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Robust and Fast Measure of Information via Low-rank Representation

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arXiv 2022年

作者： Dong, Yuxin Gong, Tieliang Yu, Shujian Chen, Hong Li, Chen School of Computer Science and Technology Xi’an Jiaotong University Xi’an710049 China Shaanxi Provincial Key Laboratory of Big Data Knowledge Engineering Ministry of Education Xi’an710049 China Machine Learning Group UiT - The Arctic University of Norway Norway College of Science Huazhong Agriculture University Wuhan430070 China Engineering Research Center of Intelligent Technology for Agriculture Ministry of Education Wuhan430070 China

The matrix-based Rényi’s entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical inference and machine learning tasks. However, this information theoretical quantity is not robust against noise in the data, and is computationally prohibitive in large-scale applications. To address these issues, we propose a novel measure of information, termed low-rank matrix-based Rényi’s entropy, based on low-rank representations of infinitely divisible kernel matrices. The proposed entropy functional inherits the specialty of of the original definition to directly quantify information from data, but enjoys additional advantages including robustness and effective calculation. Specifically, our low-rank variant is more sensitive to informative perturbations induced by changes in underlying distributions, while being insensitive to uninformative ones caused by noises. Moreover, low-rank Rényi’s entropy can be efficiently approximated by random projection and Lanczos iteration techniques, reducing the overall complexity from O(n3) to O(n2s) or even O(ns2), where n is the number of data samples and s n. We conduct large-scale experiments to evaluate the effectiveness of this new information measure, demonstrating superior results compared to matrix-based Rényi’s entropy in terms of both performance and computational efficiency. Copyright © 2022, The Authors. All rights reserved.

关键词： Entropy

The Alchemical Integral Transform revisited

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arXiv 2023年

作者： Krug, Simon León von Lilienfeld, O. Anatole Machine Learning Group Technische Universität Berlin Berlin10587 Germany Berlin Institute for the Foundations of Learning and Data Berlin10587 Germany Chemical Physics Theory Group Department of Chemistry University of Toronto St. George Campus TorontoON Canada Department of Materials Science and Engineering University of Toronto St. George Campus TorontoON Canada Vector Institute for Artificial Intelligence TorontoON Canada Department of Physics University of Toronto St. George Campus TorontoON Canada Acceleration Consortium University of Toronto TorontoON Canada

We recently introduced the Alchemical Integral Transform (AIT) enabling the prediction of energy differences, and guessed an Ansatz to parametrize space r in some alchemical change λ. Here, we present a rigorous derivation of AIT’s kernel K and discuss the parametrization r(λ) in n dimensions, i.e. necessary conditions, mathematical freedoms and additional constraints when obtaining it. Analytical expressions for changes in energy spectra and densities are given for a number of systems. Examples include homogeneous potentials like the quantum harmonic oscillator, Hydrogen-like atom, and Dirac well, both for one- and multiparticle cases, and a multiparticle system beyond coordinate scaling for harmonic potentials. © 2023, CC BY.

关键词： Choquet integral

Trace chemical and major constituents measurements of the international space station atmosphere by the vehicle cabin atmosphere monitor

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Trace chemical and major constituents measurements of the in...

42nd International Conference on Environmental Systems 2012, ICES 2012

作者： Darrach, M.R. Chutjian, A. Bornstein, B.J. Croonquist, A.P. Garkanian, V. Hofman, J. Karmon, D. Kenny, J. Kidd, R.D. Lee, S. Macaskill, J.A. Madzunkov, S.M. Mandrake, L. Schaefer, R.T. Toomarian, N. Jet Propulsion Laboratory California Institute of Technology Pasadena CA 91109 United States Atomic and Molecular Physics Group JPL/Caltech Pasadena CA 91109 United States Instrument Autonomy Group JPL/Caltech Pasadena CA 91109 United States MicroDevices Group JPL/Caltech Pasadena CA 91109 United States Optical Communications Group JPL/Caltech Pasadena CA 91109 United States Instruments and Science Data Systems JPL/Caltech Pasadena CA 91109 United States Instrument Integration and Test JPL/Caltech Pasadena CA 91109 United States Planetary Chemistry and Astrobiology JPL/Caltech Pasadena CA 91109 United States High Capacity Computing and Modeling JPL/Caltech Pasadena CA 91109 United States Machine Learning and Instrument Autonomy Group JPL/Caltech Pasadena CA 91109 United States Advanced Computer Systems and Technology JPL/Caltech Pasadena CA 91109 United States Advanced Instrument Concepts JPL/Caltech Pasadena CA 91109 United States

ISBN: (纸本)9781600869341

We report on trace gas and major atmospheric constituents results obtained by the Vehicle Cabin Atmosphere Monitor (VCAM) following almost two years of operation aboard the International Space Station (ISS). VCAM isan autonomous environmental monitor based on a highly compact gas chromatograph/quadrupole ion trap mass spectrometer. It was flown to the International Space Station (ISS) on shuttle mission STS-131 and commenced operations on June 2010. VCAM is capable of providing measurements of both parts-per-billion (ppb) levels of volatile trace-gas constituents, and of the atmospheric major constituents (nitrogen, oxygen, argon, and carbon dioxide) in a space vehicle or station. It is designed to operate autonomously and maintenance-free, approximately once per day, with a self-contained gas supply sufficient for a one-year lifetime. VCAM's performance is sufficient to detect and identify 90% of the target compounds at their 180-day Spacecraft Maximum Allowable Concentration levels. © 2012 by the American Institute of Aeronautics and Astronautics, Inc.

关键词： Gases

MambaLRP: Explaining Selective State Space Sequence Models

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arXiv 2024年

作者： Jafari, Farnoush Rezaei Montavon, Grégoire Müller, Klaus-Robert Eberle, Oliver Machine Learning Group Technische Universität Berlin Berlin10587 Germany BIFOLD Berlin Institute for the Foundations of Learning and Data Berlin10587 Germany Department of Mathematics and Computer Science Freie Universität Berlin Arnimallee 14 Berlin14195 Germany Department of Artificial Intelligence Korea University Seoul136-713 Korea Republic of Max Planck Institute for Informatics Stuhlsatzenhausweg 4 Saarbrücken66123 Germany Google DeepMind Berlin Germany

Recent sequence modeling approaches using selective state space sequence models, referred to as Mamba models, have seen a surge of interest. These models allow efficient processing of long sequences in linear time and are rapidly being adopted in a wide range of applications such as language modeling, demonstrating promising performance. To foster their reliable use in real-world scenarios, it is crucial to augment their transparency. Our work bridges this critical gap by bringing explainability, particularly Layer-wise Relevance Propagation (LRP), to the Mamba architecture. Guided by the axiom of relevance conservation, we identify specific components in the Mamba architecture, which cause unfaithful explanations. To remedy this issue, we propose MambaLRP, a novel algorithm within the LRP framework, which ensures a more stable and reliable relevance propagation through these components. Our proposed method is theoretically sound and excels in achieving state-of-the-art explanation performance across a diverse range of models and datasets. Moreover, MambaLRP facilitates a deeper inspection of Mamba architectures, uncovering various biases and evaluating their significance. It also enables the analysis of previous speculations regarding the long-range capabilities of Mamba models. Copyright © 2024, The Authors. All rights reserved.

关键词： Modeling languages

Adaptive 3D Localization of 2D Freehand Ultrasound Brain Images

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arXiv 2022年

作者： Yeung, Pak-Hei Aliasi, Moska Haak, Monique Xie, Weidi Namburete, Ana I.L. Oxford Machine Learning in NeuroImaging Lab Department of Computer Science University of Oxford Oxford United Kingdom Department of Engineering Science Institute of Biomedical Engineering University of Oxford Oxford United Kingdom Division of Fetal Medicine Department of Obstetrics Leiden University Medical Center Leiden2333 ZA Netherlands Shanghai Jiao Tong University Shanghai China Visual Geometry Group Department of Engineering Science University of Oxford Oxford United Kingdom

Two-dimensional (2D) freehand ultrasound is the mainstay in prenatal care and fetal growth monitoring. The task of matching corresponding cross-sectional planes in the 3D anatomy for a given 2D ultrasound brain scan is essential in freehand scanning, but challenging. We propose AdLocUI, a framework that Adaptively Localizes 2D Ultrasound Images in the 3D anatomical atlas without using any external tracking sensor. We first train a convolutional neural network with 2D slices sampled from co-aligned 3D ultrasound volumes to predict their locations in the 3D anatomical atlas. Next, we fine-tune it with 2D freehand ultrasound images using a novel unsupervised cycle consistency, which utilizes the fact that the overall displacement of a sequence of images in the 3D anatomical atlas is equal to the displacement from the first image to the last in that sequence. We demonstrate that AdLocUI can adapt to three different ultrasound datasets, acquired with different machines and protocols, and achieves significantly better localization accuracy than the baselines. AdLocUI can be used for sensorless 2D freehand ultrasound guidance by the bedside. The source code is available at https://***/pakheiyeung/AdLocUI. © 2022, CC BY.

关键词： Ultrasonics

Reply to chen et al.: Parametric methods for cluster inference perform worse for two-sided t-tests

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arXiv 2018年

作者： Eklund, Anders Knutsson, Hans Nichols, Thomas E. Department of Biomedical Engineering Division of Medical Informatics Linkoping University Linkoping Sweden Department of Computer and Information Science Division of Statistics and Machine Learning Linkoping University Linkoping Sweden Linkoping University Linkoping Sweden Big Data Institute University of Oxford Oxford United Kingdom United Kingdom University of Oxford Oxford United Kingdom Department of Statistics University of Warwick Coventry United Kingdom

One-sided t-tests are commonly used in the neuroimaging field, but two-sided tests should be the default unless a researcher has a strong reason for using a one-sided test. Here we extend our previous work on cluster false positive rates, which used one-sided tests, to two-sided tests. Briey, we found that parametric methods perform worse for two-sided t-tests, and that non-parametric methods perform equally well for one-sided and two-sided tests. Copyright © 2018, The Authors. All rights reserved.

关键词： Neuroimaging

A distributed block coordinate descent method for training l1regularized linear classifiers

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The Journal of Machine Learning Research

The Journal of machine learning Research 2017年第1期18卷

作者： Dhruv Mahajan S. Sathiya Keerthi S. Sundararajan Applied Machine Learning Group Facebook Research Menlo Park CA Office Data Science Group Microsoft Mountain View CA Microsoft Research Bangalore India

Distributed training of l1 regularized classifiers has received great attention recently. Most existing methods approach this problem by taking steps obtained from approximating the objective by a quadratic approximation that is decoupled at the individual variable level. These methods are designed for multicore systems where communication costs are low. They are inefficient on systems such as Hadoop running on a cluster of commodity machines where communication costs are substantial. In this paper we design a distributed algorithm for l1 regularization that is much better suited for such systems than existing algorithms. A careful cost analysis is used to support these points and motivate our method. The main idea of our algorithm is to do block optimization of many variables on the actual objective function within each computing node; this increases the computational cost per step that is matched with the communication cost, and decreases the number of outer iterations, thus yielding a faster overall method. Distributed Gauss-Seidel and Gauss-Southwell greedy schemes are used for choosing variables to update in each step. We establish global convergence theory for our algorithm, including Q-linear rate of convergence. Experiments on two benchmark problems show our method to be much faster than existing methods.

关键词： l1 regularization distributed learning

ImplicitVol: Sensorless 3D ultrasound reconstruction with deep implicit representation

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arXiv 2021年

作者： Yeung, Pak-Hei Hesse, Linde Aliasi, Moska Haak, Monique Xie, Weidi Namburete, Ana I.L. Department of Engineering Science Institute of Biomedical Engineering University of Oxford Oxford United Kingdom Oxford Machine Learning in NeuroImaging Lab Department of Computer Science University of Oxford Oxford United Kingdom Division of Fetal Medicine Department of Obstetrics Leiden University Medical Center Leiden2333 ZA Netherlands Nufield Department of Women's and Reproductive Health University of Oxford Oxford United Kingdom Visual Geometry Group Department of Engineering Science University of Oxford Oxford United Kingdom

The objective of this work is to achieve sensorless reconstruction of a 3D volume from a set of 2D freehand ultrasound images with deep implicit representation. In contrast to the conventional way that represents a 3D volume as a discrete voxel grid, we do so by parameterizing it as the zero level-set of a continuous function, i.e. implicitly representing the 3D volume as a mapping from the spatial coordinates to the corresponding intensity values. Our proposed model, termed as ImplicitVol, takes a set of 2D scans and their estimated locations in 3D as input, jointly refining the estimated 3D locations and learning a full reconstruction of the 3D volume. When testing on real 2D ultrasound images, novel cross-sectional views that are sampled from ImplicitVol show significantly better visual quality than those sampled from existing reconstruction approaches, outperforming them by over 30% (NCC and SSIM), between the output and ground-truth on the 3D volume testing data. The code will be made publicly available. © 2021, CC BY.

关键词： Image reconstruction

Accurate machine Learned Quantum-Mechanical Force Fields for Biomolecular Simulations

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arXiv 2022年

作者： Unke, Oliver T. Stöhr, Martin Ganscha, Stefan Unterthiner, Thomas Maennel, Hartmut Kashubin, Sergii Ahlin, Daniel Gastegger, Michael Sandonas, Leonardo Medrano Tkatchenko, Alexandre Müller, Klaus-Robert Google Research Brain Team Machine Learning Group Technische Universität Berlin Berlin10587 Germany Technische Universität Berlin Berlin10623 Germany Department of Physics and Materials Science University of Luxembourg Luxembourg CityL-1511 Luxembourg BASLEARN TU Berlin Berlin10587 Germany BASF Joint Lab for Machine Learning Technische Universität Berlin Berlin10587 Germany Department of Artificial Intelligence Korea University Anam-dong Seongbuk-gu Seoul02841 Korea Republic of Max Planck Institute for Informatics Stuhlsatzenhausweg Saarbrücken66123 Germany BIFOLD Berlin Institute for the Foundations of Learning and Data Berlin Germany

Molecular dynamics (MD) simulations allow atomistic insights into chemical and biological processes. Accurate MD simulations require computationally demanding quantum-mechanical calculations, being practically limited to short timescales and few atoms. For larger systems, efficient, but much less reliable empirical force fields are used. Recently, machine learned force fields (MLFFs) emerged as an alternative means to execute MD simulations, offering similar accuracy as ab initio methods at orders-of-magnitude speedup. Until now, MLFFs mainly capture short-range interactions in small molecules or periodic materials, due to the increased complexity of constructing models and obtaining reliable reference data for large molecules, where long-ranged many-body effects become important. This work proposes a general approach to constructing accurate MLFFs for large-scale molecular simulations (GEMS) by training on "bottom-up" and "top-down" molecular fragments of varying size, from which the relevant physicochemical interactions can be learned. GEMS is applied to study the dynamics of alanine-based peptides and the 46-residue protein crambin in aqueous solution, allowing nanosecond-scale MD simulations of >25k atoms at essentially ab initio quality. Our findings suggest that structural motifs in peptides and proteins are more flexible than previously thought, indicating that simulations at ab initio accuracy might be necessary to understand dynamic biomolecular processes such as protein (mis)folding, drug–protein binding, or allosteric regulation. Copyright © 2022, The Authors. All rights reserved.

关键词： Molecular dynamics