistic forecasting of spatio-temporal data with causal structure.
method MMAF-guided learning with ensemble of stochastic feed-forward neural networks.
result Forecasting remains calibrated across multiple time horizons.
Proposes a new model for complex multivariate event data.
problem Modeling complex multivariate event data with spatio-temporal dynamics.
method Integrates spatial information into latent state evolution through learned temporal and spatial decay dynamics.
result Successfully recovers sensible temporal and spatial intensity structure in multivariate spatio-temporal point patterns.
LISAL learns nonstationary spatio-temporal models efficiently.
problem Learning nonstationary spatio-temporal models in dynamic environments.
method LISAL uses Gaussian processes to model nonstationary dynamics and latent space changes.
result LISAL reduces computational cost by adaptively sampling latent space dynamics.
Scalable model detects multidimensional changes in data.
problem Detecting and characterizing smooth multidimensional changepoints.
method Random Kitchen Sink features and spectral mixture kernels for flexible and expressive modeling, with additive non-separable kernels for scalability.
result Model identifies previously unknown heterogeneous changes in space and time.
Unified framework for efficient Gaussian process inference.
problem Efficient inference in non-conjugate Gaussian process models.
method Combines expectation propagation with linearization for improved efficiency.
result Unified view of various inference schemes, including classical smoothers and EP.
Model predicts terror attacks' likelihood and casualties.
problem Predicting terror attacks' likelihood and casualties.
method Self-exciting marked spatio-temporal model with Gaussian Process prior.
result Model accurately predicts future attacks with various covariates.
Study on linear regression with dependent covariates, proving universality and error characterization.
problem Linear regression with dependent covariates in high-dimensional settings.
method Analysis of ridge regression performance, Gaussian universality theorem, spectral properties of covariance matrices.
result Asymptotic performance of ridge regression is invariant under non-Gaussian covariates with preserved mean and covariance.
Efficient method for video segmentation using spatio-temporal graph inference.
problem Efficient video segmentation with deep learning.
method VideoGCRF method that couples neuron decisions across space and time, using deep Gaussian Conditional Random Fields.
result Efficient and end-to-end trainable inference on spatio-temporal graphs for video segmentation.
Modeling solar ramping events with spatio-temporal point processes.
problem Predicting solar ramping events influenced by weather conditions.
method Novel spatio-temporal categorical point process model.
result Effective modeling of spatio-temporal correlations in solar ramping events.
Sparse Markovian Gaussian processes improve probabilistic model inference for large datasets.
problem Efficient inference for large-scale time series data.
method Combining inducing variables with Kalman filter-like recursions for linear scaling.
result General site-based approach for approximating non-Gaussian likelihoods.
ESN enhances forecasting for nonlinear spatio-temporal data.
problem Forecasting nonlinear spatio-temporal processes efficiently.
method Enhanced ESN machine learning approach.
result Reasonable uncertainty quantification for long-lead forecasts.
Estimates spatio-temporal Hawkes processes using tensor recovery.
problem Estimating influence functions for spatio-temporal Hawkes processes.
method Formulates influence function as a tensor kernel, assumes low-rank structure, solves as convex optimization problem.
result Provides theoretical guarantees and demonstrates efficiency with simulations.
Novel framework for spatio-temporal event analysis using Hawkes processes.
problem Inference of dynamics in spatio-temporal event sequences.
method Randomized Fourier feature-based transformations and gradient descent.
result Improved fitting capability in synthetic and real datasets.
New algorithms predict spatio-temporal data without assuming its structure.
problem Predicting high-dimensional spatio-temporal data without assuming its structure.
method Light cone decompositions and three simple algorithms for predictive state reconstruction.
result Good predictive performance and distributions over spatio-temporal data.
Study evaluates DGMs' ability to recover non-stationary Gaussian fields.
problem Assessing DGMs' learning of non-stationary Gaussian random fields.
method Comprehensive evaluation of four DGMs (FM, DDPM, score-SDE, VAE) on a known non-stationary Gaussian random field.
result DDPM and score-SDE recover covariance structure reasonably well, while FM and VAE struggle.
Deep models struggle with non-stationary Gaussian fields, but DDPM and score-SDE perform best.
problem Evaluating deep generative models on non-stationary Gaussian random fields.
method Comprehensive evaluation of four DGMs (FM, DDPM, score-SDE, VAE) on a known non-stationary Gaussian random field.
result DDPM and score-SDE recover the covariance structure reasonably well, while FM and VAE have difficulties.
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…
Bayesian framework extracts features from high-dimensional spatio-temporal data.
problem Sparse structure and spatio-temporal dependence in high-dimensional data.
method Develops a Bayesian feature-extraction framework using Gaussian and Diffused-gamma priors, employing Bregman divergence likelihood and MCMC for posterior computation.
result Improves recovery of sparse features and enhances interpretability in the presence of spatio-temporal dependence.