Nothing Special   »   [go: up one dir, main page]

skip to main content
10.1145/3221269.3221292acmotherconferencesArticle/Chapter ViewAbstractPublication PagesssdbmConference Proceedingsconference-collections
research-article

Order-independent constraint-based causal structure learning for gaussian distribution models using GPUs

Published: 09 July 2018 Publication History

Abstract

Learning the causal structures in high-dimensional datasets allows deriving advanced insights from observational data, thus creating the potential for new applications. One crucial limitation of state-of-the-art methods for learning causal relationships, such as the PC algorithm, is their long execution time. While, in the worst case, the execution time is exponential to the dimension of a given dataset, it is polynomial if the underlying causal structures are sparse. To address the long execution time, parallelized extensions of the algorithm have been developed addressing the Central Processing Unit (CPU) as the primary execution device. While modern multicore CPUs expose a decent level of parallelism, coprocessors, such as Graphics Processing Units (GPUs), are specifically designed to process thousands of data points in parallel, providing superior parallel processing capabilities compared to CPUs.
In our work, we leverage the parallel processing power of GPUs to address the drawback of the long execution time of the PC algorithm and develop an efficient GPU-accelerated implementation for Gaussian distribution models. Based on an experimental evaluation of various high-dimensional real-world gene expression datasets, we show that our GPU-accelerated implementation outperforms existing CPU-based versions, by factors up to 700.

References

[1]
Martín Abadi, Paul Barham, Jianmin Chen, Zhifeng Chen, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Geoffrey Irving, Michael Isard, Manjunath Kudlur, Josh Levenberg, Rajat Monga, Sherry Moore, Derek G. Murray, Benoit Steiner, Paul Tucker, Vijay Vasudevan, Pete Warden, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng. 2016. TensorFlow: A System for Large-scale Machine Learning. In Proceedings of the 12th USENIX Conference on Operating Systems Design and Implementation (OSDI'16). USENIX Association, Berkeley, CA, USA, 265--283. http://dl.acm.org/citation.cfm?id=3026877.3026899
[2]
H. Ahrens. 1975. Dempster, A. P.: Elements of Continuous Multivariate Analysis. Addison-Wesley Publ. Co., Reading, Mass. 1969. XII, 388 S. Biometrische Zeitschrift 17, 7 (1975), 468--468.
[3]
Steen A. Andersson, David Madigan, and Michael D. Perlman. 1997. A Characterization of Markov Equivalence Classes for Acyclic Digraphs. The Annals of Statistics 25, 2 (1997), 505--541. http://www.jstor.org/stable/2242556
[4]
Joshua Buckner, Justin Wilson, Mark Seligman, Brian Athey, Stanley Watson, and Fan Meng. 2010. The gputools package enables GPU computing in R. Bioinformatics 26, 1 Jan. 2010), 134--135.
[5]
A. Cano, M. Gómez-Olmedo, and S. Moral. 2008. A Score Based Ranking of the Edges for the PC Algorithm. In Proceedings of the Fourth European Workshop on Probabilistic Graphical Models, Manfred Jaeger and Thomas D. Nielsen (Eds.). 41--48.
[6]
Bryan Catanzaro, Narayanan Sundaram, and Kurt Keutzer. 2008. Fast Support Vector Machine Training and Classification on Graphics Processors. In Proceedings of the 25th International Conference on Machine Learning (ICML '08). ACM, New York, NY, USA, 104--111.
[7]
Sharan Chetlur, Cliff Woolley, Philippe Vandermersch, Jonathan Cohen, John Tran, Bryan Catanzaro, and Evan Shelhamer. 2014. cuDNN: Efficient Primitives for Deep Learning. CoRR abs/1410.0759 (2014). arXiv:1410.0759 http://arxiv.org/abs/1410.0759
[8]
David Maxwell Chickering. 2002. Learning Equivalence Classes of Bayesian-network Structures. J. Mach. Learn. Res. 2 (March 2002), 445--498.
[9]
Diego Colombo and Marloes H. Maathuis. 2014. Order-independent Constraint-based Causal Structure Learning. J. Mach. Learn. Res. 15, 1 (Jan. 2014), 3741--3782. http://dl.acm.org/citation.cfm?id=2627435.2750365
[10]
Diego Colombo, Marloes H. Maathuis, Markus Kalisch, and Thomas S. Richardson. 2011. Learning High-dimensional DAGs with Latent and Selection Variables. In Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence (UAI'11). AUAI Press, Arlington, Virginia, United States, 850--850. http://dl.acm.org/citation.cfm?id=3020548.3020648
[11]
Leonardo Dagum and Ramesh Menon. 1998. OpenMP: An Industry-Standard API for Shared-Memory Programming. IEEE Comput. Sci. Eng. 5, 1 (Jan. 1998), 46--55.
[12]
A. P. Dawid. 1979. Conditional Independence in Statistical Theory. Journal of the Royal Statistical Society. Series B (Methodological) 41, 1 (1979), 1--31. http://www.jstor.org/stable/2984718
[13]
Dirk Eddelbuettel and Conrad Sanderson. 2014. RcppArmadillo: Accelerating R with High-performance C++ Linear Algebra. Comput. Stat. Data Anal. 71 (March 2014), 1054--1063.
[14]
Marloes H Maathuis, Diego Colombo, Markus Kalisch, and Peter Bühlmann. 2010. Predicting causal effects in large-scale systems from observational data. 7 (04 2010), 247--8.
[15]
J. Abellán and M. Gómez-Olmedo and S. Moral. 2006. Some Variations on the PC Algorithm. In Proceedings of the Third European Workshop on Probabilistic Graphical Models (PGM' 06). 1--8.
[16]
Markus Kalisch and Peter Bühlmann. 2007. Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm. J. Mach. Learn. Res. 8 (May 2007), 613--636. http://dl.acm.org/citation.cfm?id=1248659.1248681
[17]
Markus Kalisch, Martin Mächler, Diego Colombo, Marloes H. Maathuis, and Peter Bühlmann. 2012. Causal Inference Using Graphical Models with the R Package pcalg. Journal of Statistical Software, Articles 47, 11 (2012), 1--26.
[18]
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton. 2012. ImageNet Classification with Deep Convolutional Neural Networks. In Proceedings of the 25th International Conference on Neural Information Processing Systems - Volume 1 (NIPS'12). Curran Associates Inc., USA, 1097--1105. http://dl.acm.org/citation.cfm?id=2999134.2999257
[19]
Steffen L Lauritzen. 1996. Graphical models. Vol. 17. Clarendon Press.
[20]
Thuc Le, Tao Hoang, Jiuyong Li, Lin Liu, Huawen Liu, and Shu Hu. 2015. A fast PC algorithm for high dimensional causal discovery with multi-core PCs. IEEE/ACM Transactions on Computational Biology and Bioinformatics (02 2015).
[21]
Thuc Duy Le, Lin Liu, Junpeng Zhang, Bing Liu, and Jiuyong Li. 2015. From miRNA regulation to miRNA-TF co-regulation: computational approaches and challenges. Briefings in Bioinformatics 16, 3 (2015), 475--496.
[22]
Joseph Lee Rodgers and W Alan Nicewander. 1988. Thirteen Ways to Look at the Correlation Coefficient. The American Statistician 42, 1 (1988), 59--66.
[23]
Erich L Lehmann and Joseph P Romano. 2006. Testing statistical hypotheses. Springer Science & Business Media.
[24]
Erik Lindholm, John Nickolls, Stuart Oberman, and John Montrym. 2008. NVIDIA Tesla: A Unified Graphics and Computing Architecture. IEEE Micro 28, 2 (March 2008), 39--55.
[25]
Ren C Luo, M-H Lin, and Ralph S Scherp. 1988. Dynamic multi-sensor data fusion system for intelligent robots. IEEE Journal on Robotics and Automation 4, 4 (Aug 1988), 386--396.
[26]
Marloes H Maathuis, Markus Kalisch, and Peter Bühlmann. 2009. Estimating high-dimensional intervention effects from observational data. The Annals of Statistics 37, 6A (12 2009), 3133--3164.
[27]
Anders L. Madsen, Frank Jensen, Antonio Salmerón, Martin Karlsen, Helge Langseth, and Thomas D. Nielsen. 2014. A New Method for Vertical Parallelisation of TAN Learning Based on Balanced Incomplete Block Designs. In Probabilistic Graphical Models, Linda C. van der Gaag and Ad J. Feelders (Eds.). Springer International Publishing, Cham, 302--317.
[28]
Anders L. Madsen, Frank Jensen, Antonio Salmerón, Helge Langseth, and Thomas D. Nielsen. 2015. Parallelisation of the PC Algorithm. In Proceedings of the 16th Conference of the Spanish Association for Artificial Intelligence on Advances in Artificial Intelligence - Volume 9422. Springer-Verlag New York, Inc., New York, NY, USA, 14--24.
[29]
Anders L. Madsen, Frank Jensen, Antonio Salmerón, Helge Langseth, and Thomas D. Nielsen. 2017. A Parallel Algorithm for Bayesian Network Structure Learning from Large Data Sets. Know.-Based Syst. 117, C (Feb. 2017), 46--55.
[30]
Katerina Marazopoulou, Rumi Ghosh, Prasanth Lade, and David Jensen. 2016. Causal Discovery for Manufacturing Domains. CoRR abs/1605.04056 (2016). arXiv:1605.04056 http://arxiv.org/abs/1605.04056
[31]
Daniel Marbach, James C. Costello, Robert Küffner, Nicole M. Vega, Robert J. Prill, Diogo M. Camacho, Kyle R. Allison, Manolis Kellis, James J. Collins, Andrej Aderhold, Gustavo Stolovitzky, and et al. 2012. Wisdom of crowds for robust gene network inference. Nature Methods 9, 8 (8 2012), 796--804.
[32]
Christopher Meek. 1995. Strong Completeness and Faithfulness in Bayesian Networks. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI'95). Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 411--418. http://dl.acm.org/citation.cfm?id=2074158.2074205
[33]
Nicolai Meinshausen and Peter Bühlmann. 2010. Stability selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72, 4 (2010), 417--473.
[34]
John Nickolls, Ian Buck, Michael Garland, and Kevin Skadron. 2008. Scalable Parallel Programming with CUDA., Article 16 (2008), 14 pages.
[35]
NVIDIA Corporation. 2017. CUDA Math API. Retrieved March 10, 2018 from http://docs.nvidia.com/cuda/pdf/CUDA_Math_API.pdf
[36]
NVIDIA Corporation. 2017. NVIDIA TESLA V100 GPU ACCELERATOR. Retrieved February 12, 2018 from http://www.nvidia.com/content/PDF/Volta-Datasheet.pdf
[37]
NVIDIA Corporation. 2018. Profiler User's Guide. Retrieved March 10, 2018 from http://docs.nvidia.com/cuda/pdf/CUDA_Profiler_Users_Guide.pdf
[38]
Judea Pearl. 2009. Causality: Models, Reasoning and Inference (2nd ed.). Cambridge University Press, New York, NY, USA.
[39]
Judea Pearl and Thomas Verma. 1991. A Theory of Inferred Causation. In Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning (KR'91). Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 441--452. http://dl.acm.org/citation.cfm?id=3087158.3087202
[40]
Roger Penrose. 1955. A generalized inverse for matrices. In Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 51. Cambridge University Press, Cambridge University Press, 406--413.
[41]
R Core Team. 2017. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/
[42]
Andrea Rau, Florence Jaffrézic, and Grégory Nuel. 2013. Joint estimation of causal effects from observational and intervention gene expression data. BMC systems biology 7, 1 (Oct 2013), 111.
[43]
Thomas Richardson. 1996. A Discovery Algorithm for Directed Cyclic Graphs. In Proceedings of the Twelfth International Conference on Uncertainty in Artificial Intelligence (UAI'96). Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 454--461. http://dl.acm.org/citation.cfm?id=2074284.2074338
[44]
Conrad Sanderson and Ryan Curtin. 2016. Armadillo: a template-based C library for linear algebra. Journal of Open Source Software 1, 2 (Oct 2016), 26. https://doi.org/
[45]
Christian Schwarz, Christopher Schmidt, Michael Hopstock, Werner Sinzig, and Hasso Plattner. 2016. Efficient Calculation and Simulation of Product Cost Leveraging In-Memory Technology and Coprocessors. In The Sixth International Conference on Business Intelligence and Technology (BUSTECH 2016).
[46]
Marco Scutari. 2010. Learning Bayesian Networks with the bnlearn R Package. Journal of Statistical Software, Articles 35, 3 (2010), 1--22.
[47]
Peter Spirtes. 2010. Introduction to Causal Inference. J. Mach. Learn. Res. 11 (Aug. 2010), 1643--1662. http://dl.acm.org/citation.cfm?id=1756006.1859905
[48]
Peter Spirtes, Clark N Glymour, and Richard Scheines. 2000. Causation, Prediction, and Search. MIT press.
[49]
Peter Spirtes and Kun Zhang. 2016. Causal discovery and inference: concepts and recent methodological advances. Applied Informatics 3, 1 (18 Feb 2016), 3.
[50]
Michail Tsagris, Giorgos Borboudakis, Vincenzo Lagani, and Ioannis Tsamardinos. 2018. Constraint-based causal discovery with mixed data. International Journal of Data Science and Analytics (02 Feb 2018).
[51]
Joe Whittaker. 2009. Graphical Models in Applied Multivariate Statistics. Wiley Publishing.

Cited By

View all
  • (2023)PEPC: Parallel and Extensible PC Implementation for Causal Structure LearningProceedings of the 2023 7th International Conference on High Performance Compilation, Computing and Communications10.1145/3606043.3606054(77-84)Online publication date: 17-Jun-2023
  • (2023)Enterprise Platform and Integration Concepts Research at HPIACM SIGMOD Record10.1145/3582302.358232251:4(68-73)Online publication date: 25-Jan-2023
  • (2023)A Parallel Framework for Constraint-Based Bayesian Network Learning via Markov Blanket DiscoveryIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2023.324413534:6(1699-1715)Online publication date: Jun-2023
  • Show More Cited By

Recommendations

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Other conferences
SSDBM '18: Proceedings of the 30th International Conference on Scientific and Statistical Database Management
July 2018
314 pages
ISBN:9781450365055
DOI:10.1145/3221269
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 09 July 2018

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. GPU-acceleration
  2. Gaussian distribution model
  3. PC algorithm
  4. causal inference
  5. conditional independence testing
  6. parallelization
  7. probabilistic statistics

Qualifiers

  • Research-article

Conference

SSDBM '18

Acceptance Rates

SSDBM '18 Paper Acceptance Rate 30 of 75 submissions, 40%;
Overall Acceptance Rate 56 of 146 submissions, 38%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)8
  • Downloads (Last 6 weeks)1
Reflects downloads up to 24 Sep 2024

Other Metrics

Citations

Cited By

View all
  • (2023)PEPC: Parallel and Extensible PC Implementation for Causal Structure LearningProceedings of the 2023 7th International Conference on High Performance Compilation, Computing and Communications10.1145/3606043.3606054(77-84)Online publication date: 17-Jun-2023
  • (2023)Enterprise Platform and Integration Concepts Research at HPIACM SIGMOD Record10.1145/3582302.358232251:4(68-73)Online publication date: 25-Jan-2023
  • (2023)A Parallel Framework for Constraint-Based Bayesian Network Learning via Markov Blanket DiscoveryIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2023.324413534:6(1699-1715)Online publication date: Jun-2023
  • (2023)ParaLiNGAMJournal of Parallel and Distributed Computing10.1016/j.jpdc.2023.01.007176:C(114-127)Online publication date: 1-Jun-2023
  • (2022)GPUCSL: GPU-Based Library for Causal Structure Learning2022 IEEE International Conference on Data Mining Workshops (ICDMW)10.1109/ICDMW58026.2022.00159(1236-1239)Online publication date: Nov-2022
  • (2021)MPCSL - A Modular Pipeline for Causal Structure LearningProceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining10.1145/3447548.3467082(3068-3076)Online publication date: 14-Aug-2021
  • (2020)cuPC: CUDA-Based Parallel PC Algorithm for Causal Structure Learning on GPUIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2019.293912631:3(530-542)Online publication date: 1-Mar-2020
  • (2020)Out-of-Core GPU-Accelerated Causal Structure LearningAlgorithms and Architectures for Parallel Processing10.1007/978-3-030-38991-8_7(89-104)Online publication date: 22-Jan-2020

View Options

Get Access

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media