Explore the vast range of titles available.

Network embedding (NE) is playing a principal role in network mining, due to its ability to map nodes into efficient low-dimensional embedding vectors. However, two major limitations exist in state-of-the-art NE methods: role preservation and uncertainty modeling. Almost all previous methods represent a node into a point in space and focus on local structural information, i.e., neighborhood information. However, neighborhood information does not capture global structural information and point vector representation fails in modeling the uncertainty of node representations. In this paper, we propose a new NE framework, struc2gauss, which learns node representations in the space of Gaussian distributions and performs network embedding based on global structural information. struc2gauss first employs a given node similarity metric to measure the global structural information, then generates structural context for nodes and finally learns node representations via Gaussian embedding. Different structural similarity measures of networks and energy functions of Gaussian embedding are investigated. Experiments conducted on real-world networks demonstrate that struc2gauss effectively captures global structural information while state-of-the-art network embedding methods fail to, outperforms other methods on the structure-based clustering and classification task and provides more information on uncertainties of node representations.

Named entity recognition (NER) in few-shot scenarios plays a critical role in entity annotation for low-resource domains. However, existing methods are often limited to learning semantic features and intermediate representations specific to the source domain, which restricts their generalization capability when applied to unseen target domains and leads to prominent performance degradation. To address this issue, we propose a novel few-shot NER model based on contrastive learning. Specifically, the model enhances token representations through Gaussian distribution embedding and a self-attention mechanism, while adaptively optimizing the weighting parameters of the contrastive loss to achieve performance improvement. This design effectively mitigates overfitting and enhances the model’s generalization ability. Experiments on multiple datasets (including CoNLL2003, GUM, and Few-NERD) demonstrate that our approach achieves performance gains of 2.05% to 15.89% compared to state-of-the-art methods. These results confirm the effectiveness of our model in few-shot NER tasks and suggest its potential for broader application in low-resource information extraction scenarios.

Learning to Rank (L2R) methods that utilize machine learning techniques to solve the ranking problems have been widely studied in the field of information retrieval. Existing methods usually concatenate query and document features as training input, without explicit understanding of relevance between queries and documents, especially in pairwise based ranking approach. Thus, it is an interesting question whether we can devise an algorithm that effectively describes the relation between queries and documents to learn a better ranking model without incurring huge parameter costs. In this paper, we present a Gaussian Embedding model for Ranking (GERank), an architecture for co-embedding queries and documents, such that each query or document is represented by a Gaussian distribution with mean and variance. Our GERank optimizes an energy-based loss based on the pairwise ranking framework. Additionally, the KL-divergence is utilized to measure the relevance between queries and documents. Experimental results on two LETOR datasets and one TREC dataset demonstrate that our model obtains a remarkable improvement in the ranking performance compared with the state-of-the-art retrieval models.

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, for nonlinear predictions for nonGaussian 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 we capture the spatial dependence 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 has multiple advantages over Kriging for nonGaussian and nonstationary data. That is, it provides nonlinear predictions, and thus has smaller approximation errors. Furthermore, it does not require operations on covariance matrices, and thus is scalable for large data sets. With sufficiently many hidden neurons, the proposed method provides an optimal prediction in terms of model capacity. In addition, we quantify prediction uncertainties based on density prediction, without assuming a data distribution. Finally, we apply the method to PM2.5 concentrations across the continental United States.

A standard problem in uncertainty quantification and in computational statistics is the sampling of stationary Gaussian random fields with given covariance in a d-dimensional (physical) domain. In many applications it is sufficient to perform the sampling on a regular grid on a cube enclosing the physical domain, in which case the corresponding covariance matrix is nested block Toeplitz. After extension to a nested block circulant matrix, this can be diagonalized by FFT—the \"circulant embedding method.\" Provided the circulant matrix is positive definite, this provides a finite expansion of the field in terms of a deterministic basis, with coefficients given by i.i.d. standard normals. In this paper we prove, under mild conditions, that the positive definiteness of the circulant matrix is always guaranteed, provided the enclosing cube is sufficiently large. We examine in detail the case of the Matérn covariance, and prove (for fixed correlation length) that, as h₀ → 0, positive definiteness is guaranteed when the random field is sampled on a cube of size order $\\left( {1 + {\\upsilon ^{1/2}}\\log h_0^{ - 1}} \\right)$ times larger than the size of the physical domain. (Here h₀ is the mesh spacing of the regular grid and υ the Matérn smoothness parameter.) We show that the sampling cube can become smaller as the correlation length decreases when h₀ and υ are fixed. Our results are confirmed by numerical experiments. We prove several results about the decay of the eigenvalues of the circulant matrix. These lead to the conjecture, verified by numerical experiment, that they decay with the same rate as the Karhunen-Loeve eigenvalues of the covariance operator. The method analyzed here complements the numerical experiments for uncertainty quantification in porous media problems in an earlier paper by the same authors in J. Comput. Phys., 230 (2011), pp. 3668-3694.

Optimizing biobased foam formulations is challenging because experiments are costly and fast-to-measure surrogate properties occupy high-dimensional spaces. Bayesian optimization (BO) with Gaussian process regression (GPR) can guide data-efficient searches, but its performance depends on the dimensionality of the inputs. Here, we evaluate nonlinear dimensionality reduction (DR) methods, namely t-distributed stochastic neighbor embedding (t-SNE) and uniform manifold approximation and projection (UMAP), in comparison with principal component analysis (PCA) for biobased foam optimization. Using an existing dataset comprising 26 distinct methylcellulose-cellulose fiber foam formulations with rheological and mechanical measurements, we first train a Gaussian process (GP) on low-dimensional representations of rheological observables. BO is then applied in a single-step, non-sequential manner on this fixed dataset, to evaluate the quality of the latent representations and identify high-yield-stress regions. A second GP maps foam-formulation compositions to the reduced rheological coordinates, enabling reconstruction of candidate formulations in the composition space. Across all DR methods, BO identifies similar high-performing formulations achieving yield stress values comparable to the experimentally validated optimum. PCA acts as a baseline due to its deterministic and hyperparameter-free nature, while nonlinear methods can achieve comparable performance when appropriately tuned. These findings demonstrate that nonlinear DR-assisted BO provides a data-efficient framework for optimizing rheology-governed soft-matter materials.

Spatially resolved transcriptomics (SRT) technologies have significantly advanced biomedical research, but their data analysis remains challenging due to the discrete nature of the data and the high levels of noise, compounded by complex spatial dependencies. Here, we propose spaVAE, a dependency-aware, deep generative spatial variational autoencoder model that probabilistically characterizes count data while capturing spatial correlations. spaVAE introduces a hybrid embedding combining a Gaussian process prior with a Gaussian prior to explicitly capture spatial correlations among spots. It then optimizes the parameters of deep neural networks to approximate the distributions underlying the SRT data. With the approximated distributions, spaVAE can contribute to several analytical tasks that are essential for SRT data analysis, including dimensionality reduction, visualization, clustering, batch integration, denoising, differential expression, spatial interpolation, resolution enhancement and identification of spatially variable genes. Moreover, we have extended spaVAE to spaPeakVAE and spaMultiVAE to characterize spatial ATAC-seq (assay for transposase-accessible chromatin using sequencing) data and spatial multi-omics data, respectively. Using a dependency-aware deep generative framework, spaVAE efficiently models spatially resolved transcriptomics data and advances diverse analysis tasks. Following similar strategies, spaPeakVAE and spaMultiVAE enable spatial ATAC-seq data and spatial multi-omics data modeling and analysis, respectively.

Multistep prediction is an open challenge in many real-world systems for a long time. Despite the advantages of previous approaches, e.g., step-by-step iteration, they have some shortcomings, such as accumulated errors, high cost, and low interpretation. To this end, Gaussian process regression and delay embedding are used to create a combination framework, namely spatial–temporal mapping (STM). Delay embedding is employed to reconstruct an isomorphic dynamical structure with the original system through a single time series, which provides the fundamental architecture for multistep predictions (interpretation). Gaussian process regression is used to achieve predictions by identifying a mapping between the reconstructed dynamical structure and the original structure. This combination framework outputs multistep ahead predictions in a single step (low cost). We test the feasibility of STM for both model systems, including the 3-species ecology system, the Lorenz chaotic system, and the Rossler chaotic system, and several real-world systems, involving energy, finance, life science, and climate. STM framework outperforms traditional iterative approaches and has the potential for many other real-world systems.

Precisely perceiving the geometric and semantic properties of real-world 3D objects is crucial for the continued evolution of augmented reality and robotic applications. To this end, we present Foundation Model Embedded Gaussian Splatting (FMGS), which incorporates vision-language embeddings of foundation models into 3D Gaussian Splatting (GS). The key contribution of this work is an efficient method to reconstruct and represent 3D vision-language models. This is achieved by distilling feature maps generated from image-based foundation models into those rendered from our 3D model. To ensure high-quality rendering and fast training, we introduce a novel scene representation by integrating strengths from both GS and multi-resolution hash encodings (MHE). Our effective training procedure also introduces a pixel alignment loss that makes the rendered feature distance of same semantic entities close, following the pixel-level semantic boundaries. Our results demonstrate remarkable multi-view semantic consistency, facilitating diverse downstream tasks, beating state-of-the-art methods by 10.2 object detection, despite that we are 851 × faster for inference. This research explores the intersection of vision, language, and 3D scene representation, paving the way for enhanced scene understanding in uncontrolled real-world environments. We plan to release the code on the [project page] .

We develop a stochastic modeling approach based on spatial point processes of log-Gaussian Cox type for a collection of around 5000 landslide events provoked by a precipitation trigger in Sicily, Italy.Through the embedding into a hierarchical Bayesian estimation framework, we can use the integrated nested Laplace approximation methodology to make inference and obtain the posterior estimates of spatially distributed covariate and random effects. Several mapping units are useful to partition a given study area in landslide prediction studies. These units hierarchically subdivide the geographic space from the highest grid-based resolution to the stronger morphodynamic-oriented slope units. Here we integrate both mapping units into a single hierarchical model, by treating the landslide triggering locations as a random point pattern. This approach diverges fundamentally from the unanimously used presence–absence structure for areal units since we focus on modeling the expected landslide count jointly within the two mapping units. Predicting this landslide intensity provides more detailed and complete information as compared to the classically used susceptibility mapping approach based on relative probabilities. To illustrate the model’s versatility, we compute absolute probability maps of landslide occurrences and check their predictive power over space. While the landslide community typically produces spatial predictive models for landslides only in the sense that covariates are spatially distributed, no actual spatial dependence has been explicitly integrated so far. Our novel approach features a spatial latent effect defined at the slope unit level, allowing us to assess the spatial influence that remains unexplained by the covariates in the model. For rainfall-induced landslides in regions where the raingauge network is not sufficient to capture the spatial distribution of the triggering precipitation event, this latent effect provides valuable imaging support on the unobserved rainfall pattern.