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log-RRIM: Yield Prediction via Local-to-global Reaction Representation Learning and Interaction Modeling. log-RRIM:通过局部到全局反应表征学习和交互建模进行产量预测。
Pub Date : 2024-11-19
Xiao Hu, Ziqi Chen, Bo Peng, Daniel Adu-Ampratwum, Xia Ning

Accurate prediction of chemical reaction yields is crucial for optimizing organic synthesis, potentially reducing time and resources spent on experimentation. With the rise of artificial intelligence (AI), there is growing interest in leveraging AI-based methods to accelerate yield predictions without conducting in vitro experiments. We present log-RRIM, an innovative graph transformer-based framework designed for predicting chemical reaction yields. Our approach implements a unique local-to-global reaction representation learning strategy. This approach initially captures detailed molecule-level information and then models and aggregates intermolecular interactions, ensuring that the impact of varying-sizes molecular fragments on yield is accurately accounted for. Another key feature of log-RRIM is its integration of a cross-attention mechanism that focuses on the interplay between reagents and reaction centers. This design reflects a fundamental principle in chemical reactions: the crucial role of reagents in influencing bond-breaking and formation processes, which ultimately affect reaction yields. log-RRIM outperforms existing methods in our experiments, especially for medium to high-yielding reactions, proving its reliability as a predictor. Its advanced modeling of reactant-reagent interactions and sensitivity to small molecular fragments make it a valuable tool for reaction planning and optimization in chemical synthesis. The data and codes of log-RRIM are accessible through https://github.com/ninglab/YieldlogRRIM.

准确预测化学反应产率对于优化有机合成至关重要,有可能减少用于实验的时间和资源。随着人工智能(AI)的兴起,人们对利用基于 AI 的方法在不进行体外实验的情况下加快产率预测越来越感兴趣。我们介绍了 log-RRIM,这是一种基于图变换器的创新框架,旨在预测化学反应产率。我们的方法实施了一种独特的从局部到全局的反应表征学习策略。这种方法首先捕捉详细的分子级信息,然后对分子间的相互作用进行建模和聚合,从而确保准确考虑不同大小的分子片段对产率的影响。log-RRIM 的另一个主要特点是整合了交叉注意机制,重点关注试剂和反应中心之间的相互作用。这一设计反映了化学反应中的一个基本原理:试剂在影响键的断裂和形成过程中起着至关重要的作用,而键的断裂和形成过程最终会影响反应产率。在我们的实验中,尤其是在中高产率反应中,log-RRIM 的表现优于现有方法,这证明了它作为预测器的可靠性。其先进的反应物-试剂相互作用建模和对小分子片段的敏感性,使其成为化学合成中反应规划和优化的重要工具。log-RRIM 的数据和代码可通过 https://github.com/ninglab/Yield_log_RRIM 访问。
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引用次数: 0
Non-unique water and contrast agent solutions in dual-energy CT. 双能 CT 中的非独特水和造影剂溶液。
Pub Date : 2024-11-19
J P Phillips, Emil Y Sidky, Fatma Terzioglu, Ingrid S Reiser, Guillaume Bal, Xiaochuan Pan

The goal of this work is to study occurrences of non-unique solutions in dual-energy CT (DECT) for objects containing water and a contrast agent. Previous studies of the Jacobian of nonlinear systems identified that a vanishing Jacobian determinant indicates the existence of multiple solutions to the system. Vanishing Jacobian determinants are identified for DECT setups by simulating intensity data for practical thickness ranges of water and contrast agent. Once existence is identified, non-unique solutions are found by simulating scan data and finding intensity contours with that intersect multiple times. With this process non-unique solutions are found for DECT setups scanning iodine and gadolinium, including setups using tube potentials in practical ranges. Non-unique solutions demonstrate a large range of differences and can result in significant discrepancies between recovered and true material mapping.

这项工作的目的是研究含有水和造影剂的物体在双能量 CT(DECT)中出现的非唯一解。以前对非线性系统雅各布的研究发现,雅各布行列式的消失表明系统存在多个解决方案。通过模拟水和造影剂实际厚度范围的强度数据,可以确定 DECT 设置的消失雅各布行列式。一旦确定存在,就可以通过模拟扫描数据和寻找多次相交的强度等值线来找到非唯一解。通过这一过程,我们找到了扫描碘和钆的 DECT 设置的非唯一解,包括在实际范围内使用管电位的设置。非唯一解显示出很大范围的差异,并可能导致恢复的材料映射与真实材料映射之间的显著差异。
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引用次数: 0
Head and Neck Tumor Segmentation from [18F]F-FDG PET/CT Images Based on 3D Diffusion Model. 基于三维扩散模型的头颈部[18F]F-FDG PET/CT 图像的肿瘤分割。
Pub Date : 2024-11-19
Yafei Dong, Kuang Gong

Head and neck (H&N) cancers are among the most prevalent types of cancer worldwide, and [18F]F-FDG PET/CT is widely used for H&N cancer management. Recently, the diffusion model has demonstrated remarkable performance in various image-generation tasks. In this work, we proposed a 3D diffusion model to accurately perform H&N tumor segmentation from 3D PET and CT volumes. The 3D diffusion model was developed considering the 3D nature of PET and CT images acquired. During the reverse process, the model utilized a 3D UNet structure and took the concatenation of PET, CT, and Gaussian noise volumes as the network input to generate the tumor mask. Experiments based on the HECKTOR challenge dataset were conducted to evaluate the effectiveness of the proposed diffusion model. Several state-of-the-art techniques based on U-Net and Transformer structures were adopted as the reference methods. Benefits of employing both PET and CT as the network input as well as further extending the diffusion model from 2D to 3D were investigated based on various quantitative metrics and the uncertainty maps generated. Results showed that the proposed 3D diffusion model could generate more accurate segmentation results compared with other methods. Compared to the diffusion model in 2D format, the proposed 3D model yielded superior results. Our experiments also highlighted the advantage of utilizing dual-modality PET and CT data over only single-modality data for H&N tumor segmentation.

头颈部癌症是全球发病率最高的癌症类型之一,[18F]F-FDG PET/CT 被广泛应用于头颈部癌症的治疗。最近,扩散模型在各种图像生成任务中表现出了卓越的性能。在这项工作中,我们提出了一种三维扩散模型,用于从三维 PET 和 CT 图像中准确地进行 H&N 肿瘤分割。三维扩散模型的开发考虑到了 PET 和 CT 图像的三维性质。在反向过程中,该模型利用三维 UNet 结构,将 PET、CT 和高斯噪声卷的串联作为网络输入,生成肿瘤掩膜。基于 HECKTOR 挑战数据集进行了实验,以评估所提出的扩散模型的有效性。实验采用了几种基于 U-Net 和 Transformer 结构的最先进技术作为参考方法。根据各种定量指标和生成的不确定性图,研究了采用 PET 和 CT 作为网络输入以及将扩散模型从二维进一步扩展到三维的益处。结果表明,与其他方法相比,所提出的三维扩散模型能生成更精确的分割结果。与二维格式的扩散模型相比,所提出的三维模型产生了更优越的结果。我们的实验还凸显了利用 PET 和 CT 双模态数据进行 H&N 肿瘤分割的优势。
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引用次数: 0
bia-binder: A web-native cloud compute service for the bioimage analysis community. bia-binder:面向生物图像分析界的网络原生云计算服务。
Pub Date : 2024-11-19
Craig T Russell, Jean-Marie Burel, Awais Athar, Simon Li, Ugis Sarkans, Jason Swedlow, Alvis Brazma, Matthew Hartley, Virginie Uhlmann

We introduce bia-binder (BioImage Archive Binder), an open-source, cloud-architectured, and web-based coding environment tailored to bioimage analysis that is freely accessible to all researchers. The service generates easy-to-use Jupyter Notebook coding environments hosted on EMBL-EBI's Embassy Cloud, which provides significant computational resources. The bia-binder architecture is free, open-source and publicly available for deployment. It features fast and direct access to images in the BioImage Archive, the Image Data Resource, and the BioStudies databases. We believe that this service can play a role in mitigating the current inequalities in access to scientific resources across academia. As bia-binder produces permanent links to compiled coding environments, we foresee the service to become widely-used within the community and enable exploratory research. bia-binder is built and deployed using helmsman and helm and released under the MIT licence. It can be accessed at binder.bioimagearchive.org and runs on any standard web browser.

我们介绍 bia-binder(生物图像档案装订器),这是一个开源、云架构和基于网络的编码环境,专为生物图像分析量身定制,所有研究人员均可免费使用。该服务生成易于使用的 Jupyter Notebook 编码环境,托管在 EMBL-EBI 的 Embassy 云上,该云提供大量计算资源。bia-binder 架构是免费、开源的,可公开部署。它的特点是可以快速、直接地访问生物图像档案、图像数据资源和生物研究数据库中的图像。我们相信,这项服务可以在缓解当前学术界在获取科学资源方面存在的不平等现象方面发挥作用。随着 bia-binder 生成与编译编码环境的永久链接,我们预计这项服务将在社区内得到广泛使用,并促进探索性研究。可通过 binder.bioimagearchive.org 进行访问,并可在任何标准网络浏览器上运行。
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引用次数: 0
Feasibility of PET-enabled dual-energy CT imaging: First physical phantom and initial patient results. PET 双能量 CT 成像的可行性:首个物理模型和患者结果。
Pub Date : 2024-11-19
Yansong Zhu, Siqi Li, Zhaoheng Xie, Edwin K Leung, Reimund Bayerlein, Negar Omidvari, Yasser G Abdelhafez, Simon R Cherry, Jinyi Qi, Ramsey D Badawi, Benjamin A Spencer, Guobao Wang

X-ray computed tomography (CT) in PET/CT is commonly operated with a single energy, resulting in a limitation of lacking tissue composition information. Dual-energy (DE) spectral CT enables material decomposition by using two different x-ray energies and may be combined with PET for improved multimodality imaging, but would either require hardware upgrade or increase radiation dose due to the added second x-ray CT scan. Recently proposed PET-enabled DECT method allows dual-energy spectral imaging using a conventional PET/CT scanner without the need for a second x-ray CT scan. A gamma-ray CT (gCT) image at 511 keV can be generated from the existing time-of-flight PET data with the maximum-likelihood attenuation and activity (MLAA) approach and is then combined with the low-energy x-ray CT image to form dual-energy spectral imaging. To improve the image quality of gCT, a kernel MLAA method was further proposed by incorporating x-ray CT as a priori information. The concept of this PET-enabled DECT has been validated using simulation studies, but not yet with 3D real data. In this work, we developed a general open-source implementation for gCT reconstruction from PET data and use this implementation for the first real data validation with both a physical phantom study and a human subject study on a uEXPLORER total-body PET/CT system. These results have demonstrated the feasibility of this method for spectral imaging and material decomposition.

正电子发射计算机断层扫描(PET/CT)中的 X 射线计算机断层扫描(CT)通常使用单一能量进行操作,因此存在缺乏组织成分信息的局限性。双能量(DE)光谱 CT 可通过使用两种不同的 X 射线能量进行物质分解,可与 PET 结合使用以改进多模态成像,但需要升级硬件,或因增加第二次 X 射线 CT 扫描而增加辐射剂量。最近提出的正电子发射计算机断层成像(PET-enabled DECT)方法可使用传统的 PET/CT 扫描仪进行双能量光谱成像,而无需进行第二次 X 射线 CT 扫描。利用最大似然衰减和活动(MLAA)方法,可从现有的飞行时间 PET 数据中生成 511 千伏的伽马射线 CT(gCT)图像,然后与低能量 X 射线 CT 图像相结合,形成双能量光谱成像。为了提高 gCT 的图像质量,还进一步提出了一种核 MLAA 方法,将 X 射线 CT 作为先验信息。这种支持 PET 的 DECT 概念已通过模拟研究得到验证,但尚未通过三维真实数据得到验证。在这项工作中,我们开发了从 PET 数据重建 gCT 的通用开源实施方案,并利用该实施方案在 uEXPLORER 全身 PET/CT 系统上进行了首次真实数据验证,包括物理模型研究和人体研究。这些结果证明了该方法在光谱成像和材料分解方面的可行性。
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引用次数: 0
Integrating Secondary Structures Information into Triangular Spatial Relationships (TSR) for Advanced Protein Classification. 将二级结构信息整合到三角空间关系(TSR)中,实现高级蛋白质分类。
Pub Date : 2024-11-19
Poorya Khajouie, Titli Sarkar, Krishna Rauniyar, Li Chen, Wu Xu, Vijay Raghavan

Protein structures represent the key to deciphering biological functions. The more detailed form of similarity among these proteins is sometimes overlooked by the conventional structural comparison methods. In contrast, further advanced methods, such as Triangular Spatial Relationship (TSR), have been demonstrated to make finer differentiations. Still, the classical implementation of TSR does not provide for the integration of secondary structure information, which is important for a more detailed understanding of the folding pattern of a protein. To overcome these limitations, we developed the SSE-TSR approach. The proposed method integrates secondary structure elements (SSEs) into TSR-based protein representations. This allows an enriched representation of protein structures by considering 18 different combinations of helix, strand, and coil arrangements. Our results show that using SSEs improves the accuracy and reliability of protein classification to varying degrees. We worked with two large protein datasets of 9.2K and 7.8K samples, respectively. We applied the SSE-TSR approach and used a neural network model for classification. Interestingly, introducing SSEs improved performance statistics for Dataset 1, with accuracy moving from 96.0% to 98.3%. For Dataset 2, where the performance statistics were already good, further small improvements were found with the introduction of SSE, giving an accuracy of 99.5% compared to 99.4%. These results show that SSE integration can dramatically improve TSR key discrimination, with significant benefits in datasets with low initial accuracies and only incremental gains in those with high baseline performance. Thus, SSE-TSR is a powerful bioinformatics tool that improves protein classification and understanding of protein function and interaction.

蛋白质结构是破译生物功能的关键。传统的结构比较方法有时会忽略这些蛋白质之间更细致的相似性。相比之下,三角形空间关系(TSR)等更先进的方法已被证明可以进行更精细的区分。然而,TSR 的经典实现方法并没有整合二级结构信息,而这对于更详细地了解蛋白质的折叠模式非常重要。为了克服这些局限性,我们开发了 SSE-TSR 方法。该方法将二级结构元素(SSE)整合到基于 TSR 的蛋白质表征中。这样就可以通过考虑 18 种不同的螺旋、链和线圈排列组合来丰富蛋白质结构的表示方法。我们的研究结果表明,使用 SSE 在不同程度上提高了蛋白质分类的准确性和可靠性。我们使用了两个大型蛋白质数据集,分别包含 9.2K 和 7.8K 个样本。我们采用了 SSE-TSR 方法,并使用神经网络模型进行分类。有趣的是,引入 SSE 改善了数据集 1 的性能统计,准确率从 96.0% 提高到 98.3%。数据集 2 的性能统计本来就不错,引入 SSE 后又有小幅提高,准确率从 99.4% 提高到 99.5%。这些结果表明,SSE 集成可以显著提高 TSR 的关键识别能力,在初始准确率较低的数据集上有明显的优势,而在基线性能较高的数据集上则只有增量收益。因此,SSE-TSR 是一种功能强大的生物信息学工具,它能改善蛋白质分类和对蛋白质功能与相互作用的理解。
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引用次数: 0
Consensus Statement on Brillouin Light Scattering Microscopy of Biological Materials. 生物材料布里渊光散射显微镜共识声明。
Pub Date : 2024-11-18
Pierre Bouvet, Carlo Bevilacqua, Yogeshwari Ambekar, Giuseppe Antonacci, Joshua Au, Silvia Caponi, Sophie Chagnon-Lessard, Juergen Czarske, Thomas Dehoux, Daniele Fioretto, Yujian Fu, Jochen Guck, Thorsten Hamann, Dag Heinemann, Torsten Jähnke, Hubert Jean-Ruel, Irina Kabakova, Kristie Koski, Nektarios Koukourakis, David Krause, Salvatore La Cavera, Timm Landes, Jinhao Li, Jeremie Margueritat, Maurizio Mattarelli, Michael Monaghan, Darryl R Overby, Fernando Perez-Cota, Emanuele Pontecorvo, Robert Prevedel, Giancarlo Ruocco, John Sandercock, Giuliano Scarcelli, Filippo Scarponi, Claudia Testi, Peter Török, Lucie Vovard, Wolfgang Weninger, Vladislav Yakovlev, Seok-Hyun Yun, Jitao Zhang, Francesca Palombo, Alberto Bilenca, Kareem Elsayad

Brillouin Light Scattering (BLS) spectroscopy is a non-invasive, non-contact, label-free optical technique that can provide information on the mechanical properties of a material on the sub-micron scale. Over the last decade it has seen increased applications in the life sciences, driven by the observed significance of mechanical properties in biological processes, the realization of more sensitive BLS spectrometers and its extension to an imaging modality. As with other spectroscopic techniques, BLS measurements not only detect signals characteristic of the investigated sample, but also of the experimental apparatus, and can be significantly affected by measurement conditions. The aim of this consensus statement is to improve the comparability of BLS studies by providing reporting recommendations for the measured parameters and detailing common artifacts. Given that most BLS studies of biological matter are still at proof-of-concept stages and use different--often self-built--spectrometers, a consensus statement is particularly timely to assure unified advancement.

布里渊光散射(BLS)光谱学是一种非侵入、非接触、无标记的光学技术,可提供材料亚微米级的机械特性信息。在过去的十年中,由于观察到机械特性在生物过程中的重要作用、灵敏度更高的 BLS 光谱仪的实现及其向成像模式的扩展,该技术在生命科学领域的应用日益增多。与其他光谱技术一样,BLS 测量不仅能检测被测样品的特征信号,还能检测实验仪器的特征信号,并且会受到测量条件的显著影响。本共识声明旨在通过提供测量参数的报告建议和详细说明常见伪影,提高 BLS 研究的可比性。鉴于大多数生物物质的 BLS 研究仍处于概念验证阶段,而且使用的光谱仪各不相同(通常是自制的),因此发表一份共识声明以确保统一进展尤为及时。
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引用次数: 0
Explainable AI for computational pathology identifies model limitations and tissue biomarkers. 用于计算病理学的可解释人工智能可识别模型限制和组织生物标记。
Pub Date : 2024-11-18
Jakub R Kaczmarzyk, Joel H Saltz, Peter K Koo

Introduction: Deep learning models hold great promise for digital pathology, but their opaque decision-making processes undermine trust and hinder clinical adoption. Explainable AI methods are essential to enhance model transparency and reliability.

Methods: We developed HIPPO, an explainable AI framework that systematically modifies tissue regions in whole slide images to generate image counterfactuals, enabling quantitative hypothesis testing, bias detection, and model evaluation beyond traditional performance metrics. HIPPO was applied to a variety of clinically important tasks, including breast metastasis detection in axillary lymph nodes, prognostication in breast cancer and melanoma, and IDH mutation classification in gliomas. In computational experiments, HIPPO was compared against traditional metrics and attention-based approaches to assess its ability to identify key tissue elements driving model predictions.

Results: In metastasis detection, HIPPO uncovered critical model limitations that were undetectable by standard performance metrics or attention-based methods. For prognostic prediction, HIPPO outperformed attention by providing more nuanced insights into tissue elements influencing outcomes. In a proof-of-concept study, HIPPO facilitated hypothesis generation for identifying melanoma patients who may benefit from immunotherapy. In IDH mutation classification, HIPPO more robustly identified the pathology regions responsible for false negatives compared to attention, suggesting its potential to outperform attention in explaining model decisions.

Conclusions: HIPPO expands the explainable AI toolkit for computational pathology by enabling deeper insights into model behavior. This framework supports the trustworthy development, deployment, and regulation of weakly-supervised models in clinical and research settings, promoting their broader adoption in digital pathology.

深度学习模型在组织病理学图像分析中大有可为,但其不透明的决策过程给高风险医疗场景带来了挑战。在此,我们介绍一种可解释的人工智能方法--HIPPO,该方法通过整张切片图像中的组织斑块修改生成反事实示例,在计算病理学中对基于注意力的多实例学习(ABMIL)模型进行检验。将 HIPPO 应用于为检测乳腺癌转移而训练的 ABMIL 模型时发现,这些模型可能会忽略小肿瘤,并可能被非肿瘤组织误导,而广泛用于解释的注意力图谱往往会突出显示不直接影响预测的区域。通过解释在预后预测任务中训练的 ABMIL 模型,HIPPO 发现了比高注意力区域具有更强预后效应的组织区域,而高注意力区域有时会对风险评分产生反直觉的影响。这些发现证明了 HIPPO 在综合模型评估、偏差检测和定量假设检验方面的能力。HIPPO 极大地扩展了可解释人工智能工具的能力,以评估计算病理学中弱监督模型的开发、部署和监管是否值得信赖和可靠。
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引用次数: 0
Twin Peak Method for Estimating Tissue Viscoelasticity using Shear Wave Elastography. 利用剪切波弹性成像估算组织粘弹性的双峰法
Pub Date : 2024-11-18
Shuvrodeb Adikary, Matthew W Urban, Murthy N Guddati

Tissue viscoelasticity is becoming an increasingly useful biomarker beyond elasticity and can theoretically be estimated using shear wave elastography (SWE), by inverting the propagation and attenuation characteristics of shear waves. Estimating viscosity is often more difficult than elasticity because attenuation, the main effect of viscosity, leads to poor signal-to-noise ratio of the shear wave motion. In the present work, we provide an alternative to existing methods of viscoelasticity estimation that is robust against noise. The method minimizes the difference between simulated and measured versions of two sets of peaks (twin peaks) in the frequency-wavenumber domain, obtained first by traversing through each frequency and then by traversing through each wavenumber. The slopes and deviation of the twin peaks are sensitive to elasticity and viscosity respectively, leading to the effectiveness of the proposed inversion algorithm for characterizing mechanical properties. This expected effectiveness is confirmed through in silico verification, followed by ex vivo validation and in vivo application, indicating that the proposed approach can be effectively used in accurately estimating viscoelasticity, thus potentially contributing to the development of enhanced biomarkers.

组织粘弹性正日益成为一种超越弹性的有用生物标志物,理论上可以利用剪切波弹性成像(SWE)技术,通过反演剪切波的传播和衰减特性来估算组织粘弹性。估算粘度通常比估算弹性更为困难,因为粘度的主要影响因素--衰减会导致剪切波运动的信噪比降低。在本研究中,我们提供了一种可替代现有粘弹性估算方法的方法,该方法对噪声具有鲁棒性。该方法首先通过遍历每个频率,然后通过遍历每个波长,将频率-波长域中两组峰值(双峰)的模拟值与测量值之间的差值最小化。孪生峰的斜率和偏差分别对弹性和粘度敏感,这说明所提出的反演算法在表征机械特性方面非常有效。这种预期的有效性通过硅学验证、体内外验证和体内应用得到了证实,表明所提出的方法可以有效地用于准确估计粘弹性,从而为开发增强型生物标记物做出潜在贡献。
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引用次数: 0
Finding high posterior density phylogenies by systematically extending a directed acyclic graph. 通过系统扩展有向无环图寻找高后代密度系统发育。
Pub Date : 2024-11-18
Chris Jennings-Shaffer, David H Rich, Matthew Macaulay, Michael D Karcher, Tanvi Ganapathy, Shosuke Kiami, Anna Kooperberg, Cheng Zhang, Marc A Suchard, Frederick A Matsen

Bayesian phylogenetics typically estimates a posterior distribution, or aspects thereof, using Markov chain Monte Carlo methods. These methods integrate over tree space by applying local rearrangements to move a tree through its space as a random walk. Previous work explored the possibility of replacing this random walk with a systematic search, but was quickly overwhelmed by the large number of probable trees in the posterior distribution. In this paper we develop methods to sidestep this problem using a recently introduced structure called the subsplit directed acyclic graph (sDAG). This structure can represent many trees at once, and local rearrangements of trees translate to methods of enlarging the sDAG. Here we propose two methods of introducing, ranking, and selecting local rearrangements on sDAGs to produce a collection of trees with high posterior density. One of these methods successfully recovers the set of high posterior density trees across a range of data sets. However, we find that a simpler strategy of aggregating trees into an sDAG in fact is computationally faster and returns a higher fraction of probable trees.

贝叶斯系统发生学通常使用马尔科夫链蒙特卡洛方法估计后验分布或后验分布的某些方面。这些方法通过局部重排,以随机行走的方式在树空间中移动树,从而对树空间进行整合。之前的研究探索了用系统搜索取代随机行走的可能性,但很快就被后验分布中的大量可能树所淹没。在本文中,我们利用一种最近引入的结构--子分裂有向无环图(sDAG)--开发了规避这一问题的方法。这种结构可以同时表示许多树,树的局部重新排列可以转化为扩大 sDAG 的方法。在这里,我们提出了两种在 sDAG 上引入、排序和选择局部重排的方法,以产生具有高后验密度的树集合。其中一种方法成功地在一系列数据集中恢复了高后验密度树的集合。然而,我们发现,将树集合到 sDAG 中的更简单策略实际上计算速度更快,而且能返回更多可能的树。
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