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Sequential Markov Chain Monte Carlo for Lagrangian Data Assimilation with Applications to Unknown Data Locations

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arXiv 2023年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging as not only is high-dimensional, but the model for the signal yields longer-range time dependencies through the observation locations. Motivated by this model we revisit a lesser-known and provably convergent computational methodology from [4, 11, 28] that uses sequential Markov Chain Monte Carlo (MCMC) chains. We extend this methodology for data filtering problems with unknown observation locations. We benchmark our algorithms on Linear Gaussian state space models against competing ensemble methods and demonstrate a significant improvement in both execution speed and accuracy. Finally, we implement a realistic case study on a high-dimensional rotating shallow water model (of about 104 - 105 dimensions) with real and synthetic data. The data is provided by the National Oceanic and Atmospheric Administration (NOAA) and contains observations from ocean drifters in a domain of the Atlantic Ocean restricted to the longitude and latitude intervals [-51◦,-41◦], [17◦,27◦] *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2023, CC BY.

关键词： Location

A BCLC Staging System for Hepatocellular Carcinoma using Swin Transformer and CT Imaging 46

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A BCLC Staging System for Hepatocellular Carcinoma using Swi...

46th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBC 2024

作者： Chang, Shun-Cheng Wang, Pochuang Wang, Weichung Su, Tung-Hung Kao, Jia-Horng Lin, Che Taipei10617 Taiwan Department of Computer Science and Information Engineering Ntu Taipei10617 Taiwan Institute of Applied Mathematical Sciences Ntu Taipei10617 Taiwan Division of Gastroenterology and Hepatology Department of Internal Medicine National Taiwan University Hospital Taipei10048 Taiwan Department of Electrical Engineering Ntu Taipei10617 Taiwan Center for Advanced Computing and Imaging in Biomedicine Ntu Taipei10617 Taiwan Smart Medicine and Health Informatics Program Ntu Taipei10617 Taiwan

ISBN: (纸本)9798350371499

The Barcelona Clinic Liver Cancer (BCLC) staging system plays a crucial role in clinical planning, offering valuable insights for effectively managing hepatocellular carcinoma. Accurate prediction of BCLC stages can significantly ease the workload on radiologists. However, few datasets are explicitly designed for discerning BCLC stages. Despite the common practice of appending BCLC labels to clinical data within datasets, the inherent imbalance in BCLC distribution is further amplified by the diverse purposes for which datasets are curated. In this study, we aim to develop a BCLC staging system using the advanced Swin Transformer model. Additionally, we explore the integration of two datasets, each originally intended for separate objectives, highlighting the critical challenge of preserving class distribution in practical study designs. This exploration is pivotal for ensuring the applicability of our developed staging system in the designed clinical settings. Our resulting BCLC staging system demonstrates an accuracy of 55.81% (±7.8%), contributing to advancing medical image-based research for predicting BCLC stages. © 2024 IEEE.

关键词： Distribution transformers

ReViT: A Hybrid Approach for BCLC Staging of Hepatocellular Carcinoma Using 3D CT with Multiple Instance Learning

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ReViT: A Hybrid Approach for BCLC Staging of Hepatocellular ...

2024 IEEE-EMBS International Conference on Biomedical and Health Informatics, BHI 2024

作者： Chang, Shun-Cheng Yu, Hsin-Pei Hsieh, Yi-Hsien Wang, Pochuang Wang, Weichung Su, Tung-Hung Kao, Jia-Horng Lin, Che Taipei10617 Taiwan Department of Computer Science and Information Engineering Ntu Taipei10617 Taiwan Institute of Applied Mathematical Sciences Ntu Taipei10617 Taiwan National Taiwan University Hospital Division of Gastroenterology and Hepatology Department of Internal Medicine Taipei10048 Taiwan Department of Electrical Engineering Ntu Taipei10617 Taiwan Center for Advanced Computing and Imaging in Biomedicine Ntu Taipei10617 Taiwan Smart Medicine and Health Informatics Program Ntu Taipei10617 Taiwan

ISBN: (纸本)9798350351552

Deep learning has revolutionized medical imaging, offering advanced methods for accurate diagnosis and treatment planning. The BCLC staging system is crucial for staging Hepatocellular Carcinoma (HCC), a high-mortality cancer. An automated BCLC staging system could significantly enhance diagnosis and treatment planning efficiency. However, we found that BCLC staging, which is directly related to the size and number of liver tumors, aligns well with the principles of the Multiple Instance Learning (MIL) framework. To effectively achieve this, we proposed a new preprocessing technique called Masked Cropping and Padding(MCP), which addresses the variability in liver volumes and ensures consistent input sizes. This technique preserves the structural integrity of the liver, facilitating more effective learning. Furthermore, we introduced Re ViT, a novel hybrid model that integrates the local feature extraction capabilities of Convolutional Neural Networks (CNNs) with the global context modeling of Vision Transformers (ViTs). Re ViT leverages the strengths of both architectures within the MIL framework, enabling a robust and accurate approach for BCLC staging. We will further explore the trade-off between performance and interpretability by employing TopK Pooling strategies, as our model focuses on the most informative instances within each bag. © 2024 IEEE.

关键词： Convolutional neural networks

A MgNO Method for Multiphase Flow in Porous Media

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arXiv 2024年

作者： Liu, Xinliang Yang, Xia Zhang, Chen-Song Zhang, Lian Zhao, Li Computer Electrical and Mathematical Science and Engineering Division King Abdullah University of Science and Technology Thuwal Saudi Arabia Xiangtan University Hunan China LSEC ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences University of Chinese Academy of Sciences China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big Data China

This research investigates the application of Multigrid Neural Operator (MgNO), a neural operator architecture inspired by multigrid methods, in the simulation for multiphase flow within porous media. The architecture is adjusted to manage a variety of crucial factors, such as permeability and porosity heterogeneity. The study extendes MgNO to time-dependent porous media flow problems and validate its accuracy in predicting essential aspects of multiphase flows. Furthermore, the research provides a detailed comparison between MgNO and Fourier Neural Opeartor (FNO), which is one of the most popular neural operator methods, on their performance regarding prediction error accumulation over time. This aspect provides valuable insights into the models' long-term predictive stability and reliability. The study demonstrates MgNO's capability to effectively simulate multiphase flow problems, offering considerable time savings compared to traditional simulation methods, marking an advancement in integrating data-driven methodologies in geoscience applications. © 2024, CC BY.

关键词： Porous materials

Spectral Extremal Connectivity of Two-State Seizure Brain Waves

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arXiv 2025年

作者： Talento, Mara Sherlin D. Richards, Jordan Pinto-Orellana, Marco Huser, Raphael Ombao, Hernando C. Statistics Program Computer Electrical and Mathematical Science & Engineering Division King Abdullah University of Science and Technology 23955 - 6900 Saudi Arabia Neuro-AI Laboratory Computer Electrical and Mathematical Science & Engineering Division King Abdullah University of Science and Technology 23955 - 6900 Saudi Arabia School of Mathematics Maxwell Institute for Mathematical Sciences University of Edinburgh EdinburghEH9 3FD United Kingdom Department of Biomedical Engineering University of California Irvine92697 United States

Coherence analysis plays a vital role in the study of functional brain connectivity. However, coherence captures only linear spectral associations, and thus can produce misleading findings when ignoring variations of connectivity in the tails of the distribution. This limitation becomes important when investigating extreme neural events that are characterized by large signal amplitudes. The focus of this paper is to examine connectivity in the tails of the distribution, as this reveals salient information that may be overlooked by standard methods. We develop a novel notion of spectral tail association of periodograms to study connectivity in the network of electroencephalogram (EEG) signals of seizure-prone neonates. We further develop a novel non-stationary extremal dependence model for multivariate time series that captures differences in extremal dependence during different brain phases, namely burst-suppression and non-burst-suppression. One advantage of our proposed approach is its ability to identify tail connectivity at key frequency bands that could be associated with outbursts of energy which may lead to seizures. We discuss these novel scientific findings alongside a comparison of the extremal behavior of brain signals for epileptic and non-epileptic patients. © 2025, CC BY.

关键词： Electroencephalography

Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology

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arXiv 2022年

作者： Hu, Zheyuan Jagtap, Ameya D. Karniadakis, George Em Kawaguchi, Kenji Department of Computer Science National University of Singapore Singapore119077 Singapore Division of Applied Mathematics Brown University ProvidenceRI02912 United States

In this paper, we propose the augmented physics-informed neural network (APINN), which adopts soft and trainable domain decomposition and flexible parameter sharing to further improve the extended PINN (XPINN) as well as the vanilla PINN methods. In particular, a trainable gate network is employed to mimic the hard decomposition of XPINN, which can be flexibly fine-tuned for discovering a potentially better partition. It weight-averages several sub-nets as the output of APINN. APINN does not require complex interface conditions, and its sub-nets can take advantage of all training samples rather than just part of the training data in their subdomains. Lastly, each sub-net shares part of the common parameters to capture the similar components in each decomposed function. Furthermore, following the PINN generalization theory in Hu et al. [2021], we show that APINN can improve generalization by proper gate network initialization and general domain & function decomposition. Extensive experiments on different types of PDEs demonstrate how APINN improves the PINN and XPINN methods. Specifically, we present examples where XPINN performs similarly to or worse than PINN, so that APINN can significantly improve both. We also show cases where XPINN is already better than PINN, so APINN can still slightly improve XPINN. Furthermore, we visualize the optimized gating networks and their optimization trajectories, and connect them with their performance, which helps discover the possibly optimal decomposition. Interestingly, if initialized by different decomposition, the performances of corresponding APINNs can differ drastically. This, in turn, shows the potential to design an optimal domain decomposition for the differential equation problem under consideration. © 2022, CC BY.

关键词： Domain decomposition methods

Automated Ensemble Multimodal Machine Learning for Healthcare

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IEEE Journal of Biomedical and Health Informatics 2025年第6期PP卷 PP页

作者： Imrie, Fergus Denner, Stefan Brunschwig, Lucas S. Maier-Hein, Klaus Van Der Schaar, Mihaela University of Oxford Department of Statistics Oxford United Kingdom Heidelberg University Faculty of Mathematics and Computer Science Germany École Polytechnique Fédérale de Lausanne Switzerland Division of Medical Image Computing Germany Heidelberg University Hospital Pattern Analysis and Learning Group Department of Radiation Oncology Germany Heidelberg Germany University of Cambridge Department of Applied Mathematics and Theoretical Physics United Kingdom

The application of machine learning in medicine and healthcare has led to the creation of numerous diagnostic and prognostic models. However, despite their success, current approaches generally issue predictions using data from a single modality. This stands in stark contrast with clinician decision-making which employs diverse information from multiple sources. While several multimodal machine learning approaches exist, significant challenges in developing multimodal systems remain that are hindering clinical adoption. In this paper, we introduce a multimodal framework, AutoPrognosis-M, that enables the integration of structured clinical (tabular) data and medical imaging using automated machine learning. AutoPrognosis-M incorporates 17 imaging models, including convolutional neural networks and vision transformers, and three distinct multimodal fusion strategies. In an illustrative application using a multimodal skin lesion dataset, we highlight the importance of multimodal machine learning and the power of combining multiple fusion strategies using ensemble learning. We have open-sourced our framework as a tool for the community and hope it will accelerate the uptake of multimodal machine learning in healthcare and spur further innovation. © 2013 IEEE.

关键词： Adversarial machine learning

On the Particle Approximation of Lagged Feynman-Kac Formulae

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arXiv 2024年

作者： Awadelkarim, Elsiddig Caffarel, Michel Moral, Pierre Del Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia University of Toulouse CNRS-Lab. de Chimie et Physique Quantiques Toulouse31062 France Centre de Recherche Inria Bordeaux Sud-Ouest Talence33405 France School of Data Science The Chinese University Hong Kong Shenzhen China

In this paper we examine the numerical approximation of the limiting invariant measure associated with Feynman-Kac formulae. These are expressed in a discrete time formulation and are associated with a Markov chain and a potential function. The typical application considered here is the computation of eigenvalues associated with non-negative operators as found, for example, in physics or particle simulation of rare-events. We focus on a novel lagged approximation of this invariant measure, based upon the introduction of a ratio of time-averaged Feynman-Kac marginals associated with a positive operator iterated l ∈ N times;a lagged Feynman-Kac formula. This estimator and its approximation using Diffusion Monte Carlo (DMC) have been extensively employed in the physics literature. In short, DMC is an iterative algorithm involving N ∈ N particles or walkers simulated in parallel, that undergo sampling and resampling operations. In this work, it is shown that for the DMC approximation of the lagged Feynman-Kac formula, one has an almost sure characterization of the L1-error as the time parameter (iteration) goes to infinity and this is at most of O(exp{−κl}/N), for_ κ > 0. In addition a non-asymptotic in time, and time uniform L1−bound is proved which is O(l/√N). We also prove a novel central limit theorem to give a characterization of the exact asymptotic in time variance. This analysis demonstrates that the strategy used in physics, namely, to run DMC with N and l small and, for long time enough, is mathematically justified. Our results also suggest how one should choose N and l in practice. We emphasize that these results are not restricted to physical applications;they have broad relevance to the general problem of particle simulation of the Feynman-Kac formula, which is utilized in a great variety of scientific and engineering fields. © 2024, CC BY.

关键词： Eigenvalues and eigenfunctions

Discovery and Recognition of Formula Concepts using Machine Learning

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arXiv 2023年

作者： Scharpf, Philipp Schubotz, Moritz Cohl, Howard S. Breitinger, Corinna Gipp, Bela University of Konstanz Germany University of Wuppertal and FIZ Karlsruhe Germany Applied and Computational Mathematics Division National Institute of Standards and Technology GaithersburgMD United States Institute of Computer Science University of Göttingen Germany

Citation-based Information Retrieval (IR) methods for scientific documents have proven effective for IR applications, such as Plagiarism Detection or Literature Recommender Systems in academic disciplines that use many references. In science, technology, engineering, and mathematics, researchers often employ mathematical concepts through formula notation to refer to prior knowledge. Our long-term goal is to generalize citation-based IR methods and apply this generalized method to both classical references and mathematical concepts. In this paper, we suggest how mathematical formulas could be cited and define a Formula Concept Retrieval task with two subtasks: Formula Concept Discovery (FCD) and Formula Concept Recognition (FCR). While FCD aims at the definition and exploration of a 'Formula Concept' that names bundled equivalent representations of a formula, FCR is designed to match a given formula to a prior assigned unique mathematical concept identifier. We present machine learning-based approaches to address the FCD and FCR tasks. We then evaluate these approaches on a standardized test collection (NTCIR arXiv dataset). Our FCD approach yields a precision of 68% for retrieving equivalent representations of frequent formulas and a recall of 72% for extracting the formula name from the surrounding text. FCD and FCR enable the citation of formulas within mathematical documents and facilitate semantic search and question answering as well as document similarity assessments for plagiarism detection or recommender *** Codes 68P20 (Primary), 68T50 (Secondary) © 2023, CC BY.

关键词： Machine learning