This paper presents an experimental validation for prediction of rare fading events using channel distribution information (CDI) maps that predict channel statistics from measurements acquired at surrounding locations using spatial interpolation. Using experimental channel measurements from 127 locations, we demonstrate the use case of providing statistical guarantees for rate selection in ultra-reliable low-latency communication (URLLC) using CDI maps. By using only the user location and the estimated map, we are able to meet the desired outage probability with a probability between 93.6-95.6% targeting 95%. On the other hand, a model-based baseline scheme that assumes Rayleigh fading meets the target outage requirement with a probability of 77.2%. The results demonstrate the practical relevance of CDI maps for resource allocation in URLLC.
Fusing abundant satellite data with sparse ground measurements constitutes a major challenge in climate modeling. To address this, we propose a strategy to augment the training dataset by introducing unlabeled satellite images paired with pseudo-labels generated through a spatial interpolation technique known as ordinary kriging, thereby making full use of the available satellite data resources. We show that the proposed data augmentation strategy helps enhance the performance of the state-of-the-art convolutional neural network-random forest (CNN-RF) model by a reasonable amount, resulting in a noteworthy improvement in spatial correlation and a reduction in prediction error.
Towards practical applications of Electroencephalography (EEG), lightweight acquisition devices garner significant attention. However, EEG channel selection methods are commonly data-sensitive and cannot establish a unified sound paradigm for EEG acquisition devices. Through reverse conceptualisation, we formulated EEG applications in an EEG super-resolution (SR) manner, but suffered from high computation costs, extra interpolation bias, and few insights into spatiotemporal dependency modelling. To this end, we propose ESTformer, an EEG SR framework that utilises spatiotemporal dependencies based on the transformer. ESTformer applies positional encoding methods and a multihead self-attention mechanism to the space and time dimensions, which can learn spatial structural correlations and temporal functional variations. ESTformer, with the fixed mask strategy, adopts a mask token to upsample low-resolution (LR) EEG data in the case of disturbance from mathematical interpolation methods. On this basis, we designed various transformer blocks to construct a spatial interpolation module (SIM) and a temporal reconstruction module (TRM). Finally, ESTformer cascades the SIM and TRM to capture and model the spatiotemporal dependencies for EEG SR with fidelity. Extensive experimental results on two EEG datasets show the effectiveness of ESTformer against previous state-of-the-art methods, demonstrating the versatility of the Transformer for EEG SR tasks. The superiority of the SR data was verified in an EEG-based person identification and emotion recognition task, achieving a 2% to 38% improvement compared with the LR data at different sampling scales.
The acquisition of accurate rainfall distribution in space is an important task in hydrological analysis and natural disaster pre-warning. However, it is impossible to install rain gauges on every corner. Spatial interpolation is a common way to infer rainfall distribution based on available raingauge data. However, the existing works rely on some unrealistic pre-settings to capture spatial correlations, which limits their performance in real scenarios. To tackle this issue, we propose the SSIN, which is a novel data-driven self-supervised learning framework for rainfall spatial interpolation by mining latent spatial patterns from historical observation data. Inspired by the Cloze task and BERT, we fully consider the characteristics of spatial interpolation and design the SpaFormer model based on the Transformer architecture as the core of SSIN. Our main idea is: by constructing rich self-supervision signals via random masking, SpaFormer can learn informative embeddings for raw data and then adaptively model spatial correlations based on rainfall spatial context. Extensive experiments on two real-world raingauge datasets show that our method outperforms the state-of-the-art solutions. In addition, we take traffic spatial interpolation as another use case to further explore the performance of our method, and SpaFormer achieves the best performance on one large real-world traffic dataset, which further confirms the effectiveness and generality of our method.
Despite advancements in real estate appraisal methods, this study primarily focuses on two pivotal challenges. Firstly, we explore the often-underestimated impact of Points of Interest (POI) on property values, emphasizing the necessity for a comprehensive, data-driven approach to feature selection. Secondly, we integrate road-network-based Areal Embedding to enhance spatial understanding for real estate appraisal. We first propose a revised method for POI feature extraction, and discuss the impact of each POI for house price appraisal. Then we present the Areal embedding-enabled Masked Multihead Attention-based Spatial Interpolation for House Price Prediction (AMMASI) model, an improvement upon the existing ASI model, which leverages masked multi-head attention on geographic neighbor houses and similar-featured houses. Our model outperforms current baselines and also offers promising avenues for future optimization in real estate appraisal methodologies.
Merging satellite and gauge data with machine learning produces high-resolution precipitation datasets, but uncertainty estimates are often missing. We addressed the gap of how to optimally provide such estimates by benchmarking six algorithms, mostly novel even for the more general task of quantifying predictive uncertainty in spatial prediction settings. On 15 years of monthly data from over the contiguous United States (CONUS), we compared quantile regression (QR), quantile regression forests (QRF), generalized random forests (GRF), gradient boosting machines (GBM), light gradient boosting machine (LightGBM), and quantile regression neural networks (QRNN). Their ability to issue predictive precipitation quantiles at nine quantile levels (0.025, 0.050, 0.100, 0.250, 0.500, 0.750, 0.900, 0.950, 0.975), approximating the full probability distribution, was evaluated using quantile scoring functions and the quantile scoring rule. Predictors at a site were nearby values from two satellite precipitation retrievals, namely PERSIANN (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks) and IMERG (Integrated Multi-satellitE Retrievals), and the site's elevation. The dependent variable was the monthly mean gauge precipitation. With respect to QR, LightGBM showed improved performance in terms of the quantile scoring rule by 11.10%, also surpassing QRF (7.96%), GRF (7.44%), GBM (4.64%) and QRNN (1.73%). Notably, LightGBM outperformed all random forest variants, the current standard in spatial prediction with machine learning. To conclude, we propose a suite of machine learning algorithms for estimating uncertainty in spatial data prediction, supported with a formal evaluation framework based on scoring functions and scoring rules.
Estimating the market price of a house is important for many busi- nesses such as real estate and mortgage lending companies. The price of a house depends not only on its structural features (e.g. area and number of bedrooms) but also on the spatial context where it is located. In this work we estimate the price of a house based solely on its structural features and the characteristics and price of its neighbors. For that, we propose a hybrid attention mechanism that weights neighbors based on their similarity to the house in terms of structural features and geographic location. For the structural features, we apply an euclidean-based attention and, for the geo- graphic location, we propose an attention layer based on a radial basis function kernel. Those attention mechanisms are then used by a neural network regressor to predict the price of a house and to generate a vector representation of the house based on its implicit context: the house embedding, which can be used as a feature set by any regressor to perform house price prediction. We have per- formed an extensive experimental evaluation on real-world datasets that shows that: (1) regressors using house embedding obtained the best results on all 4 datasets, outperforming baseline models; (2) the learned house embedding improves the performance of the evaluated regressors in almost all scenarios in comparison to raw features; and (3) simple regressor models such as Linear Regres- sion using house embedding achieved comparable results to more competitive algorithms (e.g. Random Forest and Xgboost).
High spatial resolution wind data are essential for a wide range of applications in climate, oceanographic and meteorological studies. Large-scale spatial interpolation or downscaling of bivariate wind fields having velocity in two dimensions is a challenging task because wind data tend to be non-Gaussian with high spatial variability and heterogeneity. In spatial statistics, cokriging is commonly used for predicting bivariate spatial fields. However, the cokriging predictor is not optimal except for Gaussian processes. Additionally, cokriging is computationally prohibitive for large datasets. 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 for bivariate spatial data prediction. We then develop a distribution-free uncertainty quantification method based on bootstrap and ensemble DNN. Our proposed approach outperforms the traditional cokriging predictor with commonly used covariance functions, such as the linear model of co-regionalization and flexible bivariate Mat\'ern covariance. 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. We apply the bivariate DeepKriging method to the wind data over the Middle East region at 506,771 locations. The prediction performance of the proposed method is superior over the cokriging predictors and dramatically reduces computation time.
Spatial interpolation is a class of estimation problems where locations with known values are used to estimate values at other locations, with an emphasis on harnessing spatial locality and trends. Traditional Kriging methods have strong Gaussian assumptions, and as a result, often fail to capture complexities within the data. Inspired by the recent progress of graph neural networks, we introduce Kriging Convolutional Networks (KCN), a method of combining the advantages of Graph Convolutional Networks (GCN) and Kriging. Compared to standard GCNs, KCNs make direct use of neighboring observations when generating predictions. KCNs also contain the Kriging method as a specific configuration. We further improve the model's performance by adding attention. Empirically, we show that this model outperforms GCNs and Kriging in several applications. The implementation of KCN using PyTorch is publicized at the GitHub repository: https://github.com/tufts-ml/kcn-torch.
We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive definiteness, as well as isotropy and monotonicity, on the estimators, and its hyperparameters can be decided using cross validation. We define our estimators by taking integral transforms of kernel-based distribution surrogates. We then use the iterated density estimation evolutionary algorithm, a variant of estimation of distribution algorithms, to fit the estimators. We also extend our method to estimate covariance functions for point-referenced data. Compared to alternative approaches, our method provides more reliable estimates for long-range dependence. Several numerical studies are performed to demonstrate the efficacy and performance of our method. Also, we illustrate our method using precipitation data from the Spatial Interpolation Comparison 97 project.
Knowing the actual precipitation in space and time is critical in hydrological modelling applications, yet the spatial coverage with rain gauge stations is limited due to economic constraints. Gridded satellite precipitation datasets offer an alternative option for estimating the actual precipitation by covering uniformly large areas, albeit related estimates are not accurate. To improve precipitation estimates, machine learning is applied to merge rain gauge-based measurements and gridded satellite precipitation products. In this context, observed precipitation plays the role of the dependent variable, while satellite data play the role of predictor variables. Random forests is the dominant machine learning algorithm in relevant applications. In those spatial predictions settings, point predictions (mostly the mean or the median of the conditional distribution) of the dependent variable are issued. The aim of the manuscript is to solve the problem of probabilistic prediction of precipitation with an emphasis on extreme quantiles in spatial interpolation settings. Here we propose, issuing probabilistic spatial predictions of precipitation using Light Gradient Boosting Machine (LightGBM). LightGBM is a boosting algorithm, highlighted by prize-winning entries in prediction and forecasting competitions. To assess LightGBM, we contribute a large-scale application that includes merging daily precipitation measurements in contiguous US with PERSIANN and GPM-IMERG satellite precipitation data. We focus on extreme quantiles of the probability distribution of the dependent variable, where LightGBM outperforms quantile regression forests (QRF, a variant of random forests) in terms of quantile score at extreme quantiles. Our study offers understanding of probabilistic predictions in spatial settings using machine learning.
Particulate matter (PM) is considered the primary contributor to air pollution and has severe implications for general health. PM concentration has high spatial variability and thus needs to be monitored locally. Traditional PM monitoring setups are bulky, expensive and cannot be scaled for dense deployments. This paper argues for a densely deployed network of IoT-enabled PM monitoring devices using low-cost sensors. In this work, 49 devices were deployed in a region of the Indian metropolitan city of Hyderabad out-of this, 43 devices were developed as part of this work and 6 devices were taken off the shelf. The low-cost sensors were calibrated for seasonal variations using a precise reference sensor. A thorough analysis of data collected for seven months has been presented to establish the need for dense deployment of PM monitoring devices. Different analyses such as mean, variance, spatial interpolation and correlation have been employed to generate interesting insights about temporal and seasonal variations of PM. In addition, event-driven spatio-temporal analysis is done for PM values to understand the impact of the bursting of firecrackers on the evening of the Diwali festival. A web-based dashboard is designed for real-time data visualization.
Spatial autocorrelation and spatial heterogeneity widely exist in spatial data, which make the traditional machine learning model perform badly. Spatial domain generalization is a spatial extension of domain generalization, which can generalize to unseen spatial domains in continuous 2D space. Specifically, it learns a model under varying data distributions that generalizes to unseen domains. Although tremendous success has been achieved in domain generalization, there exist very few works on spatial domain generalization. The advancement of this area is challenged by: 1) Difficulty in characterizing spatial heterogeneity, and 2) Difficulty in obtaining predictive models for unseen locations without training data. To address these challenges, this paper proposes a generic framework for spatial domain generalization. Specifically, We develop the spatial interpolation graph neural network that handles spatial data as a graph and learns the spatial embedding on each node and their relationships. The spatial interpolation graph neural network infers the spatial embedding of an unseen location during the test phase. Then the spatial embedding of the target location is used to decode the parameters of the downstream-task model directly on the target location. Finally, extensive experiments on thirteen real-world datasets demonstrate the proposed method's strength.
It is challenging to annotate large-scale datasets for supervised video shadow detection methods. Using a model trained on labeled images to the video frames directly may lead to high generalization error and temporal inconsistent results. In this paper, we address these challenges by proposing a Spatio-Temporal Interpolation Consistency Training (STICT) framework to rationally feed the unlabeled video frames together with the labeled images into an image shadow detection network training. Specifically, we propose the Spatial and Temporal ICT, in which we define two new interpolation schemes, \textit{i.e.}, the spatial interpolation and the temporal interpolation. We then derive the spatial and temporal interpolation consistency constraints accordingly for enhancing generalization in the pixel-wise classification task and for encouraging temporal consistent predictions, respectively. In addition, we design a Scale-Aware Network for multi-scale shadow knowledge learning in images, and propose a scale-consistency constraint to minimize the discrepancy among the predictions at different scales. Our proposed approach is extensively validated on the ViSha dataset and a self-annotated dataset. Experimental results show that, even without video labels, our approach is better than most state of the art supervised, semi-supervised or unsupervised image/video shadow detection methods and other methods in related tasks. Code and dataset are available at \url{https://github.com/yihong-97/STICT}.
Lagrangian trajectory or particle dispersion models as well as semi-Lagrangian advection schemes require meteorological data such as wind, temperature and geopotential at the exact spatio-temporal locations of the particles that move independently from a regular grid. Traditionally, this high-resolution data has been obtained by interpolating the meteorological parameters from the gridded data of a meteorological model or reanalysis, e.g. using linear interpolation in space and time. However, interpolation errors are a large source of error for these models. Reducing them requires meteorological input fields with high space and time resolution, which may not always be available and can cause severe data storage and transfer problems. Here, we interpret this problem as a single image superresolution task. We interpret meteorological fields available at their native resolution as low-resolution images and train deep neural networks to up-scale them to higher resolution, thereby providing more accurate data for Lagrangian models. We train various versions of the state-of-the-art Enhanced Deep Residual Networks for Superresolution on low-resolution ERA5 reanalysis data with the goal to up-scale these data to arbitrary spatial resolution. We show that the resulting up-scaled wind fields have root-mean-squared errors half the size of the winds obtained with linear spatial interpolation at acceptable computational inference costs. In a test setup using the Lagrangian particle dispersion model FLEXPART and reduced-resolution wind fields, we demonstrate that absolute horizontal transport deviations of calculated trajectories from "ground-truth" trajectories calculated with undegraded 0.5{\deg} winds are reduced by at least 49.5% (21.8%) after 48 hours relative to trajectories using linear interpolation of the wind data when training on 2{\deg} to 1{\deg} (4{\deg} to 2{\deg}) resolution data.
The weather phenomenon of frost poses great threats to agriculture. As recent frost prediction methods are based on on-site historical data and sensors, extra development and deployment time are required for data collection in any new site. The aim of this article is to eliminate the dependency on on-site historical data and sensors for frost prediction methods. In this article, a frost prediction method based on spatial interpolation is proposed. The models use climate data from existing weather stations, digital elevation models surveys, and normalized difference vegetation index data to estimate a target site's next hour minimum temperature. The proposed method utilizes ensemble learning to increase the model accuracy. Climate datasets are obtained from 75 weather stations across New South Wales and Australian Capital Territory areas of Australia. The results show that the proposed method reached a detection rate up to 92.55%.
Graph neural networks (GNNs) provide a powerful and scalable solution for modeling continuous spatial data. However, they often rely on Euclidean distances to construct the input graphs. This assumption can be improbable in many real-world settings, where the spatial structure is more complex and explicitly non-Euclidean (e.g., road networks). Here, we propose PE-GNN, a new framework that incorporates spatial context and correlation explicitly into the models. Building on recent advances in geospatial auxiliary task learning and semantic spatial embeddings, our proposed method (1) learns a context-aware vector encoding of the geographic coordinates and (2) predicts spatial autocorrelation in the data in parallel with the main task. On spatial interpolation and regression tasks, we show the effectiveness of our approach, improving performance over different state-of-the-art GNN approaches. We observe that our approach not only vastly improves over the GNN baselines, but can match Gaussian processes, the most commonly utilized method for spatial interpolation problems.
In our previous work, we designed a systematic policy to prioritize sampling locations to lead significant accuracy improvement in spatial interpolation by using the prediction uncertainty of Gaussian Process Regression (GPR) as "attraction force" to deployed robots in path planning. Although the integration with Traveling Salesman Problem (TSP) solvers was also shown to produce relatively short travel distance, we here hypothesise several factors that could decrease the overall prediction precision as well because sub-optimal locations may eventually be included in their paths. To address this issue, in this paper, we first explore "local planning" approaches adopting various spatial ranges within which next sampling locations are prioritized to investigate their effects on the prediction performance as well as incurred travel distance. Also, Reinforcement Learning (RL)-based high-level controllers are trained to adaptively produce blended plans from a particular set of local planners to inherit unique strengths from that selection depending on latest prediction states. Our experiments on use cases of temperature monitoring robots demonstrate that the dynamic mixtures of planners can not only generate sophisticated, informative plans that a single planner could not create alone but also ensure significantly reduced travel distances at no cost of prediction reliability without any assist of additional modules for shortest path calculation.
The interpolation of spatial data can be of tremendous value in various applications, such as forecasting weather from only a few measurements of meteorological or remote sensing data. Existing methods for spatial interpolation, such as variants of kriging and spatial autoregressive models, tend to suffer from at least one of the following limitations: (a) the assumption of stationarity, (b) the assumption of isotropy, and (c) the trade-off between modelling local or global spatial interaction. Addressing these issues in this work, we propose the use of Markov reward processes (MRPs) as a spatial interpolation method, and we introduce three variants thereof: (i) a basic static discount MRP (SD-MRP), (ii) an accurate but mostly theoretical optimised MRP (O-MRP), and (iii) a transferable weight prediction MRP (WP-MRP). All variants of MRP interpolation operate locally, while also implicitly accounting for global spatial relationships in the entire system through recursion. Additionally, O-MRP and WP-MRP no longer assume stationarity and are robust to anisotropy. We evaluated our proposed methods by comparing the mean absolute errors of their interpolated grid cells to those of 7 common baselines, selected from models based on spatial autocorrelation, (spatial) regression, and deep learning. We performed detailed evaluations on two publicly available datasets (local GDP values, and COVID-19 patient trajectory data). The results from these experiments clearly show the competitive advantage of MRP interpolation, which achieved significantly lower errors than the existing methods in 23 out of 40 experimental conditions, or 35 out of 40 when including O-MRP.
Spatial data is a rich source of information for actuarial applications: knowledge of a risk's location could improve an insurance company's ratemaking, reserving or risk management processes. Insurance companies with high exposures in a territory typically have a competitive advantage since they may use historical losses in a region to model spatial risk non-parametrically. Relying on geographic losses is problematic for areas where past loss data is unavailable. This paper presents a method based on data (instead of smoothing historical insurance claim losses) to construct a geographic ratemaking model. In particular, we construct spatial features within a complex representation model, then use the features as inputs to a simpler predictive model (like a generalized linear model). Our approach generates predictions with smaller bias and smaller variance than other spatial interpolation models such as bivariate splines in most situations. This method also enables us to generate rates in territories with no historical experience.