DeepKriging: Spatially Dependent Deep Neural Networks for Spatial Prediction

• URL: http://arxiv.org/abs/2007.11972v4
• Date: Tue, 24 May 2022 03:16:36 GMT
• Title: DeepKriging: Spatially Dependent Deep Neural Networks for Spatial Prediction
• Authors: Wanfang Chen, Yuxiao Li, Brian J Reich and Ying Sun
• Abstract summary: 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.
• Score: 2.219504240642369
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In spatial statistics, a common objective is to predict values of a spatial process at unobserved locations by exploiting spatial dependence. Kriging provides the best linear unbiased predictor using covariance functions and is often associated with Gaussian processes. However, when considering non-linear prediction for non-Gaussian and categorical data, the Kriging prediction is no longer optimal, and the associated variance is often overly optimistic. Although deep neural networks (DNNs) are widely used for general classification and prediction, they have not been studied thoroughly for data with spatial dependence. In this work, we propose a novel DNN structure for spatial prediction, where the spatial dependence is captured by adding an embedding layer of spatial coordinates with basis functions. We show in theory and simulation studies that the proposed 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, i.e., it provides non-linear predictions and thus has smaller approximation errors, it does not require operations on covariance matrices and thus is scalable for large datasets, and with sufficiently many hidden neurons, it provides the optimal prediction in terms of model capacity. We further explore the possibility of quantifying prediction uncertainties based on density prediction without assuming any data distribution. Finally, we apply the method to predicting PM2.5 concentrations across the continental United States.

Related papers

• Positional Encoder Graph Quantile Neural Networks for Geographic Data [4.277516034244117]
  We introduce the Positional Graph Quantile Neural Network (PE-GQNN), a novel method that integrates PE-GNNs, Quantile Neural Networks, and recalibration techniques in a fully nonparametric framework. Experiments on benchmark datasets demonstrate that PE-GQNN significantly outperforms existing state-of-the-art methods in both predictive accuracy and uncertainty quantification.
  arXiv  Detail & Related papers  (2024-09-27T16:02:12Z)
• Bivariate DeepKriging for Large-scale Spatial Interpolation of Wind Fields [2.586710925821896]
  High spatial resolution wind data are essential for a wide range of applications in climate, oceanographic and meteorological studies. Large-scale spatial computation or downscaling of bivariate wind fields having velocity in two dimensions is a challenging task. In this paper, we propose a method, called bivariate DeepKriging, which is a spatially dependent deep neural network (DNN) with an embedding layer constructed by spatial radial basis functions. We demonstrate the computational efficiency and scalability of the proposed DNN model, with computations that are, on average, 20 times faster than those of conventional techniques.
  arXiv  Detail & Related papers  (2023-07-16T13:34:44Z)
• Spatio-temporal DeepKriging for Interpolation and Probabilistic Forecasting [2.494500339152185]
  We propose a deep neural network (DNN) based two-stage model fortemporal-temporal and forecasting. We adopt the quant-based loss function in the processes to provide probabilistic forecasting. It is suitable for large-scale prediction of complex-temporal processes.
  arXiv  Detail & Related papers  (2023-06-20T11:51:44Z)
• Uncertainty Quantification over Graph with Conformalized Graph Neural Networks [52.20904874696597]
  Graph Neural Networks (GNNs) are powerful machine learning prediction models on graph-structured data. GNNs lack rigorous uncertainty estimates, limiting their reliable deployment in settings where the cost of errors is significant. We propose conformalized GNN (CF-GNN), extending conformal prediction (CP) to graph-based models for guaranteed uncertainty estimates.
  arXiv  Detail & Related papers  (2023-05-23T21:38:23Z)
• Neural networks for geospatial data [0.0]
  NN-GLS is a new neural network estimation algorithm for the non-linear mean in GP models. We show that NN-GLS admits a representation as a special type of graph neural network (GNN) Theoretically, we show that NN-GLS will be consistent for irregularly observed spatially correlated data processes.
  arXiv  Detail & Related papers  (2023-04-18T17:52:23Z)
• Uncertainty estimation of pedestrian future trajectory using Bayesian approximation [137.00426219455116]
  Under dynamic traffic scenarios, planning based on deterministic predictions is not trustworthy. The authors propose to quantify uncertainty during forecasting using approximation which deterministic approaches fail to capture. The effect of dropout weights and long-term prediction on future state uncertainty has been studied.
  arXiv  Detail & Related papers  (2022-05-04T04:23:38Z)
• Dense Uncertainty Estimation [62.23555922631451]
  In this paper, we investigate neural networks and uncertainty estimation techniques to achieve both accurate deterministic prediction and reliable uncertainty estimation. We work on two types of uncertainty estimations solutions, namely ensemble based methods and generative model based methods, and explain their pros and cons while using them in fully/semi/weakly-supervised framework.
  arXiv  Detail & Related papers  (2021-10-13T01:23:48Z)
• Improving Uncertainty Calibration via Prior Augmented Data [56.88185136509654]
  Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. They are often overconfident in their predictions, which leads to inaccurate and miscalibrated probabilistic predictions. We propose a solution by seeking out regions of feature space where the model is unjustifiably overconfident, and conditionally raising the entropy of those predictions towards that of the prior distribution of the labels.
  arXiv  Detail & Related papers  (2021-02-22T07:02:37Z)
• Improving predictions of Bayesian neural nets via local linearization [79.21517734364093]
  We argue that the Gauss-Newton approximation should be understood as a local linearization of the underlying Bayesian neural network (BNN) Because we use this linearized model for posterior inference, we should also predict using this modified model instead of the original one. We refer to this modified predictive as "GLM predictive" and show that it effectively resolves common underfitting problems of the Laplace approximation.
  arXiv  Detail & Related papers  (2020-08-19T12:35:55Z)
• On Cokriging, Neural Networks, and Spatial Blind Source Separation for Multivariate Spatial Prediction [3.416170716497814]
  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.
  arXiv  Detail & Related papers  (2020-07-01T10:59:45Z)
• Unlabelled Data Improves Bayesian Uncertainty Calibration under Covariate Shift [100.52588638477862]
  We develop an approximate Bayesian inference scheme based on posterior regularisation. We demonstrate the utility of our method in the context of transferring prognostic models of prostate cancer across globally diverse populations.
  arXiv  Detail & Related papers  (2020-06-26T13:50:19Z)

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.