Gaussian Processes (GPs) are vital for modeling and predicting irregularly-spaced, large geospatial datasets. However, their computations often pose significant challenges in large-scale applications. One popular method to approximate GPs is the Vecchia approximation, which approximates the full likelihood via a series of conditional probabilities. The classical Vecchia approximation uses univariate conditional distributions, which leads to redundant evaluations and memory burdens. To address this challenge, our study introduces block Vecchia, which evaluates each multivariate conditional distribution of a block of observations, with blocks formed using the K-means algorithm. The proposed GPU framework for the block Vecchia uses varying batched linear algebra operations to compute multivariate conditional distributions concurrently, notably diminishing the frequent likelihood evaluations. Diving into the factor affecting the accuracy of the block Vecchia, the neighbor selection criterion is investigated, where we found that the random ordering markedly enhances the approximated quality as the block count becomes large. To verify the scalability and efficiency of the algorithm, we conduct a series of numerical studies and simulations, demonstrating their practical utility and effectiveness compared to the exact GP. Moreover, we tackle large-scale real datasets using the block Vecchia method, i.e., high-resolution 3D profile wind speed with a million points.
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There is an urgent need to identify both short and long-term risks from newly emerging types of Artificial Intelligence (AI), as well as available risk management measures. In response, and to support global efforts in regulating AI and writing safety standards, we compile an extensive catalog of risk sources and risk management measures for general-purpose AI (GPAI) systems, complete with descriptions and supporting examples where relevant. This work involves identifying technical, operational, and societal risks across model development, training, and deployment stages, as well as surveying established and experimental methods for managing these risks. To the best of our knowledge, this paper is the first of its kind to provide extensive documentation of both GPAI risk sources and risk management measures that are descriptive, self-contained and neutral with respect to any existing regulatory framework. This work intends to help AI providers, standards experts, researchers, policymakers, and regulators in identifying and mitigating systemic risks from GPAI systems. For this reason, the catalog is released under a public domain license for ease of direct use by stakeholders in AI governance and standards.
Monitored Natural Attenuation (MNA) is gaining prominence as an effective method for managing soil and groundwater contamination due to its cost-efficiency and minimal environmental disruption. Despite its benefits, MNA necessitates extensive groundwater monitoring to ensure that contaminant levels decrease to meet safety standards. This study expands the capabilities of PyLEnM, a Python package designed for long-term environmental monitoring, by incorporating new algorithms to enhance its predictive and analytical functionalities. We introduce methods to estimate the timeframe required for contaminants like Sr-90 and I-129 to reach regulatory safety standards using linear regression and to forecast future contaminant levels with the Bidirectional Long Short-Term Memory (Bi-LSTM) networks. Additionally, Random Forest regression is employed to identify factors influencing the time to reach safety standards. Our methods are illustrated using data from the Savannah River Site (SRS) F-Area, where preliminary findings reveal a notable downward trend in contaminant levels, with variability linked to initial concentrations and groundwater flow dynamics. The Bi-LSTM model effectively predicts contaminant concentrations for the next four years, demonstrating the potential of advanced time series analysis to improve MNA strategies and reduce reliance on manual groundwater sampling. The code, along with its usage instructions, validation, and requirements, is available at: //github.com/csplevuanh/pylenm_extension.
Deep neural network approaches show promise in solving partial differential equations. However, unlike traditional numerical methods, they face challenges in enforcing essential boundary conditions. The widely adopted penalty-type methods, for example, offer a straightforward implementation but introduces additional complexity due to the need for hyper-parameter tuning; moreover, the use of a large penalty parameter can lead to artificial extra stiffness, complicating the optimization process. In this paper, we propose a novel, intrinsic approach to impose essential boundary conditions through a framework inspired by intrinsic structures. We demonstrate the effectiveness of this approach using the deep Ritz method applied to Poisson problems, with the potential for extension to more general equations and other deep learning techniques. Numerical results are provided to substantiate the efficiency and robustness of the proposed method.
The Yang and Prentice (YP) regression models have garnered interest from the scientific community due to their ability to analyze data whose survival curves exhibit intersection. These models include proportional hazards (PH) and proportional odds (PO) models as specific cases. However, they encounter limitations when dealing with multivariate survival data due to potential dependencies between the times-to-event. A solution is introducing a frailty term into the hazard functions, making it possible for the times-to-event to be considered independent, given the frailty term. In this study, we propose a new class of YP models that incorporate frailty. We use the exponential distribution, the piecewise exponential distribution (PE), and Bernstein polynomials (BP) as baseline functions. Our approach adopts a Bayesian methodology. The proposed models are evaluated through a simulation study, which shows that the YP frailty models with BP and PE baselines perform similarly to the generator parametric model of the data. We apply the models in two real data sets.
Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the distributions of given graphs and generating more novel graphs. Owing to their wide range of applications, generative models for graphs, which have a rich history, however, are traditionally hand-crafted and only capable of modeling a few statistical properties of graphs. Recent advances in deep generative models for graph generation is an important step towards improving the fidelity of generated graphs and paves the way for new kinds of applications. This article provides an extensive overview of the literature in the field of deep generative models for graph generation. Firstly, the formal definition of deep generative models for the graph generation and the preliminary knowledge are provided. Secondly, taxonomies of deep generative models for both unconditional and conditional graph generation are proposed respectively; the existing works of each are compared and analyzed. After that, an overview of the evaluation metrics in this specific domain is provided. Finally, the applications that deep graph generation enables are summarized and five promising future research directions are highlighted.
Recently, graph neural networks (GNNs) have been widely used for document classification. However, most existing methods are based on static word co-occurrence graphs without sentence-level information, which poses three challenges:(1) word ambiguity, (2) word synonymity, and (3) dynamic contextual dependency. To address these challenges, we propose a novel GNN-based sparse structure learning model for inductive document classification. Specifically, a document-level graph is initially generated by a disjoint union of sentence-level word co-occurrence graphs. Our model collects a set of trainable edges connecting disjoint words between sentences and employs structure learning to sparsely select edges with dynamic contextual dependencies. Graphs with sparse structures can jointly exploit local and global contextual information in documents through GNNs. For inductive learning, the refined document graph is further fed into a general readout function for graph-level classification and optimization in an end-to-end manner. Extensive experiments on several real-world datasets demonstrate that the proposed model outperforms most state-of-the-art results, and reveal the necessity to learn sparse structures for each document.
Graph Neural Networks (GNNs) are widely used for analyzing graph-structured data. Most GNN methods are highly sensitive to the quality of graph structures and usually require a perfect graph structure for learning informative embeddings. However, the pervasiveness of noise in graphs necessitates learning robust representations for real-world problems. To improve the robustness of GNN models, many studies have been proposed around the central concept of Graph Structure Learning (GSL), which aims to jointly learn an optimized graph structure and corresponding representations. Towards this end, in the presented survey, we broadly review recent progress of GSL methods for learning robust representations. Specifically, we first formulate a general paradigm of GSL, and then review state-of-the-art methods classified by how they model graph structures, followed by applications that incorporate the idea of GSL in other graph tasks. Finally, we point out some issues in current studies and discuss future directions.
Text in natural images is of arbitrary orientations, requiring detection in terms of oriented bounding boxes. Normally, a multi-oriented text detector often involves two key tasks: 1) text presence detection, which is a classification problem disregarding text orientation; 2) oriented bounding box regression, which concerns about text orientation. Previous methods rely on shared features for both tasks, resulting in degraded performance due to the incompatibility of the two tasks. To address this issue, we propose to perform classification and regression on features of different characteristics, extracted by two network branches of different designs. Concretely, the regression branch extracts rotation-sensitive features by actively rotating the convolutional filters, while the classification branch extracts rotation-invariant features by pooling the rotation-sensitive features. The proposed method named Rotation-sensitive Regression Detector (RRD) achieves state-of-the-art performance on three oriented scene text benchmark datasets, including ICDAR 2015, MSRA-TD500, RCTW-17 and COCO-Text. Furthermore, RRD achieves a significant improvement on a ship collection dataset, demonstrating its generality on oriented object detection.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
Image segmentation is considered to be one of the critical tasks in hyperspectral remote sensing image processing. Recently, convolutional neural network (CNN) has established itself as a powerful model in segmentation and classification by demonstrating excellent performances. The use of a graphical model such as a conditional random field (CRF) contributes further in capturing contextual information and thus improving the segmentation performance. In this paper, we propose a method to segment hyperspectral images by considering both spectral and spatial information via a combined framework consisting of CNN and CRF. We use multiple spectral cubes to learn deep features using CNN, and then formulate deep CRF with CNN-based unary and pairwise potential functions to effectively extract the semantic correlations between patches consisting of three-dimensional data cubes. Effective piecewise training is applied in order to avoid the computationally expensive iterative CRF inference. Furthermore, we introduce a deep deconvolution network that improves the segmentation masks. We also introduce a new dataset and experimented our proposed method on it along with several widely adopted benchmark datasets to evaluate the effectiveness of our method. By comparing our results with those from several state-of-the-art models, we show the promising potential of our method.
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