High-dimensional dependency structure learning for physical processes

Jamal Golmohammadi, Imme Ebert-Uphoff, Sijie He, Yi Deng, Arindam Banerjee

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this paper, we consider the use of structure learning methods for probabilistic graphical models to identify statistical dependencies in high-dimensional physical processes. Such processes are often synthetically characterized using PDEs (partial differential equations) and are observed in a variety of natural phenomena. In this paper, we present ACLIME-ADMM, an efficient two-step algorithm for adaptive structure learning, which decides a suitable edge specific threshold in a data-driven statistically rigorous manner. Both steps of our algorithm use (inexact) ADMM to solve suitable linear programs, and all iterations can be done in closed form in an efficient block parallel manner. We compare ACLIME-ADMM with baselines on both synthetic data simulated by PDEs that model advection-diffusion processes, and real data of daily global geopotential heights to study information flow in the atmosphere. ACLIME-ADMM is shown to be efficient, stable, and competitive, usually better than the baselines especially on difficult problems. On real data, ACLIME-ADMM recovers the underlying structure of global atmospheric circulation, including switches in wind directions at the equator and tropics entirely from the data.

Original languageEnglish (US)
Title of host publicationProceedings - 17th IEEE International Conference on Data Mining, ICDM 2017
EditorsGeorge Karypis, Srinivas Alu, Vijay Raghavan, Xindong Wu, Lucio Miele
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781538638347
StatePublished - Dec 15 2017
Event17th IEEE International Conference on Data Mining, ICDM 2017 - New Orleans, United States
Duration: Nov 18 2017Nov 21 2017

Publication series

NameProceedings - IEEE International Conference on Data Mining, ICDM
ISSN (Print)1550-4786


Other17th IEEE International Conference on Data Mining, ICDM 2017
Country/TerritoryUnited States
CityNew Orleans

Bibliographical note

Funding Information:
Acknowledgements. JG, SH, and AB acknowledge the support of NSF grants IIS-1563950, IIS-1447566, IIS-1447574, IIS-1422557, CCF-1451986, CNS-1314560, and the support from UMN MSI. YD and I. E-U acknowledge support from AGS-1445956 and AGS-1445978.

Publisher Copyright:
© 2017 IEEE.


  • Geoscience
  • High-dimensional physical process
  • PC stable
  • Structure learning


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