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The $\gamma$γ-OMP Algorithm for Feature Selection With Application to Gene Expression Data

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IEEE/ACM Transactions on computational Biology and Bioinformatics 2020年第2期19卷 1214-1224页

作者： Michail Tsagris Zacharias Papadovasilakis Kleanthi Lakiotaki Ioannis Tsamardinos Department of Economics University of Crete Rethymnon Greece Department of Computer Science University of Crete Herakleion Greece Department of Computer Science Institute of Applied and Computational Mathematics FORTH University of Crete Herakleion Greece

Feature selection for predictive analytics is the problem of identifying a minimal-size subset of features that is maximally predictive of an outcome of interest. To apply to molecular data, feature selection algorithms need to be scalable to tens of thousands of features. In this paper, we propose $\gamma$ -OMP, a generalisation of the highly-scalable Orthogonal Matching Pursuit feature selection algorithm. $\gamma$ -OMP can handle (a)various types of outcomes, such as continuous, binary, nominal, time-to-event, (b)discrete (categorical)features, (c)different statistical-based stopping criteria, (d)several predictive models (e.g., linear or logistic regression), (e)various types of residuals, and (f)different types of association. We compare $\gamma$ -OMP against LASSO, a prototypical, widely used algorithm for high-dimensional data. On both simulated data and several real gene expression datasets, $\gamma$ -OMP is on par, or outperforms LASSO in binary classification (case-control data), regression (quantified outcomes), and time-to-event data (censored survival times). $\gamma$ -OMP is based on simple statistical ideas, it is easy to implement and to extend, and our extensive evaluation shows that it is also effective in bioinformatics analysis settings.

关键词： Matching pursuit algorithms Prediction algorithms Feature extraction Gene expression Signal processing algorithms Bioinformatics computational modeling

Subdiffusive wave transport and weak localization transition in three-dimensional stealthy hyperuniform disordered systems

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Physical Review B 2022年第6期105卷 064204-064204页

作者： F. Sgrignuoli S. Torquato L. Dal Negro Department of Electrical and Computer Engineering & Photonics Center Boston University 8 Saint Mary's Street Boston Massachusetts 02215 USA Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA Division of Material Science and Engineering Boston University 15 Saint Mary's Street Brookline Massachusetts 02446 USA Department of Physics Boston University 590 Commonwealth Avenue Boston Massachusetts 02215 USA

The purpose of this work is to understand the fundamental connection between structural correlations and light localization in three-dimensional (3D) open scattering systems of finite size. We numerically investigate the transport of vector electromagnetic waves scattered by resonant electric dipoles spatially arranged in 3D space by stealthy hyperuniform disordered point patterns. Three-dimensional stealthy hyperuniform disordered systems are engineered with different structural correlation properties determined by their degree of stealthiness χ. Such fine control of exotic states of amorphous matter enables the systematic design of optical media that interpolate in a tunable fashion between uncorrelated random structures and crystalline materials. By solving the electromagnetic multiple scattering problem using Green's matrix spectral method, we establish a transport phase diagram that demonstrates a distinctive transition from a diffusive to a weak localization regime beyond a critical scattering density that depends on χ. The transition is characterized by studying the Thouless number and the spectral statistics of the scattering resonances. In particular, by tuning the χ parameter, we demonstrate large spectral gaps and suppressed subradiant proximity resonances, facilitating light localization. Moreover, consistently with previous studies, our results show a region of the transport phase diagram where the investigated scattering systems become transparent. Our work provides a systematic description of the transport and weak localization properties of light in stealthy hyperuniform structures and motivates the engineering of photonic systems with enhanced light-matter interactions for applications to both classical and quantum devices.

关键词： Anderson localization Light-matter interaction Mesoscopics Photonics Scattering theory Weak localization Metamaterials

Lower Bounds on Quantum Annealing Times

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Physical Review Letters 2023年第14期130卷 140601-140601页

作者： Luis Pedro García-Pintos Lucas T. Brady Jacob Bringewatt Yi-Kai Liu Joint Center for Quantum Information and Computer Science University of Maryland College Park Maryland 20742 USA Joint Quantum Institute University of Maryland College Park Maryland 20742 USA Theoretical Division (T4) Los Alamos National Laboratory Los Alamos New Mexico 87545 USA Quantum Artificial Intelligence Laboratory NASA Ames Research Center Moffett Field California 94035 USA KBR 601 Jefferson Street Houston Texas 77002 USA Applied and Computational Mathematics Division National Institute of Standards and Technology Gaithersburg Maryland 20899 USA

The adiabatic theorem provides sufficient conditions for the time needed to prepare a target ground state. While it is possible to prepare a target state much faster with more general quantum annealing protocols, rigorous results beyond the adiabatic regime are rare. Here, we provide such a result, deriving lower bounds on the time needed to successfully perform quantum annealing. The bounds are asymptotically saturated by three toy models where fast annealing schedules are known: the Roland and Cerf unstructured search model, the Hamming spike problem, and the ferromagnetic p-spin model. Our bounds demonstrate that these schedules have optimal scaling. Our results also show that rapid annealing requires coherent superpositions of energy eigenstates, singling out quantum coherence as a computational resource.

关键词： Adiabatic quantum optimization Quantum algorithms Quantum computation

Foundation Models for Atomistic Simulation of Chemistry and Materials

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arXiv 2025年

作者： Yuan, Eric C.-Y. Liu, Yunsheng Chen, Junmin Zhong, Peichen Raja, Sanjeev Kreiman, Tobias Vargas, Santiago Xu, Wenbin Head-Gordon, Martin Yang, Chao Blau, Samuel M. Cheng, Bingqing Krishnapriyan, Aditi Head-Gordon, Teresa Kenneth S. Pitzer Theory Center Department of Chemistry United States Department of Chemical and Biomolecular Engineering United States Electrical Engineering and Computer Science United States Bakar Institute of Digital Materials for the Planet University of California BerkeleyCA94720 United States Chemical Sciences Division United States Applied Mathematics and Computational Research Division United States Energy Technologies Area United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

Given the power of large language and large vision models, it is of profound and fundamental interest to ask if a foundational model based on data and parameter scaling laws and pre-training strategies is possible for learned simulations of chemistry and materials. The scaling of large and diverse datasets and highly expressive architectures for chemical and materials sciences should result in a foundation model that is more efficient and broadly transferable, robust to out-of-distribution challenges, and easily fine-tuned to a variety of downstream observables, when compared to specific training from scratch on targeted applications in atomistic simulation. In this Perspective we aim to cover the rapidly advancing field of machine learned interatomic potentials (MLIP), and to illustrate a path to create chemistry and materials MLIP foundation models at larger scale. © 2025, CC BY-SA.

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TensorKMC: Kinetic Monte Carlo Simulation of 50 Trillion Atoms Driven by Deep Learning on a New Generation of Sunway Supercomputer

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TensorKMC: Kinetic Monte Carlo Simulation of 50 Trillion Ato...

Supercomputing Conference

作者： Honghui Shang Xin Chen Xingyu Gao Rongfen Lin Lifang Wang Fang Li Qian Xiao Lei Xu Qiang Sun Leilei Zhu Fei Wang Yunquan Zhang Haifeng Song SKL of Computer Architecture Institute of Computing Technology Chinese Academy of Sciences Beijing China Institute of Applied Physics and Computational Mathematics Beijing China Department of Computer Science and Technology Tsinghua University Wuxin China National Supercomputer Center in Wuxi Wuxi China

ISBN: (数字)9781450384421

ISBN: (纸本)9781665483902

The atomic kinetic Monte Carlo method plays an important role in multi-scale physical simulations because it bridges the micro and macro worlds. However, its accuracy is limited by empirical potentials. We therefore propose herein a triple-encoding algorithm and vacancy-cache mechanism to efficiently integrate ab initio neural network potentials (NNPs) with AKMC and implement them in our TensorKMC codes. We port our program to SW26010-pro and innovate a fast feature operator and a big fusion operator for the NNPs for fully utilizing the powerful heterogeneous computing units of the new-generation Sunway supercomputer. We further optimize memory usage. With these improvements, TensorKMC can simulate up to 54 trillions of atoms and achieve excellent strong and weak scaling performance up to 27,456,000 cores.

关键词： Technological innovation Monte Carlo methods Codes Quantum chemistry High performance computing Optimization methods Artificial neural networks

Position: Bayesian deep learning is needed in the age of large-scale AI 24

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Position: Bayesian deep learning is needed in the age of lar...

Proceedings of the 41st International Conference on Machine Learning

作者： Theodore Papamarkou Maria Skoularidou Konstantina Palla Laurence Aitchison Julyan Arbel David Dunson Maurizio Filippone Vincent Fortuin Philipp Hennig José Miguel Hernández-Lobato Aliaksandr Hubin Alexander Immer Theofanis Karaletsos Mohammad Emtiyaz Khan Agustinus Kristiadi Yingzhen Li Stephan Mandt Christopher Nemeth Michael A. Osborne Tim G. J. Rudner David Rügamer Yee Whye Teh Max Welling Andrew Gordon Wilson Ruqi Zhang Department of Mathematics The University of Manchester Manchester UK Eric and Wendy Schmidt Center Broad Institute of MIT and Harvard Cambridge Spotify London UK Computational Neuroscience Unit University of Bristol Bristol UK Centre Inria de l'Université Grenoble Alpes Grenoble France Department of Statistical Science Duke University Statistics Program KAUST Saudi Arabia Helmholtz AI Munich Germany and Department of Computer Science Technical University of Munich Munich Germany and Munich Center for Machine Learning Munich Germany Tübingen AI Center University of Tübingen Tübingen Germany Department of Engineering University of Cambridge Cambridge UK Department of Mathematics University of Oslo Oslo Norway and Bioinformatics and Applied Statistics Norwegian University of Life Sciences Ås Norway Department of Computer Science ETH Zurich Switzerland Chan Zuckerberg Initiative California Center for Advanced Intelligence Project RIKEN Tokyo Japan Vector Institute Toronto Canada Department of Computing Imperial College London London UK Department of Computer Science UC Irvine Irvine Department of Mathematics and Statistics Lancaster University Lancaster UK Department of Engineering Science University of Oxford Oxford UK Center for Data Science New York University New York Munich Center for Machine Learning Munich Germany and Department of Statistics LMU Munich Munich Germany DeepMind London UK and Department of Statistics University of Oxford Oxford UK Informatics Institute University of Amsterdam Amsterdam Netherlands Courant Institute of Mathematical Sciences and Center for Data Science Computer Science Department New York University New York Department of Computer Science Purdue University West Lafayette

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

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Semantic preserving bijective mappings of mathematical formulae between document preparation systems and computer algebra systems

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arXiv 2021年

作者： Cohl, Howard S. Schubotz, Moritz Youssef, Abdou Greiner-Petter, André Gerhard, Jürgen Saunders, Bonita V. McClain, Marjorie A. Applied and Computational Mathematics Division NIST GaithersburgMD United States Dept. of Computer and Information Science University of Konstanz Konstanz Germany Dept. of Computer Science GWU WashingtonDC United States DSIMG Technische Universität Berlin Germany Maplesoft WaterlooON Canada

Document preparation systems like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Using LaTeX, LaTeXML, and tools generated for use in the National Institute of Standards (NIST) Digital Library of Mathematical Functions, semantically enhanced mathematical LaTeX markup (semantic LaTeX) is achieved by using a semantic macro set. computer algebra systems (CAS) such as Maple and Mathematica use alternative markup to represent mathematical expressions. By taking advantage of Youssef's Part-of-Math tagger and CAS internal representations, we develop algorithms to translate mathematical expressions represented in semantic LaTeX to corresponding CAS representations and vice versa. We have also developed tools for translating the entire Wolfram Encoding Continued Fraction Knowledge and University of Antwerp Continued Fractions for Special Functions datasets, for use in the NIST Digital Repository of Mathematical Formulae. The overall goal of these efforts is to provide semantically enriched standard conforming MathML representations to the public for formulae in digital mathematics libraries. These representations include presentation MathML, content MathML, generic LaTeX, semantic LaTeX, and now CAS representations as well. © 2021, CC BY.

关键词： Semantics

Improving the Accuracy of the Variational Quantum Eigensolver for Molecular Systems by the Explicitly-Correlated Perturbative R12-Correction

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arXiv 2021年

作者： Schleich, Philipp Kottmann, Jakob S. Aspuru-Guzik, Alan Department of Computer Science University of Toronto Canada Applied and Computational Mathematics Department of Mathematics Rwth Aachen University Aachen Germany Vector Institute for Artificial Intelligence Toronto Canada Chemical Physics Theory Group Department of Chemistry University of Toronto Canada Toronto Canada

We provide an integration of the universal, perturbative explicitly correlated [2]R12-correction in the context of the Variational Quantum Eigensolver (VQE). This approach is able to increase the accuracy of the underlying reference method significantly while requiring no additional quantum resources. The proposed approach only requires knowledge of the one- and two-particle reduced density matrices (RDMs) of the reference wavefunction;these can be measured after having reached convergence in the VQE. This computation comes at a cost that scales as the sixth power of the number of electrons. We explore the performance of the VQE+[2]R12approach using both conventional Gaussian basis sets and our recently proposed directly determined pair-natural orbitals obtained by multiresolution analysis (MRA-PNOs). Both Gaussian orbital and PNOs are investigated as a potential set of complementary basis functions in the computation of [2]R12. In particular the combination of MRA-PNOs with [2]R12has turned out to be very promising - persistently throughout our data, this allowed very accurate simulations at a quantum cost of a minimal basis set. Additionally, we found that the deployment of PNOs as complementary basis can greatly reduce the number of complementary basis functions that enter the computation of the correction at a complexity. Copyright © 2021, The Authors. All rights reserved.

关键词： Functions

Generative AI Enables Medical Image Segmentation in Ultra Low-Data Regimes

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arXiv 2024年

作者： Zhang, Li Jindal, Basu Alaa, Ahmed Weinreb, Robert Wilson, David Segal, Eran Zou, James Xie, Pengtao Department of Electrical and Computer Engineering University of California La Jolla San DiegoCA United States Bakar Computational Health Sciences Institute University of California San Francisco San FranciscoCA United States Department of Electrical Engineering and Computer Sciences University of California Berkeley BerkeleyCA United States Hamilton Glaucoma Center Shiley Eye Institute Viterbi Family Department of Ophthalmology University of California La Jolla San DiegoCA United States Division of Pulmonary Allergy and Critical Care Medicine Department of Medicine University of Pittsburgh PittsburghPA United States Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel Department of Molecular Cell Biology Weizmann Institute of Science Rehovot Israel Department of Biomedical Data Science Stanford University School of Medicine StanfordCA United States Department of Computer Science Stanford University StanfordCA United States Department of Medicine University of California La Jolla San DiegoCA United States

Semantic segmentation of medical images is pivotal in applications like disease diagnosis and treatment planning. While deep learning has excelled in automating this task, a major hurdle is the need for numerous annotated segmentation masks, which are resource-intensive to produce due to the required expertise and time. This scenario often leads to ultra low-data regimes, where annotated images are extremely limited, posing significant challenges for the generalization of conventional deep learning methods on test images. To address this, we introduce a generative deep learning framework, which uniquely generates high-quality paired segmentation masks and medical images, serving as auxiliary data for training robust models in data-scarce environments. Unlike traditional generative models that treat data generation and segmentation model training as separate processes, our method employs multi-level optimization for end-to-end data generation. This approach allows segmentation performance to directly influence the data generation process, ensuring that the generated data is specifically tailored to enhance the performance of the segmentation model. Our method demonstrated strong generalization performance across 9 diverse medical image segmentation tasks and on 16 datasets, in ultra-low data regimes, spanning various diseases, organs, and imaging modalities. When applied to various segmentation models, it achieved performance improvements of 10-20% (absolute), in both same-domain and out-of-domain scenarios. Notably, it requires 8 to 20 times less training data than existing methods to achieve comparable results. This advancement significantly improves the feasibility and cost-effectiveness of applying deep learning in medical imaging, particularly in scenarios with limited data availability. Copyright © 2024, The Authors. All rights reserved.

关键词： Semantic Segmentation