This work presents the analysis of semantically segmented, longitudinally, and spatially rich thermal images collected at the neighborhood scale to identify hot and cool spots in urban areas. An infrared observatory was operated over a few months to collect thermal images of different types of buildings on the educational campus of the National University of Singapore. A subset of the thermal image dataset was used to train state-of-the-art deep learning models to segment various urban features such as buildings, vegetation, sky, and roads. It was observed that the U-Net segmentation model with `resnet34' CNN backbone has the highest mIoU score of 0.99 on the test dataset, compared to other models such as DeepLabV3, DeeplabV3+, FPN, and PSPnet. The masks generated using the segmentation models were then used to extract the temperature from thermal images and correct for differences in the emissivity of various urban features. Further, various statistical measure of the temperature extracted using the predicted segmentation masks is shown to closely match the temperature extracted using the ground truth masks. Finally, the masks were used to identify hot and cool spots in the urban feature at various instances of time. This forms one of the very few studies demonstrating the automated analysis of thermal images, which can be of potential use to urban planners for devising mitigation strategies for reducing the urban heat island (UHI) effect, improving building energy efficiency, and maximizing outdoor thermal comfort.
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In Radhakrishnan et al. [2020], the authors empirically show that autoencoders trained with usual SGD methods shape out basins of attraction around their training data. We consider network functions of width not exceeding the input dimension and prove that in this situation basins of attraction are bounded and their complement cannot have bounded components. Our conditions in these results are met in several experiments of the latter work and we thus address a question posed therein. We also show that under some more restrictive conditions the basins of attraction are path-connected. The tightness of the conditions in our results is demonstrated by means of several examples. Finally, the arguments used to prove the above results allow us to derive a root cause why scalar-valued neural network functions that fulfill our bounded width condition are not dense in spaces of continuous functions.
With advances in scientific computing and mathematical modeling, complex scientific phenomena such as galaxy formations and rocket propulsion can now be reliably simulated. Such simulations can however be very time-intensive, requiring millions of CPU hours to perform. One solution is multi-fidelity emulation, which uses data of different fidelities to train an efficient predictive model which emulates the expensive simulator. For complex scientific problems and with careful elicitation from scientists, such multi-fidelity data may often be linked by a directed acyclic graph (DAG) representing its scientific model dependencies. We thus propose a new Graphical Multi-fidelity Gaussian Process (GMGP) model, which embeds this DAG structure (capturing scientific dependencies) within a Gaussian process framework. We show that the GMGP has desirable modeling traits via two Markov properties, and admits a scalable algorithm for recursive computation of the posterior mean and variance along at each depth level of the DAG. We also present a novel experimental design methodology over the DAG given an experimental budget, and propose a nonlinear extension of the GMGP via deep Gaussian processes. The advantages of the GMGP are then demonstrated via a suite of numerical experiments and an application to emulation of heavy-ion collisions, which can be used to study the conditions of matter in the Universe shortly after the Big Bang. The proposed model has broader uses in data fusion applications with graphical structure, which we further discuss.
This paper addresses the problem of estimating entropy-regularized optimal transport (EOT) maps with squared-Euclidean cost between source and target measures that are subGaussian. In the case that the target measure is compactly supported or strongly log-concave, we show that for a recently proposed in-sample estimator, the expected squared $L^2$-error decays at least as fast as $O(n^{-1/3})$ where $n$ is the sample size. For the general subGaussian case we show that the expected $L^1$-error decays at least as fast as $O(n^{-1/6})$, and in both cases we have polynomial dependence on the regularization parameter. While these results are suboptimal compared to known results in the case of compactness of both the source and target measures (squared $L^2$-error converging at a rate $O(n^{-1})$) and for when the source is subGaussian while the target is compactly supported (squared $L^2$-error converging at a rate $O(n^{-1/2})$), their importance lie in eliminating the compact support requirements. The proof technique makes use of a bias-variance decomposition where the variance is controlled using standard concentration of measure results and the bias is handled by T1-transport inequalities along with sample complexity results in estimation of EOT cost under subGaussian assumptions. Our experimental results point to a looseness in controlling the variance terms and we conclude by posing several open problems.
Through the use of cutting-edge unsupervised classification techniques from statistics and machine learning, we characterise symptom phenotypes among symptomatic SARS-CoV-2 PCR-positive community cases. We first analyse each dataset in isolation and across age bands, before using methods that allow us to compare multiple datasets. While we observe separation due to the total number of symptoms experienced by cases, we also see a separation of symptoms into gastrointestinal, respiratory and other types, and different symptom co-occurrence patterns at the extremes of age. In this way, we are able to demonstrate the deep structure of symptoms of COVID-19 without usual biases due to study design. This is expected to have implications for the identification and management of community SARS-CoV-2 cases and could be further applied to symptom-based management of other diseases and syndromes.
Recently, there has been an upsurge in the research on maritime vision, where a lot of works are influenced by the application of computer vision for Unmanned Surface Vehicles (USVs). Various sensor modalities such as camera, radar, and lidar have been used to perform tasks such as object detection, segmentation, object tracking, and motion planning. A large subset of this research is focused on the video analysis, since most of the current vessel fleets contain the camera's onboard for various surveillance tasks. Due to the vast abundance of the video data, video scene change detection is an initial and crucial stage for scene understanding of USVs. This paper outlines our approach to detect dynamic scene changes in USVs. To the best of our understanding, this work represents the first investigation of scene change detection in the maritime vision application. Our objective is to identify significant changes in the dynamic scenes of maritime video data, particularly those scenes that exhibit a high degree of resemblance. In our system for dynamic scene change detection, we propose completely unsupervised learning method. In contrast to earlier studies, we utilize a modified cutting-edge generative picture model called VQ-VAE-2 to train on multiple marine datasets, aiming to enhance the feature extraction. Next, we introduce our innovative similarity scoring technique for directly calculating the level of similarity in a sequence of consecutive frames by utilizing grid calculation on retrieved features. The experiments were conducted using a nautical video dataset called RoboWhaler to showcase the efficient performance of our technique.
This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped sample covariance matrix under mild conditions. After bootstrap, the spiked eigenvalues which are driven by common factors will converge weakly to Gaussian limits after proper scaling and centralization. However, the largest non-spiked eigenvalue is mainly determined by the order statistics of the bootstrap resampling weights, and follows extreme value distribution. Based on the disparate behavior of the spiked and non-spiked eigenvalues, we propose innovative methods to test the number of common factors. Indicated by extensive numerical and empirical studies, the proposed methods perform reliably and convincingly under the existence of both weak factors and cross-sectionally correlated errors. Our technical details contribute to random matrix theory on spiked covariance model with convexly decaying density and unbounded support, or with general elliptical distributions.
Heterogeneous computing and exploiting integrated CPU-GPU architectures has become a clear current trend since the flattening of Moore's Law. In this work, we propose a numerical and algorithmic re-design of a p-adaptive quadrature-free discontinuous Galerkin method (DG) for the shallow water equations (SWE). Our new approach separates the computations of the non-adaptive (lower-order) and adaptive (higher-order) parts of the discretization form each other. Thereby, we can overlap computations of the lower-order and the higher-order DG solution components. Furthermore, we investigate execution times of main computational kernels and use automatic code generation to optimize their distribution between the CPU and GPU. Several setups, including a prototype of a tsunami simulation in a tide-driven flow scenario, are investigated, and the results show that significant performance improvements can be achieved in suitable setups.
The task of simplifying the complex spatio-temporal variables associated with climate modeling is of utmost importance and comes with significant challenges. In this research, our primary objective is to tailor clustering techniques to handle compound extreme events within gridded climate data across Europe. Specifically, we intend to identify subregions that display asymptotic independence concerning compound precipitation and wind speed extremes. To achieve this, we utilise daily precipitation sums and daily maximum wind speed data derived from the ERA5 reanalysis dataset spanning from 1979 to 2022. Our approach hinges on a tuning parameter and the application of a divergence measure to spotlight disparities in extremal dependence structures without relying on specific parametric assumptions. We propose a data-driven approach to determine the tuning parameter. This enables us to generate clusters that are spatially concentrated, which can provide more insightful information about the regional distribution of compound precipitation and wind speed extremes. In the process, we aim to elucidate the respective roles of extreme precipitation and wind speed in the resulting clusters. The proposed method is able to extract valuable information about extreme compound events while also significantly reducing the size of the dataset within reasonable computational timeframes.
We study the stability of the Lanczos algorithm run on problems whose eigenvector empirical spectral distribution is near to a reference measure with well-behaved orthogonal polynomials. We give a backwards stability result which can be upgraded to a forward stability result when the reference measure has a density supported on a single interval with square root behavior at the endpoints. Our analysis implies the Lanczos algorithm run on many large random matrix models is in fact forward stable, and hence nearly deterministic, even when computations are carried out in finite precision arithmetic. Since the Lanczos algorithm is not forward stable in general, this provides yet another example of the fact that random matrices are far from "any old matrix", and care must be taken when using them to test numerical algorithms.
Despite the increasing use of deep learning in medical image segmentation, acquiring sufficient training data remains a challenge in the medical field. In response, data augmentation techniques have been proposed; however, the generation of diverse and realistic medical images and their corresponding masks remains a difficult task, especially when working with insufficient training sets. To address these limitations, we present an end-to-end architecture based on the Hamiltonian Variational Autoencoder (HVAE). This approach yields an improved posterior distribution approximation compared to traditional Variational Autoencoders (VAE), resulting in higher image generation quality. Our method outperforms generative adversarial architectures under data-scarce conditions, showcasing enhancements in image quality and precise tumor mask synthesis. We conduct experiments on two publicly available datasets, MICCAI's Brain Tumor Segmentation Challenge (BRATS), and Head and Neck Tumor Segmentation Challenge (HECKTOR), demonstrating the effectiveness of our method on different medical imaging modalities.
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