Graph-based two-sample tests and graph-based change-point detection that utilize similarity graphs provide powerful tools for analyzing high-dimensional and non-Euclidean data as these methods do not impose distributional assumptions and have good performance across various scenarios. Current graph-based tests that deliver efficacy across a broad spectrum of alternatives typically reply on the $K$-nearest neighbor graph or the $K$-minimum spanning tree. However, these graphs can be vulnerable for high-dimensional data due to the curse of dimensionality. To mitigate this issue, we propose to use a robust graph that is considerably less influenced by the curse of dimensionality. We also establish a theoretical foundation for graph-based methods utilizing this proposed robust graph and demonstrate its consistency under fixed alternatives for both low-dimensional and high-dimensional data.
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Three-dimensional facial stereophotogrammetry provides a detailed representation of craniofacial soft tissue without the use of ionizing radiation. While manual annotation of landmarks serves as the current gold standard for cephalometric analysis, it is a time-consuming process and is prone to human error. The aim in this study was to develop and evaluate an automated cephalometric annotation method using a deep learning-based approach. Ten landmarks were manually annotated on 2897 3D facial photographs by a single observer. The automated landmarking workflow involved two successive DiffusionNet models and additional algorithms for facial segmentation. The dataset was randomly divided into a training and test dataset. The training dataset was used to train the deep learning networks, whereas the test dataset was used to evaluate the performance of the automated workflow. The precision of the workflow was evaluated by calculating the Euclidean distances between the automated and manual landmarks and compared to the intra-observer and inter-observer variability of manual annotation and the semi-automated landmarking method. The workflow was successful in 98.6% of all test cases. The deep learning-based landmarking method achieved precise and consistent landmark annotation. The mean precision of 1.69 (+/-1.15) mm was comparable to the inter-observer variability (1.31 +/-0.91 mm) of manual annotation. The Euclidean distance between the automated and manual landmarks was within 2 mm in 69%. Automated landmark annotation on 3D photographs was achieved with the DiffusionNet-based approach. The proposed method allows quantitative analysis of large datasets and may be used in diagnosis, follow-up, and virtual surgical planning.
Diffusion-based generative models have recently gained attention in speech enhancement (SE), providing an alternative to conventional supervised methods. These models transform clean speech training samples into Gaussian noise centered at noisy speech, and subsequently learn a parameterized model to reverse this process, conditionally on noisy speech. Unlike supervised methods, generative-based SE approaches usually rely solely on an unsupervised loss, which may result in less efficient incorporation of conditioned noisy speech. To address this issue, we propose augmenting the original diffusion training objective with a mean squared error (MSE) loss, measuring the discrepancy between estimated enhanced speech and ground-truth clean speech at each reverse process iteration. Experimental results demonstrate the effectiveness of our proposed methodology.
Recently, conditional score-based diffusion models have gained significant attention in the field of supervised speech enhancement, yielding state-of-the-art performance. However, these methods may face challenges when generalising to unseen conditions. To address this issue, we introduce an alternative approach that operates in an unsupervised manner, leveraging the generative power of diffusion models. Specifically, in a training phase, a clean speech prior distribution is learnt in the short-time Fourier transform (STFT) domain using score-based diffusion models, allowing it to unconditionally generate clean speech from Gaussian noise. Then, we develop a posterior sampling methodology for speech enhancement by combining the learnt clean speech prior with a noise model for speech signal inference. The noise parameters are simultaneously learnt along with clean speech estimation through an iterative expectationmaximisation (EM) approach. To the best of our knowledge, this is the first work exploring diffusion-based generative models for unsupervised speech enhancement, demonstrating promising results compared to a recent variational auto-encoder (VAE)-based unsupervised approach and a state-of-the-art diffusion-based supervised method. It thus opens a new direction for future research in unsupervised speech enhancement.
We evaluate using Julia as a single language and ecosystem paradigm powered by LLVM to develop workflow components for high-performance computing. We run a Gray-Scott, 2-variable diffusion-reaction application using a memory-bound, 7-point stencil kernel on Frontier, the US Department of Energy's first exascale supercomputer. We evaluate the feasibility, performance, scaling, and trade-offs of (i) the computational kernel on AMD's MI250x GPUs, (ii) weak scaling up to 4,096 MPI processes/GPUs or 512 nodes, (iii) parallel I/O writes using the ADIOS2 library bindings, and (iv) Jupyter Notebooks for interactive data analysis. Our results suggest that although Julia generates a reasonable LLVM-IR kernel, a nearly 50\% performance difference exists vs. native AMD HIP stencil codes when running on the GPUs. As expected, we observed near-zero overhead when using MPI and parallel I/O bindings for system-wide installed implementations. Consequently, Julia emerges as a compelling high-performance and high-productivity workflow composition strategy, as measured on the fastest supercomputer in the world.
Recent span-based joint extraction models have demonstrated significant advantages in both entity recognition and relation extraction. These models treat text spans as candidate entities, and span pairs as candidate relationship tuples, achieving state-of-the-art results on datasets like ADE. However, these models encounter a significant number of non-entity spans or irrelevant span pairs during the tasks, impairing model performance significantly. To address this issue, this paper introduces a span-based multitask entity-relation joint extraction model. This approach employs the multitask learning to alleviate the impact of negative samples on entity and relation classifiers. Additionally, we leverage the Intersection over Union(IoU) concept to introduce the positional information into the entity classifier, achieving a span boundary detection. Furthermore, by incorporating the entity Logits predicted by the entity classifier into the embedded representation of entity pairs, the semantic input for the relation classifier is enriched. Experimental results demonstrate that our proposed SpERT.MT model can effectively mitigate the adverse effects of excessive negative samples on the model performance. Furthermore, the model demonstrated commendable F1 scores of 73.61\%, 53.72\%, and 83.72\% on three widely employed public datasets, namely CoNLL04, SciERC, and ADE, respectively.
We present a nonparametric graphical model. Our model uses an undirected graph that represents conditional independence for general random variables defined by the conditional dependence coefficient (Azadkia and Chatterjee (2021)). The set of edges of the graph are defined as $E=\{(i,j):R_{i,j}\neq 0\}$, where $R_{i,j}$ is the conditional dependence coefficient for $X_i$ and $X_j$ given $(X_1,\ldots,X_p) \backslash \{X_{i},X_{j}\}$. We propose a graph structure learning by two steps selection procedure: first, we compute the matrix of sample version of the conditional dependence coefficient $\widehat{R_{i,j}}$; next, for some prespecificated threshold $\lambda>0$ we choose an edge $\{i,j\}$ if $ \left|\widehat{R_{i,j}} \right| \geq \lambda.$ The graph recovery structure has been evaluated on artificial and real datasets. We also applied a slight modification of our graph recovery procedure for learning partial correlation graphs for the elliptical distribution.
A change point detection (CPD) framework assisted by a predictive machine learning model called "Predict and Compare" is introduced and characterised in relation to other state-of-the-art online CPD routines which it outperforms in terms of false positive rate and out-of-control average run length. The method's focus is on improving standard methods from sequential analysis such as the CUSUM rule in terms of these quality measures. This is achieved by replacing typically used trend estimation functionals such as the running mean with more sophisticated predictive models (Predict step), and comparing their prognosis with actual data (Compare step). The two models used in the Predict step are the ARIMA model and the LSTM recursive neural network. However, the framework is formulated in general terms, so as to allow the use of other prediction or comparison methods than those tested here. The power of the method is demonstrated in a tribological case study in which change points separating the run-in, steady-state, and divergent wear phases are detected in the regime of very few false positives.
In this paper, we discuss a general framework for multicontinuum homogenization. Multicontinuum models are widely used in many applications and some derivations for these models are established. In these models, several macroscopic variables at each macroscale point are defined and the resulting multicontinuum equations are formulated. In this paper, we propose a general formulation and associated ingredients that allow performing multicontinuum homogenization. Our derivation consists of several main parts. In the first part, we propose a general expansion, where the solution is expressed via the product of multiple macro variables and associated cell problems. The second part consists of formulating the cell problems. The cell problems are formulated as saddle point problems with constraints for each continua. Defining the continua via test functions, we set the constraints as an integral representation. Finally, substituting the expansion to the original system, we obtain multicontinuum systems. We present an application to the mixed formulation of elliptic equations. This is a challenging system as the system does not have symmetry. We discuss the local problems and various macroscale representations for the solution and its gradient. Using various order approximations, one can obtain different systems of equations. We discuss the applicability of multicontinuum homogenization and relate this to high contrast in the cell problem. Numerical results are presented.
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.
Machine-learning models have demonstrated great success in learning complex patterns that enable them to make predictions about unobserved data. In addition to using models for prediction, the ability to interpret what a model has learned is receiving an increasing amount of attention. However, this increased focus has led to considerable confusion about the notion of interpretability. In particular, it is unclear how the wide array of proposed interpretation methods are related, and what common concepts can be used to evaluate them. We aim to address these concerns by defining interpretability in the context of machine learning and introducing the Predictive, Descriptive, Relevant (PDR) framework for discussing interpretations. The PDR framework provides three overarching desiderata for evaluation: predictive accuracy, descriptive accuracy and relevancy, with relevancy judged relative to a human audience. Moreover, to help manage the deluge of interpretation methods, we introduce a categorization of existing techniques into model-based and post-hoc categories, with sub-groups including sparsity, modularity and simulatability. To demonstrate how practitioners can use the PDR framework to evaluate and understand interpretations, we provide numerous real-world examples. These examples highlight the often under-appreciated role played by human audiences in discussions of interpretability. Finally, based on our framework, we discuss limitations of existing methods and directions for future work. We hope that this work will provide a common vocabulary that will make it easier for both practitioners and researchers to discuss and choose from the full range of interpretation methods.
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