New method recovers relative rates in spatial compositional data from IMS.
problem Challenges in analyzing spatial data from IMS due to competitive sampling.
method Hierarchical Variational Graph Fused Lasso using heavy-tailed graphical lasso prior and automatic differentiation variational inference.
result Our method outperforms state-of-the-practice point estimate methodologies in IMS and has superior posterior coverage.
Connected sum and trivalent vertex sum are natural operations on genus 2 spatial graphs and, as with knots, tunnel number behaves in interesting ways under these operations. We prove sharp Scharlemann-Schultens type bounds for the tunnel number of a composite genus 2 spatial graph. For the tunnel number of a composite …
Spatial processes with nonstationary and anisotropic covariance structure are often used when modelling, analysing and predicting complex environmental phenomena. Such processes may often be expressed as ones that have stationary and isotropic covariance structure on a warped spatial domain. However, the warping functi…
CTGAN synthesizes population data for travel behavior simulation.
problem Synthesizing population data for agent-based transportation modeling.
method Composite Travel Generative Adversarial Network (CTGAN).
result Consistent and accurate generation of synthetic populations with tabular and sequential mobility data.
Generative Adversarial Networks (GANs) can produce images of remarkable complexity and realism but are generally structured to sample from a single latent source ignoring the explicit spatial interaction between multiple entities that could be present in a scene. Capturing such complex interactions between different ob…
We study the minimal crossing number c(K1#K2) of composite knots K1#K2, where K1 and K2 are prime, by relating it to the minimal crossing number of spatial graphs, in particular the 2n-theta curve θK1,K2n that results from tying n of the edges of the planar embedding of the $2n…
Develops deep models to handle nonstationary spatial extremal dependence.
problem Challenges in modeling nonstationary extremal dependence in spatial data.
method Deep compositional spatial models to capture nonstationarity in extremal dependence.
result Efficient estimation of warped space for nonstationary spatial data.
During the past decade, with the significant progress of computational power as well as ever-rising data availability, deep learning techniques became increasingly popular due to their excellent performance on computer vision problems. The size of the Protein Data Bank has increased more than 15 fold since 1999, which …
Enhances neural networks with prior knowledge through a composite kernel.
problem Lack of effective methods to incorporate prior knowledge into neural networks.
method Integrates a composite kernel combining a neural network kernel and a GP kernel for modeling known properties.
result Demonstrates superior performance and flexibility of the Implicit Composite Kernel (ICK) on synthetic and real-world data.
BKP R package models spatially varying binomial probabilities efficiently.
problem Modeling spatially varying binomial probabilities efficiently.
method Beta Kernel Process (BKP) combining localized kernel-weighted likelihoods with conjugate beta priors.
result Closed-form posterior inference without requiring latent variables or intensive MCMC sampling.
Deep Learning has been shown to learn efficient representations for structured data such as image, text or audio. In this chapter, we present neural network architectures that are able to learn efficient representations of molecules and materials. In particular, the continuous-filter convolutional network SchNet accura…
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.
Agents learn to communicate and solve navigation tasks efficiently.
problem Understanding and developing communication in artificial agents.
method Multi-agent navigation tasks in gridworld environments.
result Agents develop an interpretable communication protocol that optimally solves tasks.
A new neural network captures and explains trajectory patterns.
problem Analyzing complex spatial trajectories in urban planning and neuroscience.
method Composite Signal Neural Networks (CompSNN) combining three interpretable ANN modules.
result CompSNN outperforms individual modules and visualizes useful signal parts.
New geometric approach for analyzing compositional data like gut microbiomes.
problem Analyzing non-negative compositional data with relative values only.
method Reinterpret compositional data as quotient topology of a sphere, using spherical harmonics and reflection group actions.
result Construction of Reproducing Kernel Hilbert Space (RKHS) for compositional data.
Improved SVMs learn from few samples with composition and multiple scales.
problem Learning with small sample sizes.
method Transformation-invariant SVMs with composition and locality at multiple scales.
result Kernels based on maximum similarity are positive definite and yield superior accuracy.
Develops methods for causal inference in compositional data using instrumental variables.
problem Interpreting summary statistics like diversity indices as causal effects in compositional data.
method Statistical data transformations and regression techniques tailored for compositional data.
result Advantages and limitations of the proposed methods demonstrated on synthetic and real microbiome data.
In this paper we propose novel Deformable Part Networks (DPNs) to learn {\em pose-invariant} representations for 2D object recognition. In contrast to the state-of-the-art pose-aware networks such as CapsNet \cite{sabour2017dynamic} and STN \cite{jaderberg2015spatial}, DPNs can be naturally {\em interpreted} as an effi…
Proposes a new tensor decomposition method for functional temporal data with adaptive complexity.
problem Challenges in temporal tensor decomposition for general tensor data with continuous indexes.
method Encodes continuous spatial indexes as learnable Fourier features and uses neural ODEs for temporal trajectories. Introduces a sparsity-inducing prior for complexity adaptation.
result Significantly outperforms existing methods in prediction performance and robustness against noise.
A new geometry-preserving method for interpreting compositional data.
problem Statistical challenges in high-dimensional compositional data.
method Geometry-preserving framework for dimension reduction of compositional data.
result Identification of a central compositional subspace for compositional predictors.
The Ck-equivalence is an equivalence relation generated by Ck-moves defined by Habiro. Habiro showed that the set of Ck-equivalence classes of the knots forms an abelian group under the connected sum and it can be classified by the additive Vassiliev invariant of order ≤k−1. We see that the set of Ck-…
We establish conditions for compositional generalization in machine learning.
problem Achieving compositional generalization in machine learning models.
method We reformulate compositionality as a property of the data-generating process and derive mild conditions on the training distribution and model architecture.
result Our theoretical framework enables compositional generalization under mild conditions.
This paper extends compositional data analysis using graph signal processing.
problem Traditional log-ratios between all variables are not suitable for specific variable relationships.
method Linking compositional data analysis with graph signal processing, it considers only selected log-ratios.
result The approach retains desirable properties of scale invariance and compositional coherence.
This paper introduces compositional data analysis for financial ratios, improving industry-level analysis.
problem Statistical issues with standard financial ratios at industry level.
method Compositional data analysis techniques for financial ratios.
result Improved analysis of financial ratios using compositional data methods.
New ANN method for imputing rounded zeros in compositional data.
problem Imputing missing values in compositional data with rounded zeros.
method Artificial Neural Networks (ANNs) for imputation of compositional data.
result ANNs are competitive or better than conventional methods for imputing rounded zeros.
A registration-free framework monitors shape and color in 4D point clouds.
problem Monitoring shape and color changes in complex parts without registration.
method Laplace-Beltrami operator spectral properties for geometric and color feature capture; combined monitoring scheme for shape and color anomalies.
result Effective detection of shape deformations and color anomalies without registration or mesh reconstruction.
Machine learning algorithms find frequent application in spatial prediction of biotic and abiotic environmental variables. However, the characteristics of spatial data, especially spatial autocorrelation, are widely ignored. We hypothesize that this is problematic and results in models that can reproduce training data …
CARE method estimates precision matrix for compositional data, achieving optimality in high dimensions.
problem Challenges in inferring conditional dependence relationships in high-dimensional compositional data.
method Composition adaptive regularized estimation (CARE) method for sparse basis precision matrix.
result CARE estimator achieves minimax optimality in high dimensions, performing as well as if the basis were observed.
Compositional diffusion models simulate coupled PDEs efficiently.
problem Efficiently simulating long-horizon coupled PDE systems.
method Diffusion models trained on decoupled data are composed at inference time.
result Compositional diffusion models recover coupled trajectories with low error.
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.
DeepCoDA provides personalized interpretability for complex health data.
problem Interpreting complex health data, especially compositional data, is challenging.
method DeepCoDA framework for high-dimensional compositional data, personalized interpretability through patient-specific weights.
result DeepCoDA maintains state-of-the-art performance and provides coherent, personalized interpretations.
New method for analyzing compositional data, addressing biases in summary statistics.
problem Inadequate effect measures for compositional data, especially in high-dimensionality and sparsity.
method Perturbation-based effect measures, average perturbation effects.
result Proposed estimators efficiently estimate average perturbation effects, outperforming existing techniques.
Humans perceive the seemingly chaotic world in a structured and compositional way with the prerequisite of being able to segregate conceptual entities from the complex visual scenes. The mechanism of grouping basic visual elements of scenes into conceptual entities is termed as perceptual grouping. In this work, we pro…
A framework converts spatial data into embeddings for insurance risk modelling.
problem Improving underwriting precision and risk management in insurance with spatial data.
method Multi-view contrastive learning framework for generating spatial embeddings.
result Spatial embeddings consistently improve predictive accuracy across various models.
Adapts Altman's model to compositional data for bankruptcy prediction.
problem Predicting business default using standard financial ratios has issues.
method Uses compositional data methodology with log-ratios and machine learning.
result Compositional methods improve predictive performance, especially random forests.
Bayesian spatial predictive synthesis improves spatial data predictions.
problem Model misspecification and heterogeneity in spatial data.
method Bayesian ensemble methodology capturing spatially-varying model uncertainty and performance heterogeneity.
result Synthesized predictions outperform standard methods in accuracy and uncertainty quantification.
New sparse GP model learns compositional kernels efficiently.
problem Learning accurate Gaussian Process models with complex kernel structures.
method MultiSVGP model with Horseshoe prior for kernel selection.
result Our model provides better fit and faster computation for large-scale data.
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.
The understanding of geographical reality is a process of data representation and pattern discovery. Former studies mainly adopted continuous-field models to represent spatial variables and to investigate the underlying spatial continuity/heterogeneity in the regular spatial domain. In this article, we introduce a more…
Compositional data have two unique characteristics compared to typical multivariate data: the observed values are nonnegative and their summand is exactly one. To reflect these characteristics, a specific regularized regression model with linear constraints is commonly used. However, linear constraints incur additional…
State-of-the-art deep learning methods have shown a remarkable capacity to model complex data domains, but struggle with geospatial data. In this paper, we introduce SpaceGAN, a novel generative model for geospatial domains that learns neighbourhood structures through spatial conditioning. We propose to enhance spatial…
MSFA clusters high-dimensional spatial data using spline-based covariance structures.
problem Clustering high-dimensional spatial data with flexible covariance structures.
method Mixture of spatial factor analyzers with spline-based covariance and matrix variate factor analyzers for dimensionality reduction.
result Proposed models accurately infer and differentiate distinct spatial patterns in tensor-variate data.
Proposes LSCP for spatial data uncertainty quantification.
problem Uncertainty quantification in spatial statistics, especially for complex and heterogeneous datasets.
method Localized quantile regression for spatial conformal prediction.
result LSCP provides more accurate and consistent prediction intervals.
In this work, we propose a composition/decomposition framework for adversarially training generative models on composed data - data where each sample can be thought of as being constructed from a fixed number of components. In our framework, samples are generated by sampling components from component generators and fee…
Proposes a new model for clustering multiplex networks with compositional data.
problem Clustering multiplex networks with multiple types of relations and compositional data.
method Multiplex Dirichlet stochastic block model for compositional networks.
result Validated through simulation and applied to international export data.
Traditionally it had been a problem that researchers did not have access to enough spatial data to answer pressing research questions or build compelling visualizations. Today, however, the problem is often that we have too much data. Spatially redundant or approximately redundant points may refer to a single feature (…
Proposes a method to forecast spatial-temporal data with limited training data.
problem Forecasting with nodes having no temporal training data.
method Temporal data augmentation and spatial graph topology learning.
result Improves forecasting performance on nodes without training data.
Spatially constrained Gaussian mixture models reduce covariance complexity.
problem High dimensionality in finite mixture models for spatial data.
method Spatial covariance constraint with only four free parameters.
result Improves clustering of multi-way spatial data and inference of spatial patterns.