Spatial smoothing improves BNNs' accuracy, uncertainty, and robustness without increasing computational cost.
problem Large ensembles in BNNs increase computational cost and reduce performance.
method Spatial smoothing adds blur layers to convolutional neural networks to ensemble neighboring feature map points.
result Spatial smoothing improves BNNs' performance with fewer ensembles and enhances robustness.
Defines concordance for spatial graphs and proves sliceness equivalence.
problem Understanding concordance and sliceness for spatial graphs.
method Smooth definitions and linking number conditions.
result Sliceness of a spatial graph is equivalent to a condition on linking numbers and a link.
New method provides valid confidence intervals for spatial associations.
problem Limited insight into covariate-response relationships in spatial settings.
method Lipschitz-driven uncertainty quantification for spatial association.
result Valid frequentist confidence intervals for associations in spatial settings.
This research optimizes Andrews plots for better visual clarity in high-dimensional data.
problem Visualizing high-dimensional datasets with clarity and aesthetics.
method Developed a method to add spectral smoothing to Andrews plots to reduce visual clutter.
result Optimal spatial-spectral smoothing leads to more aesthetically pleasing and clutter-free visualizations.
Proves some flat spacetimes can't be extended smoothly.
problem Proving smooth extension of certain FLRW spacetimes.
method Utilizing Sbierski's C0-inextendibility techniques. result Proves C0-inextendibility of spatially flat FLRW spacetimes. SpaCE tackles spatial confounding in scientific studies.
problem Spatial confounding influences treatment and outcome, leading to spurious associations.
method Introduces SpaCE toolkit for benchmark datasets and tools to evaluate causal inference methods.
result Facilitates automated evaluation of machine learning and causal inference models.
CutMix training technique improves spatial locality in Vision Transformers.
problem Improving spatial locality in Vision Transformers trained from scratch.
method Comparison of Baseline and Modern training protocols on CIFAR-10, CIFAR-100, and Tiny-ImageNet.
result CutMix training component significantly reduces Mean Attention Distance (MAD) in early layers of Vision Transformers.
Post-estimation smoothing improves prediction accuracy with structural indices.
problem Using natural structural indices in machine learning without losing robustness.
method A post-estimation smoothing operator that separates from the original predictor.
result Post-estimation smoothing improves accuracy over original predictors under simple conditions.
Adaptive smoothing in fMRI improves brain activity analysis.
problem Optimizing spatial smoothing in fMRI data processing pipelines.
method Integrating adaptive spatial smoothing as a neural network layer.
result Adaptive smoothing enhances brain activity analysis accuracy.
Spatial Adapter adds structured spatial representation to frozen predictors.
problem Efficiently adding spatial structure to pre-trained models.
method Structured spatial decomposition and closed-form covariance for residual fields.
result Adapter improves spatial prediction and uncertainty quantification.
A 3-stage method enhances hyperspectral image classification accuracy.
problem Classifying detailed classes in hyperspectral images with limited labeled data.
method Uses Nested Sliding Window and PCA for spatial consistency, SVM for spectral estimation, and TV model for spatial smoothing.
result Our method outperforms state-of-the-art algorithms, especially in scenarios with small training sets.
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.
Proposes a continuous scan statistic to detect anomalies more accurately.
problem Binary region definitions limit the detection of smooth anomalies.
method Kernel Spatial Scan Statistic (KSS) that allows continuous point contributions.
result Efficient computation and high statistical power for detecting anomalous regions.
Forest-guided smoothing uses random forest outputs for interpretable local smoothers.
problem Creating interpretable local smoothers from complex random forest outputs.
method Uses random forest outputs to define spatially adaptive bandwidth matrices for a linear smoother.
result Improves interpretability and applicability of random forest outputs for various analyses.
Proposes a deep neural network approach for image response regression.
problem Associations between medical images and covariates.
method Spatially varying coefficient models with deep neural networks.
result Explicitly accounts for spatial smoothness and subject heterogeneity.
Deep learning method for semiparametric regression of spatial data.
problem Estimating relationships between response and covariates in spatially dependent data.
method A sparsely connected deep neural network with ReLU activation function.
result The method is consistent and can handle large datasets.
Study proves unique foliation of spacetimes by constant mean curvature surfaces.
problem Proving unique foliation of open spacetimes by constant mean curvature surfaces.
method Spatially asymptotic to Robertson-Walker spacetime, proving existence and smoothness of mean curvature function.
result Existence and smoothness of unique foliation by constant mean curvature surfaces.
Smooth metrics satisfying Penrose inequality are necessarily smooth.
problem Rigidity of Penrose inequality with singular metrics.
method Showed suitable singular metrics attaining the optimal value in the Riemannian Penrose inequality are smooth in specified coordinates.
result Smooth metrics satisfying Penrose inequality are necessarily smooth.
In the framework of Lorentzian warped products, we study the Friedmann-Robertson-Walker cosmological model to investigate non-smooth curvatures associated with multiple discontinuities involved in the evolution of the universe. In particular we analyze non-smooth features of the spatially flat Friedmann-Robertson-Walke…
Proposes a deep neural network for spatial data regression.
problem Regression of spatial data using deep neural networks.
method Localized two-layer deep neural network for spatial data, proving consistency and asymptotic convergence.
result Asymptotic convergence rate is faster than existing methods, demonstrating effectiveness on temperature estimation.
Paper introduces an unsupervised tensor-based anomaly detection method for spatiotemporal data.
problem Challenges in detecting anomalies in spatiotemporal data, especially in urban traffic monitoring and medical imaging.
method Formulates anomaly detection as a regularized robust low-rank + sparse tensor decomposition, incorporating spatiotemporal smoothness and local dependencies.
result Demonstrates improved anomaly detection performance on both synthetic and real data.
Spatially transformed adversarial examples are perceptually realistic and harder to defend against.
problem Vulnerability of deep neural networks to adversarial examples.
method Spatial transformation of images to generate adversarial examples.
result Spatially transformed adversarial examples are more difficult to defend against existing methods.
Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, resp…
Model place cells as spatial embeddings for efficient path planning and cognitive map construction.
problem Encoding spatial navigation in the hippocampus.
method Model place cells using spectral decomposition of multi-step random walk transition kernels, inducing sparsity and adjacency.
result Place cells encode spatial information through non-negativity and inner-product structure, forming a cognitive map.
Predictive models can be used on high-dimensional brain images for diagnosis of a clinical condition. Spatial regularization through structured sparsity offers new perspectives in this context and reduces the risk of overfitting the model while providing interpretable neuroimaging signatures by forcing the solution to …
A new method aligns spatial and temporal data, improving on Dynamic Time Warping.
problem Comparing data over space and time, accounting for both spatial and temporal variability.
method Spatio-Temporal Alignments (STA) using regularized optimal transport (OT) and soft-DTW.
result Soft-DTW increases quadratically with time shifts, effectively handling spatio-temporal data.
Extended wMEM approach for MEG inverse problem using wavelet and spatial filters.
problem Infer brain activity from full space-time data in MEG.
method Wavelet decomposition, spatial filters, Kronecker product modeling, numerical optimization.
result Smooth numerical optimization problem solved with reasonable dimensionality.
VIND infers smooth nonlinear dynamics from electrophysiology data.
problem Analyzing smooth, nonlinear time series data from neuroscience experiments.
method Variational Inference for Nonlinear Dynamics (VIND) with structured approximate posterior and fixed-point iteration.
result VIND reconstructs 5D latent space variables similar to Hodgkin-Huxley models, and excels in predicting future neural activity.
Deep nets with massive data learn spatially sparse functions.
problem Understanding the importance of massive data in deep learning.
method Established a sampling theorem and proved optimal learning rates.
result Massive data is crucial for deep nets to learn spatially sparse functions.
Neural network optimizes MRI pipeline for better brain activity analysis.
problem Inaccurate parameter setting across MRI pipeline modules.
method Converted pipeline into a deep neural network, jointly optimising parameters.
result Adaptive spatial smoothing module improves brain decoding accuracy.
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.
New cosmological spacetimes without CMC Cauchy surfaces found.
problem Finding CMC Cauchy surfaces in cosmological spacetimes.
method Generalized Bartnik's construction to connected sums of three-manifolds.
result Cosmological spacetimes without CMC Cauchy surfaces for any compact three-manifolds.
Develops statistical methods for rates of change on Riemannian manifolds.
problem Statistical inference for rates of change in spatial processes over non-Euclidean domains.
method Formalizes smoothness and constructs differential processes for Riemannian manifolds, derives conditions for kernel existence, and develops predictive inference.
result Validates theoretical findings through simulation experiments for derivatives over polyhedral meshes.
Deep ReLU networks learn optimally in Besov spaces, overcoming dimensionality issues.
problem Understanding the adaptivity and optimal performance of deep learning in complex function spaces.
method Approximation and estimation error analysis of deep learning with ReLU activation in Besov and mixed smooth Besov spaces.
result Deep learning achieves the minimax optimal rate and outperforms non-adaptive estimators in Besov spaces.
Hyperspectral remote sensing images (HSIs) are characterized by having a low spatial resolution and a high spectral resolution, whereas multispectral images (MSIs) are characterized by low spectral and high spatial resolutions. These complementary characteristics have stimulated active research in the inference of imag…
The paper studies singularities in discrete indefinite affine minimal surfaces.
problem Characterizing singularities in discrete indefinite affine minimal surfaces.
method Discretizing smooth curves and applying discrete Lelieuvre's formulas to study the resulting surfaces.
result The definition of singular edges and vertices in discrete asymptotic nets mirrors properties of smooth surfaces.
Study of evolutes of polygons and curves in higher dimensions.
problem Understanding evolutes of spatial polygons and curves in higher dimensions.
method Analyzing iterations of evolute transformations and studying properties of evolutes for polygons and curves.
result Eigenvalues of the second evolute map have double multiplicity, and evolutes of certain curves are homothetic to the curves themselves.
A new method for brain tissue segmentation across medical centers using a smoothness prior.
problem Tissue segmentation challenges due to center-specific acquisition protocols.
method Developed a smoothness prior that is fit to segmentations from another medical center, integrated into an unsupervised Bayesian model.
result Segmentations are similarly smooth across centers, improving generalization.
SaR-SVM-STV improves hyperspectral image classification with shape-adaptive reconstruction and denoising.
problem Classifying hyperspectral images with limited labeled data.
method Shape-adaptive Reconstruction (SaR) for pixel preprocessing, SVM for probability estimation, and Smoothed Total Variation (STV) for denoising.
result SaR-SVM-STV outperforms SVM-STV with fewer labeled data.
In this paper, we investigate the moduli of continuity for viscosity solutions of a wide class of nonsingular quasilinear evolution equations and also for the level set mean curvature flow, which is an example of singular degenerate equations. We prove that the modulus of continuity is a viscosity subsolution of some o…
New analysis improves convergence guarantees for diffusion-based samplers in Wasserstein distance.
problem Improving convergence guarantees for diffusion-based generative models.
method Simple framework to analyze discretization, initialization, and score estimation errors.
result First Wasserstein convergence bound for the Heun sampler and improved results for Euler sampler.
Flexible spatial models improve predictive performance over nonstationary alternatives.
problem Improving predictive performance in nonstationary spatial modeling.
method Introduces a modular parametric covariance function that extends nonstationary spatial models.
result The proposed covariance function outperforms nonparametric methods in predictive performance.
The paper improves curvature estimates for Ricci flow solutions with bounded scalar curvature.
problem Proving curvature estimates for Ricci flow solutions with bounded scalar curvature.
method Localised weighted curvature integral estimates for solutions to Ricci flow.
result Integral curvature estimates imply a uniform bound on the spatial L2 norm of the Riemannian curvature tensor. Deep learning performs well on high-dimensional data with anisotropic smoothness.
problem Understanding the performance of deep learning on high-dimensional datasets with varying smoothness.
method Investigated approximation and estimation errors in anisotropic Besov spaces.
result Deep learning's performance depends on the average smoothness, avoiding curse of dimensionality.
New equations reveal how cylinder power in progressive lenses depends on geodesic curvature.
problem Current understanding of cylinder power in progressive lenses is incomplete.
method Derived complete compatibility equations for spatially-varying curvature surfaces.
result Cylinder power depends on geodesic curvature, not just principal curvature.
Spatial variable selection is crucial for reliable spatial predictions in machine learning.
problem Spatial autocorrelation leads to overfitting and poor spatial predictions.
method Used Random Forests with non-spatial and spatial cross-validation strategies.
result Spatial variable selection is essential for reliable spatial predictions.
Spatial blind source separation simplifies multivariate spatial prediction.
problem Predicting multivariate measurements at unobserved locations with spatial dependencies.
method Spatial blind source separation as a pre-processing tool compared to Cokriging and neural networks.
result Spatial blind source separation simplifies spatial prediction by avoiding cross-dependencies.
Smooth kernel regularizer improves deep neural networks' performance with less data.
problem Deep neural networks need large datasets for effective learning.
method Proposes a smooth kernel regularizer that encourages spatial correlations in convolution kernel weights, learned from previous experience.
result The smooth kernel regularizer improves visual recognition models over an L2 regularization baseline.