On Cokriging, Neural Networks, and Spatial Blind Source Separation for Multivariate Spatial Prediction

• URL: http://arxiv.org/abs/2007.03747v1
• Date: Wed, 1 Jul 2020 10:59:45 GMT
• Title: On Cokriging, Neural Networks, and Spatial Blind Source Separation for Multivariate Spatial Prediction
• Authors: Christoph Muehlmann, Klaus Nordhausen, Mengxi Yi
• Abstract summary: Blind source separation is a pre-processing tool for spatial prediction. In this paper we investigate the use of spatial blind source separation as a pre-processing tool for spatial prediction. We compare it with predictions from Cokriging and neural networks in an extensive simulation study as well as a geochemical dataset.
• Score: 3.416170716497814
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multivariate measurements taken at irregularly sampled locations are a common form of data, for example in geochemical analysis of soil. In practical considerations predictions of these measurements at unobserved locations are of great interest. For standard multivariate spatial prediction methods it is mandatory to not only model spatial dependencies but also cross-dependencies which makes it a demanding task. Recently, a blind source separation approach for spatial data was suggested. When using this spatial blind source separation method prior the actual spatial prediction, modelling of spatial cross-dependencies is avoided, which in turn simplifies the spatial prediction task significantly. In this paper we investigate the use of spatial blind source separation as a pre-processing tool for spatial prediction and compare it with predictions from Cokriging and neural networks in an extensive simulation study as well as a geochemical dataset.

Related papers

• Embedding Trajectory for Out-of-Distribution Detection in Mathematical Reasoning [50.84938730450622]
  We propose a trajectory-based method TV score, which uses trajectory volatility for OOD detection in mathematical reasoning. Our method outperforms all traditional algorithms on GLMs under mathematical reasoning scenarios. Our method can be extended to more applications with high-density features in output spaces, such as multiple-choice questions.
  arXiv  Detail & Related papers  (2024-05-22T22:22:25Z)
• Conformal inference for regression on Riemannian Manifolds [49.7719149179179]
  We investigate prediction sets for regression scenarios when the response variable, denoted by $Y$, resides in a manifold, and the covariable, denoted by X, lies in Euclidean space. We prove the almost sure convergence of the empirical version of these regions on the manifold to their population counterparts.
  arXiv  Detail & Related papers  (2023-10-12T10:56:25Z)
• Efficient Large-scale Nonstationary Spatial Covariance Function Estimation Using Convolutional Neural Networks [3.5455896230714194]
  We use ConvNets to derive subregions from the nonstationary data. We employ a selection mechanism to identify subregions that exhibit similar behavior to stationary fields. We assess the performance of the proposed method with synthetic and real datasets at a large scale.
  arXiv  Detail & Related papers  (2023-06-20T12:17:46Z)
• Geo-Adaptive Deep Spatio-Temporal predictive modeling for human mobility [5.864710987890994]
  Deep GA-vLS assumes data to be of fixed and regular shaped tensor shaped and face challenges of handling irregular data. We present a novel geo-aware enabled learning operation based on a novel data structure for dependencies while maintaining the recurrent mechanism.
  arXiv  Detail & Related papers  (2022-11-27T16:51:28Z)
• TACTiS: Transformer-Attentional Copulas for Time Series [76.71406465526454]
  estimation of time-varying quantities is a fundamental component of decision making in fields such as healthcare and finance. We propose a versatile method that estimates joint distributions using an attention-based decoder. We show that our model produces state-of-the-art predictions on several real-world datasets.
  arXiv  Detail & Related papers  (2022-02-07T21:37:29Z)
• Spatial machine-learning model diagnostics: a model-agnostic distance-based approach [91.62936410696409]
  This contribution proposes spatial prediction error profiles (SPEPs) and spatial variable importance profiles (SVIPs) as novel model-agnostic assessment and interpretation tools. The SPEPs and SVIPs of geostatistical methods, linear models, random forest, and hybrid algorithms show striking differences and also relevant similarities. The novel diagnostic tools enrich the toolkit of spatial data science, and may improve ML model interpretation, selection, and design.
  arXiv  Detail & Related papers  (2021-11-13T01:50:36Z)
• The Exploitation of Distance Distributions for Clustering [3.42658286826597]
  In cluster analysis, different properties for distance distributions are judged to be relevant for appropriate distance selection. By systematically investigating this specification using distribution analysis through a mirrored-density plot, it is shown that multimodal distance distributions are preferable in cluster analysis. Experiments are performed on several artificial datasets and natural datasets for the task of clustering.
  arXiv  Detail & Related papers  (2021-08-22T06:22:08Z)
• Featurized Density Ratio Estimation [82.40706152910292]
  In our work, we propose to leverage an invertible generative model to map the two distributions into a common feature space prior to estimation. This featurization brings the densities closer together in latent space, sidestepping pathological scenarios where the learned density ratios in input space can be arbitrarily inaccurate. At the same time, the invertibility of our feature map guarantees that the ratios computed in feature space are equivalent to those in input space.
  arXiv  Detail & Related papers  (2021-07-05T18:30:26Z)
• Graph Embedding with Data Uncertainty [113.39838145450007]
  spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. Most subspace learning methods do not take into consideration possible measurement inaccuracies or artifacts that can lead to data with high uncertainty.
  arXiv  Detail & Related papers  (2020-09-01T15:08:23Z)
• DeepKriging: Spatially Dependent Deep Neural Networks for Spatial Prediction [2.219504240642369]
  In spatial statistics, a common objective is to predict values of a spatial process at unobserved locations by exploiting spatial dependence. DeepKriging method has a direct link to Kriging in the Gaussian case, and it has multiple advantages over Kriging for non-Gaussian and non-stationary data. We apply the method to predicting PM2.5 concentrations across the continental United States.
  arXiv  Detail & Related papers  (2020-07-23T12:38:53Z)
• Estimation of the spatial weighting matrix for regular lattice data -- An adaptive lasso approach with cross-sectional resampling [0.38073142980733]
  We investigate the estimation of sparse spatial dependence structures for regular lattice data. To recover the spatial dependence structure, we propose cross-sectional resampling, assuming that the random process is exchangeable. The two-step adaptive lasso approach with cross-sectional resampling is verified using Monte Carlo simulations.
  arXiv  Detail & Related papers  (2020-01-06T12:51:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.