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Communication-avoiding kernel ridge regression on parallel and distributed systems

CCF TRANSACTIONS ON HIGH PERFORMANCE COMPUTING 2021年第3期3卷 252-270页

作者： You, Yang Huang, Jingyue Hsieh, Cho-Jui Vuduc, Richard Demmel, James Natl Univ Singapore Dept Comp Sci Singapore Singapore Fudan Univ Sch Data Sci Shanghai Peoples R China Univ Calif Los Angeles Dept Comp Sci Los Angeles CA 90024 USA Georgia Inst Technol Coll Comp Atlanta GA 30332 USA Univ Calif Berkeley Div Comp Sci Berkeley CA 94720 USA

Kernel ridge regression (KRR) is a fundamental method in machine learning. Given an n-by-d data matrix as input, a traditional implementation requires Theta(n(2)) memory to form an n-by-n kernel matrix and Theta(n(3)) flops to compute the final model. These time and storage costs prohibit KRR from scaling up to large datasets. For example, even on a relatively small dataset (a 520k-by-90 input requiring 357 MB), KRR requires 2 TB memory just to store the kernel matrix. The reason is that n usually is much larger than d for real-world applications. On the other hand, weak scaling becomes a problem: if we keep d and n/p fixed as p grows (p is the number of machines), the memory needed grows as Theta(p) per processor and the flops as Theta(p(2)) per processor. In the perfect weak scaling situation, both the memory needed and the flops grow as Theta(1) per processor (i.e. memory and flops are constant). The traditional Distributed KRR implementation (DKRR) only achieved 0.32% weak scaling efficiency from 96 to 1536 processors. We propose two new methods to address these problems: the balanced KRR (BKRR) and K-means KRR (KKRR). These methods consider alternative ways to partition the input dataset into pdifferent parts, generating pdifferent models, and then selecting the best model among them. Compared to a conventional implementation, KKRR2 (optimized version of KKRR) improves the weak scaling efficiency from 0.32 to 38% and achieves a 591x speedup for getting the same accuracy by using the same data and the same hardware (1536 processors). BKRR2 (optimized version of BKRR) achieves a higher accuracy than the current fastest method using less training time for a variety of datasets. For the applications requiring only approximate solutions, BKRR2 improves the weak scaling efficiency to 92% and achieves 3505x speedup (theoretical speedup: 4096x). The source code of this paper is available at https://***/similar to youyang/***.

关键词： Distributed machine learning Knights landing scalable algorithm

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The conjugate gradient method solves the neutron transport equation h-optimally

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NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 2007年第10期14卷 751-769页

作者： Chang, B. Lawrence Livermore Natl Lab Ctr Appl Sci Comp Livermore CA 94551 USA

We report a serendipitous finding that the conjugate gradient method is able to obtain the solution to the linear system derived by the discontinuous Galerkin method for the discrete-ordinate approximation of the mono-energetic time-independent neutron transport equation to a specified accuracy in a number of iterations which is bounded independently of the order of the system. A theoretical explanation for this phenomenon is given. The results of an experiment to test the theory are presented. Copyright (c) 2007 John Wiley & Sons, Ltd.

关键词： neutron transport equation conjugate gradient method discontinuous Galerkin method scalable algorithm

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A molecular simulation protocol to avoid sampling redundancy and discover new states

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BIOCHIMICA ET BIOPHYSICA ACTA-GENERAL SUBJECTS 2015年第5期1850卷 889-902页

作者： Bacci, Marco Vitalis, Andreas Caflisch, Amedeo Univ Zurich Dept Biochem CH-8057 Zurich Switzerland

Background: For biomacromolecules or their assemblies, experimental knowledge is often restricted to specific states. Ambiguity pervades simulations of these complex systems because there is no prior knowledge of relevant phase space domains, and sampling recurrence is difficult to achieve. In molecular dynamics methods, ruggedness of the free energy surface exacerbates this problem by slowing down the unbiased exploration of phase space. Sampling is inefficient if dwell times in metastable states are large. Methods: We suggest a heuristic algorithm to terminate and reseed trajectories run in multiple copies in parallel. It uses a recent method to order snapshots, which provides notions of "interesting" and "unique" for individual simulations. We define criteria to guide the reseeding of runs from more "interesting" points if they sample overlapping regions of phase space. Results: Using a pedagogical example and an ct-helical peptide, the approach is demonstrated to amplify the rate of exploration of phase space and to discover metastable states not found by conventional sampling schemes. Evidence is provided that accurate kinetics and pathways can be extracted from the simulations. Conclusions: The method, termed PIGS for Progress Index Guided Sampling, proceeds in unsupervised fashion, is scalable, and benefits synergistically from larger numbers of replicas. Results confirm that the underlying ideas are appropriate and sufficient to enhance sampling. General Significance: In molecular simulations, errors caused by not exploring relevant domains in phase space are always unquantifiable and can be arbitrarily large. Our protocol adds to the toollcit available to researchers in reducing these types of errors. This article is part of a Special Issue entitled "Recent Developments of Molecular Dynamics." (C) 2014 Elsevier B.V. All rights reserved.

关键词： Enhanced sampling Molecular dynamics Biomolecules Simulation convergence Transition path scalable algorithm

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Single- and multi-level network sparsification by algebraic distance

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JOURNAL OF COMPLEX NETWORKS 2017年第3期5卷 352-388页

作者： John, Emmanuel Safro, Ilya Clemson Univ Sch Comp 821 McMillan Rd Clemson SC 29634 USA

Network sparsification methods play an important role in modern network analysis when fast estimation of computationally expensive properties (such as the diameter, centrality indices and paths) is required. We propose a method of network sparsification that preserves a wide range of structural properties. Depending on the analysis goals, the method allows to distinguish between local and global range edges that can be filtered out during the sparsification. First we rank edges by their algebraic distances and then we sample them. We also introduce a multilevel framework for sparsification that can be used to control the sparsification process at various coarse-grained resolutions. Based primarily on the matrix-vector multiplications, our method is easily parallelized for different architectures.

关键词： networks sparsification multilevel methods software scalable algorithm

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Convergence guarantee for the sparse monotone single index model

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ELECTRONIC JOURNAL OF STATISTICS 2022年第2期16卷 4449-4496页

作者： Dai, Ran Song, Hyebin Barber, Rina Foygel Raskutti, Garvesh Univ Nebraska Med Ctr Dept Biostat Omaha NE 68198 USA Penn State Univ Dept Stat State Coll PA USA Univ Chicago Dept Stat Chicago IL USA Univ Wisconsin Dept Stat Madison WI USA

We consider a high-dimensional monotone single index model (hdSIM), which is a semiparametric extension of a high-dimensional gen-eralize linear model (hdGLM), where the link function is unknown, but constrained with monotone non-decreasing shape. We develop a scalable projection-based iterative approach, the "Sparse Orthogonal Descent Single -Index Model" (SOD-SIM), which alternates between sparse-thresholded or-thogonalized "gradient-like" steps and isotonic regression steps to recover the coefficient vector. Our main contribution is that we provide finite sam-ple estimation bounds for both the coefficient vector and the link function in high-dimensional settings under very mild assumptions on the design matrix X, the error term E, and their dependence. The convergence rate for the link function matches the low-dimensional isotonic regression minimax rate up to some poly-log terms (n-1/3). The convergence rate for the coeffi-cients is also n-1/3 up to some poly-log terms. This method can be applied to many real data problems, including GLMs with mis-specified link, clas-sification with mislabeled data, and classification with positive-unlabeled (PU) data. We study the performance of this method via both numerical studies and also an application on a PU data example.

关键词： Single-index model isotonic regression scalable algorithm high-dimensional

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Multimillion atom molecular dynamics simulations of nanostructures on parallel computers

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JOURNAL OF NANOPARTICLE RESEARCH 2003年第1-2期5卷 119-135页

作者： Vashishta, P Kalia, RK Nakano, A Univ So Calif Dept Mat Sci & Engn CACS Dept Phys & Astron Los Angeles CA 90089 USA Univ So Calif Dept Biomed Engn Los Angeles CA 90089 USA

scalable space - time multiresolution algorithms implemented on massively parallel computers enable large-scale molecular dynamics (MD) simulations involving up to a billion atoms. Multimillion atom MD simulations are performed to study critical issues in the area of structural and dynamical correlations in nanostructures. Our simulation research is focused on a few semiconductor, ceramic, and metallic nanostructures. These nanostructures systems include: nanometer-scale stress patterns in silicon/silicon nitride nanopixels;self-limiting growth and critical lateral sizes in gallium arsenide/indium arsenide nanomesas;structural transformation in colloidal semiconductor nanocrystals;nanoindentation of crystalline and amorphous silicon nitride films;and dynamics of oxidation of metallic aluminum nanoparticles.

关键词： molecular dynamics nanopixel nanomesa nanoparticle structural transformation indentation oxidation scalable algorithm

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High-Performance Computing based scalable Online Fuzzy Clustering algorithms for Big Data

High-Performance Computing based Scalable Online Fuzzy Clust...

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IEEE Symposium Series on Computational Intelligence (IEEE SSCI)

作者： Jha, Preeti Tiwari, Aruna Bharill, Neha Ratnaparkhe, Milind Patel, Om Prakash Pulakitha, Rapolu Chauhan, Aditi Indian Inst Technol Indore Comp Sci & Engn Indore India Mahindra Univ Comp Sci & Engn Hyderabad India ICAR Indian Inst Soybean Res Biotechnol Indore India

ISBN: (纸本)9781665487689

With the rise of big data trends so quickly, realtime stream data processing has become very important. Stream data is a type of big, fast, and unreliable dataset that cannot be handled well by traditional algorithms. Designing the algorithm that can efficiently process streaming data is a challenging task. This paper shows how important is to make a real-time clustering algorithm for data streams with high concept drift and an algorithm that can adapt to different dimensions. We propose scalable Random Sampling Online Optimization Weighted Fuzzy c-Means (SRSOO-WFCM) algorithms for handling Big Data in a High-Performance Computing (HPC) environment using an Apache Spark cluster. To compare SRSOO-WFCM with the traditional Online Fuzzy c-Means (OFCM) algorithm, we made a scalable version of OFCM named SOFCM. The proposed SRSOO-WFCM and SOFCM are incremental algorithms that involve making one sequential run through the data subsets. We employ both loadable and very large datasets to perform extensive experiments that facilitate comparing the proposed SRSOO-WFCM and SOFCM algorithms. The proposed SRSOOWFCM algorithm performs better than the SOFCM in terms of Normalized Mutual Information (NMI), Adjusted Rand Index (ARI), and F-score, respectively.

关键词： scalable algorithm Online Fuzzy Clustering Incremental Streaming algorithm Apache Spark HPC Big Data

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Effectiveness of P-scheme algorithm with message vectorization for solving recurrence equations.

Effectiveness of P-scheme algorithm with message vectorizati...

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33rd International Conference on Parallel Processing

作者： Wakatani, A Kobayashi, H Faculty of Science and Engineering Konan University Japan

ISBN: (纸本)0769521983

We propose "P-scheme" for solving recurrence equations for a tridiagonal linear system of equations on distributed-memory parallel computers, but its effectiveness is limited to the case where the problem is enough large. The limitation is mainly due to the communication cost of propagation phase of P-scheme. In order to overcome the difficulty, we use "message vectorization", which aggregates several communication messages into one, to alleviates the communication cost of P-scheme and evaluate the effectiveness of message vectorization for tridiagonal matrix solver Our experiments prove that the improved version of P-scheme works well for smaller problems on distributed environment like PC cluster systems and show linear and super-linear speedups can be achieved for 8194 x 8194 and 16386 x 16386 problems, respectively.

关键词： tridiagonal matrix message vectorization super-linear speedup scalable algorithm ADI

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Analytical performance evaluation for autonomous sensor fusion

Analytical performance evaluation for autonomous sensor fusi...

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Conference on Signal Processing, Sensor Fusion, and Target Recognition XVII

作者： Chang, K. C. George Mason Univ Dept Syst Engn & Operat Res Fairfax VA 22030 USA

ISBN: (纸本)9780819471598

A distributed data fusion system consists of a network of sensors, each capable of local processing and fusion of sensor data. There has been a great deal of work in developing distributed fusion algorithms applicable to a network centric architecture. Currently there are at least a few approaches including naive fusion, cross-correlation fusion, information graph fusion, maximum a posteriori (MAP) fusion, channel filter fusion, and covariance intersection fusion. However, in general, in a distributed system such as the ad hoc sensor networks, the communication architecture is not fixed. Each node has knowledge of only its local connectivity but not the global network topology. In those cases, the distributed fusion algorithm based on information graph type of approach may not scale due to its requirements to carry long pedigree information for decorrelation. In this paper, we focus on scalable fusion algorithms and conduct analytical performance evaluation to compare their performance. The goal is to understand the performance of those algorithms under different operating conditions. Specifically, we evaluate the performance of channel filter fusion, Chernoff fusion, Shannon Fusion, and Battachayya fusion algorithms. We also compare their results to Naive fusion and "optimal" centralized fusion algorithms under a specific communication pattern.

关键词： distributed fusion net-centric autonomous sensor scalable algorithm fusion performance analysis

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scalable Fuzzy Clustering-based Regression to Predict the Isoelectric Points of the Plant Protein Sequences using Apache Spark

Scalable Fuzzy Clustering-based Regression to Predict the Is...

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IEEE CIS International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： Choudhary, Ajay Jha, Preeti Tiwari, Aruna Bharill, Neha Ratnaparkhe, Milind Indian Inst Technol Indore Comp Sci & Engn Indore India Mahindra Univ Ecole Cent Sch Engn Comp Sci & Engn Hyderabad India ICAR Indian Inst Soybean Res Indore India

ISBN: (纸本)9781665444071

Learning in non-stationary environments require modern tools and algorithms to quickly adapt to the new pattern because concept drift can change the underlying distribution. So, the existing assumption that the data is independent and identically distributed may be invalid in data stream scenarios. Given the massive volume of high-speed data streams and the concept drift, traditional machine learning algorithms must be self-adapting. One of the difficulties in handling regression tasks is the complexities of equations for the regression models when combined with drift handling techniques. The high dimensional protein data is a major challenge for bioinformatics researchers to analyse the dynamics of the sequences. This paper proposes a scalable Fuzzy Clustering induced Regression (SFC-R) algorithm to predict the isoelectric point of the plant protein sequences using Apache Spark clusters. The SFC-R algorithm uses the input features extracted from the plant protein sequences and validates performance in terms of mean squared error (MAE) and root-mean-square error (RMSE). Experiments on plant protein datasets are carried out to validate the high accuracy and robustness of our approach.

关键词： Fuzzy Clustering scalable algorithm Apache Spark Regression

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