CNNs predict spatial fields from sparse data.
problem Predicting complete spatial fields from limited observations.
method Convolutional Neural Networks (CNNs) trained on a single partially observed field.
result CNNs can flexibly capture local spatial patterns without explicit covariance modeling.
Hybrid framework merges data and domain knowledge for better spatial interpolation.
problem Spatial interpolation overlooks domain knowledge and limits to spatial coordinates.
method Integrates data-driven features with rule-assisted spatial dependency function mapping.
result Superior performance in two application scenarios, capturing localized features.
FFRK automatically extracts features for spatial interpolation without external variables.
problem Spatial interpolation challenges, especially nonstationarity and lack of explanatory variables.
method Feature-Free Regression Kriging (FFRK) method that extracts geospatial features.
result FFRK outperforms classical methods in predicting heavy metal concentrations.
Geometrically interpolates rigid body motions with initial and terminal twists.
problem Finding spatial trajectories between prescribed initial and terminal poses.
method Derives solutions for k-IV-TIP and k-BV-TIP for k=1,...,4.
result Automatic cubic interpolation identical to minimum acceleration curve when twists are zero.
Managing and hedging the risks associated with Variable Annuity (VA) products require intraday valuation of key risk metrics for these products. The complex structure of VA products and computational complexity of their accurate evaluation have compelled insurance companies to adopt Monte Carlo (MC) simulations to valu…
Proposes bivariate DeepKriging for efficient wind field prediction.
problem Challenges in predicting large-scale bivariate wind fields with high spatial variability and heterogeneity.
method Spatially dependent deep neural network (DNN) with embedding layer using spatial radial basis functions.
result Outperforms traditional cokriging predictors and reduces computation time.
Study improves sugarcane plot prediction using data interpolation.
problem Predicting adventive plants in sugarcane plots with limited data.
method Interpolation techniques (Gaussian processes, kriging) for geo-referenced data augmentation.
result GP-COMB outperforms other methods with less additional data.
DCK improves air quality index prediction with probabilistic spatial models.
problem Non-Gaussian, complex spatial structure of air quality index.
method Deep classifier kriging (DCK) for non-Gaussian, nonlinear spatial prediction.
result DCK outperforms conventional methods in predictive accuracy and uncertainty quantification.
DDPMs can reproduce medical image context, showing interpolation between samples.
problem Understanding DDPMs' ability to learn spatial context in medical imaging.
method Used stochastic context models (SCMs) to produce training data and assess DDPMs' performance.
result DDPMs can generate contextually correct images, interpolating between samples.
A new machine learning method for spatial regression.
problem Spatial/temporal regression with scattered data and arbitrary dimensions.
method Modified Planar Rotator (MPRS) method, a non-parametric model with distance-dependent interactions.
result MPRS predictions are competitive with standard interpolation methods and superior in handling rough and non-Gaussian data.
GeoConformal predicts spatial uncertainty without relying on specific models.
problem Measuring uncertainty in spatial predictions to enhance model credibility.
method GeoConformal Prediction integrates geographical weighting into conformal prediction.
result GeoConformal achieves higher coverage rates in uncertainty assessment compared to Bootstrap methods.
New algorithm combines Geostatistics and Quantile Random Forests for non-stationary spatial modelling.
problem Non-stationary spatial modelling with multiple secondary variables.
method Combines Geostatistics and Quantile Random Forests to estimate conditional distributions and simulate spatial data.
result Consistent results similar to geostatistical and Quantile Random Forests, allowing for embedding simpler interpolation techniques.
The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs), introduced in [21], uses a uniform space grid. In this paper we utilize a tree-like spatial discretization that approximates the BSDE on the tree, so that no spatial interpolation procedure is necessary. In…
Variable Annuity (VA) products expose insurance companies to considerable risk because of the guarantees they provide to buyers of these products. Managing and hedging these risks requires insurers to find the value of key risk metrics for a large portfolio of VA products. In practice, many companies rely on nested Mon…
A-BLINK speeds up Gaussian process covariance estimation.
problem Slow covariance matrix inversion in Gaussian processes.
method Two pre-trained neural networks learn Kriging weights and spatial variance.
result Significant computational speedups and posterior inference.
Paper presents a method for geographic ratemaking using spatial embeddings.
problem Lack of historical loss data in areas with high exposures.
method Construct spatial features within a complex representation model and use them as inputs to a predictive model.
result Predictions have smaller bias and variance than other spatial interpolation models.
In this paper, we propose a nonlinear distance metric learning scheme based on the fusion of component linear metrics. Instead of merging displacements at each data point, our model calculates the velocities induced by the component transformations, via a geodesic interpolation on a Lie transfor- mation group. Such vel…
A new framework enhances IDW models for complex industrial datasets.
problem Low performance of IDW models in complex industrial datasets.
method Deep reinforcement learning network to enhance IDW models and learn hyperparameters.
result The proposed framework achieves differential spatial prediction and is more accurate than current IDW models.
PriorVAE uses VAEs to efficiently encode spatial priors for small-area estimation.
problem Efficiently encoding spatial priors for small-area estimation using Gaussian processes.
method Approximating Gaussian process priors with a variational autoencoder (VAE).
result Efficient spatial inference through a low-dimensional latent Gaussian space representation.
Infinite CNNs lose spatial correlations, but can be restored by correlated weights.
problem Infinite CNNs lose spatial correlations, which are crucial for their performance.
method Introduced correlated weights to restore spatial correlations in infinite CNNs.
result Optimal performance is achieved with a moderate level of weight correlation.
This work proposes a novel method for interpolating ROMs without solving FEM models.
problem Interpolating ROMs for unseen parameter values without solving FEM models.
method Non-intrusive Space-Time POD interpolation on compact Stiefel manifolds.
result Robust ROMs derived for unseen parameter values with strong correlations to high-fidelity simulations.
SXL embeds spatial autocorrelation into neural networks for better geographic data learning.
problem Difficulties in learning spatial effects for neural networks in geographic data.
method SXL uses auxiliary tasks and autoregressive embeddings to learn spatial autocorrelation.
result SXL improves neural network training in unsupervised and supervised learning tasks.
STARK improves denoising of low-depth spatial transcriptomics images.
problem Denoising spatial transcriptomics images at ultra-low sequencing depths.
method Adaptive regularization with kernel ridge regression and graph Laplacian.
result STARK optimizes denoising performance over competing methods.
This work ensures stability in POD basis interpolation for pMOR in hyperelasticity.
problem Stability of POD basis interpolation on Grassmann manifolds for pMOR in hyperelasticity.
method Stability conditions derived from Grassmannian Exponential map and principal angles.
result Explicit stability conditions for practical pMOR applications and non-monotonic error behavior.
Recently, air pollution is one of the most concerns for big cities. Predicting air quality for any regions and at any time is a critical requirement of urban citizens. However, air pollution prediction for the whole city is a challenging problem. The reason is, there are many spatiotemporal factors affecting air pollut…
An important problem in geostatistics is to build models of the subsurface of the Earth given physical measurements at sparse spatial locations. Typically, this is done using spatial interpolation methods or by reproducing patterns from a reference image. However, these algorithms fail to produce realistic patterns and…
A new model for point processes without intensity function trade-offs.
problem Inefficiency and trade-offs in existing point process models.
method Point Set Diffusion, a diffusion-based latent variable model.
result Achieves state-of-the-art performance in point process generation.
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.
Researchers develop a new spatial process model for non-Gaussian data.
problem Non-Gaussian spatial data with asymmetry and heavy-tailedness.
method Re-parameterized Unified Skew-Normal (SUN) distribution, GSUN process, neural Bayes inference with GATs.
result GSUN process captures non-Gaussian spatial data properties and outperforms conventional models.
Pattern ensembling fills in missing or inaccurate trajectory data.
problem Incompleteness, missing information, and inaccuracies in geolocation data.
method Probabilistically ensemble similar trajectory patterns from the vicinity.
result Reconstructs missing or unreliable trajectory segments effectively.
A framework uses deep learning for spatio-temporal data prediction.
problem Interpolation of continuous spatio-temporal fields on irregular points.
method Decomposes spatio-temporal processes into products of basis functions and spatial coefficients.
result Effectiveness in reconstructing coherent spatio-temporal fields.
This paper introduces a novel approach to texture synthesis based on generative adversarial networks (GAN) (Goodfellow et al., 2014). We extend the structure of the input noise distribution by constructing tensors with different types of dimensions. We call this technique Periodic Spatial GAN (PSGAN). The PSGAN has sev…
GAGA learns a warped metric for geometry-aware data generation and interpolation.
problem Challenges in generating data with meaningful geometry in high-dimensional datasets.
method Combines manifold learning with generative modeling to learn a warped Riemannian metric.
result GAGA improves trajectory inference by 30% in single-cell population-level data.
Spatial statisticians and quantitative investors use the same mathematical object: a Schur complement, damped by one parameter.
problem The Schur complement is used in both spatial modeling and portfolio allocation, but the parameters are different.
method The Schur complement is interpreted as reliability shrinkage of a conditional Gaussian.
result The Schur complement is the same in both applications.
New neural network captures spatial correlations in wind speed predictions.
problem Uncertainty quantification in neural network predictions for high-dimensional, correlated data.
method Training neural networks with multidimensional Gaussian loss, preserving spatial correlation and computational tractability.
result Demonstrated super-resolution of surface wind speed with explicit correlation modeling.
Efficiently maps indoor magnetic fields with SKI and D-SKI.
problem Computing large-scale magnetic field maps in indoor environments.
method Structured kernel interpolation (SKI) with derivatives (D-SKI) for Gaussian process regression.
result Achieves better accuracy and faster computation than state-of-the-art methods.
New method speeds up analysis of computer experiments.
problem Computational infeasibility of direct GP inference for large datasets.
method Adapted Vecchia's ordered conditional approximation to scaled input space.
result Significant performance improvement over existing methods.
Optimal transport learns Riemannian metrics for evolving probability measures.
problem Learning metrics for evolving probability measures on Riemannian manifolds.
method Neural parametrization of a metric tensor via optimal transport, alternating optimization scheme.
result Improved trajectory inference on scRNA and bird migration data.
In this paper, we study the problem of multi-band (frequency-variant) covariance interpolation with a particular emphasis towards massive MIMO applications. In a massive MIMO system, the communication between each BS with M≫1 antennas and each single-antenna user occurs through a collection of scatterers in the e…
Model infers functions for attributes using multi-aggregate datasets with knowledge transfer.
problem Modeling aggregate data with varying granularities and spatial supports.
method Multi-output Gaussian process (MoGP) with linear mixing of independent latent GPs, aggregation process, and prior distribution of mixing weights.
result Proposed model outperforms in refining coarse-grained aggregate data.
The hedonic approach based on a regression model has been widely adopted for the prediction of real estate property price and rent. In particular, a spatial regression technique called Kriging, a method of interpolation that was advanced in the field of spatial statistics, are known to enable high accuracy prediction i…
The aim of this chapter is to show how option prices in jump-diffusion models can be computed using meshless methods based on Radial Basis Function (RBF) interpolation. The RBF technique is demonstrated by solving the partial integro-differential equation (PIDE) in one-dimension for the American put and the European va…
Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the Stochastic Local Interaction (SLI) model, which employs a local representation to impr…
Paper presents voxel graph operators for vector data models.
problem Efficient conversion and analysis of geometric models.
method Topological voxelization, graph construction, differential operator derivation.
result Discrete differential and integral operators from voxel complexes.
This paper shows how forward rate interpolations are equivalent to discount factor interpolations in yield curve construction.
problem The challenge of choosing between different interpolation methods for yield curve construction.
method Demonstrates the equivalence between forward rate interpolations and discount factor interpolations.
result Some popular interpolation methods on forward rates are equivalent to classical interpolation methods on discount factors.
Maps of infectious disease---charting spatial variations in the force of infection, degree of endemicity, and the burden on human health---provide an essential evidence base to support planning towards global health targets. Contemporary disease mapping efforts have embraced statistical modelling approaches to properly…
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…
The paper proposes a method for generating uniform interpolations on data manifolds.
problem Generating high-quality interpolations between data samples on complex manifolds.
method Autoencoder network with interpolation network, regularized by a Riemannian metric.
result The method generates interpolations that remain within the manifold's distribution.