We investigate the use of spatial interpolation methods for reconstructing the horizontal near-surface wind field given a sparse set of measurements. In particular, random Fourier features is compared to a set of benchmark methods including Kriging and Inverse distance weighting. Random Fourier features is a linear model $\beta(\pmb x) = \sum_{k=1}^K \beta_k e^{i\omega_k \pmb x}$ approximating the velocity field, with frequencies $\omega_k$ randomly sampled and amplitudes $\beta_k$ trained to minimize a loss function. We include a physically motivated divergence penalty term $|\nabla \cdot \beta(\pmb x)|^2$, as well as a penalty on the Sobolev norm. We derive a bound on the generalization error and derive a sampling density that minimizes the bound. Following (arXiv:2007.10683 [math.NA]), we devise an adaptive Metropolis-Hastings algorithm for sampling the frequencies of the optimal distribution. In our experiments, our random Fourier features model outperforms the benchmark models.
The U-shape structure has shown its advantage in salient object detection for efficiently combining multi-scale features. However, most existing U-shape based methods focused on improving the bottom-up and top-down pathways while ignoring the connections between them. This paper shows that by centralizing these connections, we can achieve the cross-scale information interaction among them, hence obtaining semantically stronger and positionally more precise features. To inspire the potential of the newly proposed strategy, we further design a relative global calibration module that can simultaneously process multi-scale inputs without spatial interpolation. Benefiting from the above strategy and module, our proposed approach can aggregate features more effectively while introducing only a few additional parameters. Our approach can cooperate with various existing U-shape-based salient object detection methods by substituting the connections between the bottom-up and top-down pathways. Experimental results demonstrate that our proposed approach performs favorably against the previous state-of-the-arts on five widely used benchmarks with less computational complexity. The source code will be publicly available.
During the winter season, real-time monitoring of road surface conditions is critical for the safety of drivers and road maintenance operations. Previous research has evaluated the potential of image classification methods for detecting road snow coverage by processing images from roadside cameras installed in RWIS (Road Weather Information System) stations. However, there are a limited number of RWIS stations across Ontario, Canada; therefore, the network has reduced spatial coverage. In this study, we suggest improving performance on this task through the integration of images and weather data collected from the RWIS stations with images from other MTO (Ministry of Transportation of Ontario) roadside cameras and weather data from Environment Canada stations. We use spatial statistics to quantify the benefits of integrating the three datasets across Southern Ontario, showing evidence of a six-fold increase in the number of available roadside cameras and therefore improving the spatial coverage in the most populous ecoregions in Ontario. Additionally, we evaluate three spatial interpolation methods for inferring weather variables in locations without weather measurement instruments and identify the one that offers the best tradeoff between accuracy and ease of implementation.
Current air pollution monitoring systems are bulky and expensive resulting in a very sparse deployment. In addition, the data from these monitoring stations may not be easily accessible. This paper focuses on studying the dense deployment based air pollution monitoring using IoT enabled low-cost sensor nodes. For this, total nine low-cost IoT nodes monitoring particulate matter (PM), which is one of the most dominant pollutants, are deployed in a small educational campus in Indian city of Hyderabad. Out of these, eight IoT nodes were developed at IIIT-H while one was bought off the shelf. A web based dashboard website is developed to easily monitor the real-time PM values. The data is collected from these nodes for more than five months. Different analyses such as correlation and spatial interpolation are done on the data to understand efficacy of dense deployment in better understanding the spatial variability and time-dependent changes to the local pollution indicators.
Variable Annuity (VA) products expose insurance companies to considerable risk because of the guarantees they provide to buyers of these products. Managing and hedging these risks requires insurers to find the value of key risk metrics for a large portfolio of VA products. In practice, many companies rely on nested Monte Carlo (MC) simulations to find key risk metrics. MC simulations are computationally demanding, forcing insurance companies to invest hundreds of thousands of dollars in computational infrastructure per year. Moreover, existing academic methodologies are focused on fair valuation of a single VA contract, exploiting ideas in option theory and regression. In most cases, the computational complexity of these methods surpasses the computational requirements of MC simulations. Therefore, academic methodologies cannot scale well to large portfolios of VA contracts. In this paper, we present a framework for valuing such portfolios based on spatial interpolation. We provide a comprehensive study of this framework and compare existing interpolation schemes. Our numerical results show superior performance, in terms of both computational efficiency and accuracy, for these methods compared to nested MC simulations. We also present insights into the challenge of finding an effective interpolation scheme in this framework, and suggest guidelines that help us build a fully automated scheme that is efficient and accurate.
Managing and hedging the risks associated with Variable Annuity (VA) products require intraday valuation of key risk metrics for these products. The complex structure of VA products and computational complexity of their accurate evaluation have compelled insurance companies to adopt Monte Carlo (MC) simulations to value their large portfolios of VA products. Because the MC simulations are computationally demanding, especially for intraday valuations, insurance companies need more efficient valuation techniques. Recently, a framework based on traditional spatial interpolation techniques has been proposed that can significantly decrease the computational complexity of MC simulation (Gan and Lin, 2015). However, traditional interpolation techniques require the definition of a distance function that can significantly impact their accuracy. Moreover, none of the traditional spatial interpolation techniques provide all of the key properties of accuracy, efficiency, and granularity (Hejazi et al., 2015). In this paper, we present a neural network approach for the spatial interpolation framework that affords an efficient way to find an effective distance function. The proposed approach is accurate, efficient, and provides an accurate granular view of the input portfolio. Our numerical experiments illustrate the superiority of the performance of the proposed neural network approach compared to the traditional spatial interpolation schemes.
The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs), introduced in [21], uses a uniform space grid. In this paper we utilize a tree-like spatial discretization that approximates the BSDE on the tree, so that no spatial interpolation procedure is necessary. In addition to suppressing extrapolation error, leading to a globally convergent numerical solution for the FBSDE, we provide explicit convergence rates. On this alternative grid the conditional expectations involved in the time discretization of the BSDE are computed using Fourier analysis and the fast Fourier transform (FFT) algorithm. The method is then extended to higher-order time discretizations of FBSDEs. Numerical results demonstrating convergence are presented using a commodity price model, incorporating seasonality, and forward prices.
For geospatial modelling and mapping tasks, variants of kriging - the spatial interpolation technique developed by South African mining engineer Danie Krige - have long been regarded as the established geostatistical methods. However, kriging and its variants (such as regression kriging, in which auxiliary variables or derivatives of these are included as covariates) are relatively restrictive models and lack capabilities that have been afforded to us in the last decade by deep neural networks. Principal among these is feature learning - the ability to learn filters to recognise task-specific patterns in gridded data such as images. Here we demonstrate the power of feature learning in a geostatistical context, by showing how deep neural networks can automatically learn the complex relationships between point-sampled target variables and gridded auxiliary variables (such as those provided by remote sensing), and in doing so produce detailed maps of chosen target variables. At the same time, in order to cater for the needs of decision makers who require well-calibrated probabilities, we obtain uncertainty estimates via a Bayesian approximation known as Monte Carlo dropout. In our example, we produce a national-scale probabilistic geochemical map from point-sampled assay data, with auxiliary information provided by a terrain elevation grid. Unlike traditional geostatistical approaches, auxiliary variable grids are fed into our deep neural network raw. There is no need to provide terrain derivatives (e.g. slope angles, roughness, etc) because the deep neural network is capable of learning these and arbitrarily more complex derivatives as necessary to maximise predictive performance. We hope our results will raise awareness of the suitability of Bayesian deep learning - and its feature learning capabilities - for large-scale geostatistical applications where uncertainty matters.
Machine learning is gaining popularity in a broad range of areas working with geographic data, such as ecology or atmospheric sciences. Here, data often exhibit spatial effects, which can be difficult to learn for neural networks. In this study, we propose SXL, a method for embedding information on the autoregressive nature of spatial data directly into the learning process using auxiliary tasks. We utilize the local Moran's I, a popular measure of local spatial autocorrelation, to "nudge" the model to learn the direction and magnitude of local spatial effects, complementing the learning of the primary task. We further introduce a novel expansion of Moran's I to multiple resolutions, thus capturing spatial interactions over longer and shorter distances simultaneously. The novel multi-resolution Moran's I can be constructed easily and as a multi-dimensional tensor offers seamless integration into existing machine learning frameworks. Throughout a range of experiments using real-world data, we highlight how our method consistently improves the training of neural networks in unsupervised and supervised learning tasks. In generative spatial modeling experiments, we propose a novel loss for auxiliary task GANs utilizing task uncertainty weights. Our proposed method outperforms domain-specific spatial interpolation benchmarks, highlighting its potential for downstream applications. This study bridges expertise from geographic information science and machine learning, showing how this integration of disciplines can help to address domain-specific challenges. The code for our experiments is available on Github: https://github.com/konstantinklemmer/sxl.
The large volumes of Sentinel-1 data produced over Europe are being used to develop pan-national ground motion services. However, simple analysis techniques like thresholding cannot detect and classify complex deformation signals reliably making providing usable information to a broad range of non-expert stakeholders a challenge. Here we explore the applicability of deep learning approaches by adapting a pre-trained convolutional neural network (CNN) to detect deformation in a national-scale velocity field. For our proof-of-concept, we focus on the UK where previously identified deformation is associated with coal-mining, ground water withdrawal, landslides and tunnelling. The sparsity of measurement points and the presence of spike noise make this a challenging application for deep learning networks, which involve calculations of the spatial convolution between images. Moreover, insufficient ground truth data exists to construct a balanced training data set, and the deformation signals are slower and more localised than in previous applications. We propose three enhancement methods to tackle these problems: i) spatial interpolation with modified matrix completion, ii) a synthetic training dataset based on the characteristics of real UK velocity map, and iii) enhanced over-wrapping techniques. Using velocity maps spanning 2015-2019, our framework detects several areas of coal mining subsidence, uplift due to dewatering, slate quarries, landslides and tunnel engineering works. The results demonstrate the potential applicability of the proposed framework to the development of automated ground motion analysis systems.
Example-guided image synthesis has recently been attempted to synthesize an image from a semantic label map and an exemplary image. In the task, the additional exemplar image provides the style guidance that controls the appearance of the synthesized output. Despite the controllability advantage, the existing models are designed on datasets with specific and roughly aligned objects. In this paper, we tackle a more challenging and general task, where the exemplar is an arbitrary scene image that is semantically different from the given label map. To this end, we first propose a Masked Spatial-Channel Attention (MSCA) module which models the correspondence between two arbitrary scenes via efficient decoupled attention. Next, we propose an end-to-end network for joint global and local feature alignment and synthesis. Finally, we propose a novel self-supervision task to enable training. Experiments on the large-scale and more diverse COCO-stuff dataset show significant improvements over the existing methods. Moreover, our approach provides interpretability and can be readily extended to other content manipulation tasks including style and spatial interpolation or extrapolation.
Stochastic processes provide a mathematically elegant way model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. In practice, however, efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($\pi$VAE). The $\pi$VAE is finitely exchangeable and Kolmogorov consistent, and thus is a continuous stochastic process. We use $\pi$VAE to learn low dimensional embeddings of function classes. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions to enable statistical inference (such as the integral of a log Gaussian process). For popular tasks, such as spatial interpolation, $\pi$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate that the low dimensional independently distributed latent space representation learnt provides an elegant and scalable means of performing Bayesian inference for stochastic processes within probabilistic programming languages such as Stan.
Example-guided image synthesis has been recently attempted to synthesize an image from a semantic label map and an exemplary image. In the task, the additional exemplary image serves to provide style guidance that controls the appearance of the synthesized output. Despite the controllability advantage, the previous models are designed on datasets with specific and roughly aligned objects. In this paper, we tackle a more challenging and general task, where the exemplar is an arbitrary scene image that is semantically unaligned to the given label map. To this end, we first propose a new Masked Spatial-Channel Attention (MSCA) module which models the correspondence between two unstructured scenes via cross-attention. Next, we propose an end-to-end network for joint global and local feature alignment and synthesis. In addition, we propose a novel patch-based self-supervision scheme to enable training. Experiments on the large-scale CCOO-stuff dataset show significant improvements over existing methods. Moreover, our approach provides interpretability and can be readily extended to other tasks including style and spatial interpolation or extrapolation, as well as other content manipulation.
Despite the long history of image and video stitching research, existing academic and commercial solutions still produce strong artifacts. In this work, we propose a wide-baseline video stitching algorithm for linear camera arrays that is temporally stable and tolerant to strong parallax. Our key insight is that stitching can be cast as a problem of learning a smooth spatial interpolation between the input videos. To solve this problem, inspired by pushbroom cameras, we introduce a fast pushbroom interpolation layer and propose a novel pushbroom stitching network, which learns a dense flow field to smoothly align the multiple input videos for spatial interpolation. Our approach outperforms the state-of-the-art by a significant margin, as we show with a user study, and has immediate applications in many areas such as virtual reality, immersive telepresence, autonomous driving, and video surveillance.
We propose a novel single-image super-resolution approach based on the geostatistical method of kriging. Kriging is a zero-bias minimum-variance estimator that performs spatial interpolation based on a weighted average of known observations. Rather than solving for the kriging weights via the traditional method of inverting covariance matrices, we propose a supervised form in which we learn a deep network to generate said weights. We combine the kriging weight generation and kriging process into a joint network that can be learned end-to-end. Our network achieves competitive super-resolution results as other state-of-the-art methods. In addition, since the super-resolution process follows a known statistical framework, we are able to estimate bias and variance, something which is rarely possible for other deep networks.
High resolution depth-maps, obtained by upsampling sparse range data from a 3D-LIDAR, find applications in many fields ranging from sensory perception to semantic segmentation and object detection. Upsampling is often based on combining data from a monocular camera to compensate the low-resolution of a LIDAR. This paper, on the other hand, introduces a novel framework to obtain dense depth-map solely from a single LIDAR point cloud; which is a research direction that has been barely explored. The formulation behind the proposed depth-mapping process relies on local spatial interpolation, using sliding-window (mask) technique, and on the Bilateral Filter (BF) where the variable of interest, the distance from the sensor, is considered in the interpolation problem. In particular, the BF is conveniently modified to perform depth-map upsampling such that the edges (foreground-background discontinuities) are better preserved by means of a proposed method which influences the range-based weighting term. Other methods for spatial upsampling are discussed, evaluated and compared in terms of different error measures. This paper also researches the role of the mask's size in the performance of the implemented methods. Quantitative and qualitative results from experiments on the KITTI Database, using LIDAR point clouds only, show very satisfactory performance of the approach introduced in this work.
Maps of infectious disease---charting spatial variations in the force of infection, degree of endemicity, and the burden on human health---provide an essential evidence base to support planning towards global health targets. Contemporary disease mapping efforts have embraced statistical modelling approaches to properly acknowledge uncertainties in both the available measurements and their spatial interpolation. The most common such approach is that of Gaussian process regression, a mathematical framework comprised of two components: a mean function harnessing the predictive power of multiple independent variables, and a covariance function yielding spatio-temporal shrinkage against residual variation from the mean. Though many techniques have been developed to improve the flexibility and fitting of the covariance function, models for the mean function have typically been restricted to simple linear terms. For infectious diseases, known to be driven by complex interactions between environmental and socio-economic factors, improved modelling of the mean function can greatly boost predictive power. Here we present an ensemble approach based on stacked generalisation that allows for multiple, non-linear algorithmic mean functions to be jointly embedded within the Gaussian process framework. We apply this method to mapping Plasmodium falciparum prevalence data in Sub-Saharan Africa and show that the generalised ensemble approach markedly out-performs any individual method.
An important problem in geostatistics is to build models of the subsurface of the Earth given physical measurements at sparse spatial locations. Typically, this is done using spatial interpolation methods or by reproducing patterns from a reference image. However, these algorithms fail to produce realistic patterns and do not exhibit the wide range of uncertainty inherent in the prediction of geology. In this paper, we show how semantic inpainting with Generative Adversarial Networks can be used to generate varied realizations of geology which honor physical measurements while matching the expected geological patterns. In contrast to other algorithms, our method scales well with the number of data points and mimics a distribution of patterns as opposed to a single pattern or image. The generated conditional samples are state of the art.
The UN Sustainable Development Goals allude to the importance of infrastructure quality in three of its seventeen goals. However, monitoring infrastructure quality in developing regions remains prohibitively expensive and impedes efforts to measure progress toward these goals. To this end, we investigate the use of widely available remote sensing data for the prediction of infrastructure quality in Africa. We train a convolutional neural network to predict ground truth labels from the Afrobarometer Round 6 survey using Landsat 8 and Sentinel 1 satellite imagery. Our best models predict infrastructure quality with AUROC scores of 0.881 on Electricity, 0.862 on Sewerage, 0.739 on Piped Water, and 0.786 on Roads using Landsat 8. These performances are significantly better than models that leverage OpenStreetMap or nighttime light intensity on the same tasks. We also demonstrate that our trained model can accurately make predictions in an unseen country after fine-tuning on a small sample of images. Furthermore, the model can be deployed in regions with limited samples to predict infrastructure outcomes with higher performance than nearest neighbor spatial interpolation.