NDLI: The Pairwise Gaussian Random Field for High-Dimensional Data Imputation

Content Provider	IEEE Xplore Digital Library
Author	Zhuhua Cai Jermaine, C. Vagena, Z. Logothetis, D. Perez, L.L.
Copyright Year	2013
Abstract	In this paper, we consider the problem of imputation (recovering missing values) in very high-dimensional data with an arbitrary covariance structure. The modern solution to this problem is the Gaussian Markov random field (GMRF). The problem with applying a GMRF to very high-dimensional data imputation is that while the GMRF model itself can be useful even for data having tens of thousands of dimensions, utilizing a GMRF requires access to a sparsified, inverse covariance matrix for the data. Computing this matrix using even state-of-the-art methods is very costly, as it typically requires first estimating the covariance matrix from the data (at a O(nm2) cost for m dimensions and n data points) and then performing a regularized inversion of the estimated covariance matrix, which is also very expensive. This is impractical for even moderately-sized, high-dimensional data sets. In this paper, we propose a very simple alternative to the GMRF called the pair wise Gaussian random field or PGRF for short. The PGRF is a graphical, factor-based model. Unlike traditional Gaussian or GMRF models, a PGRF does not require a covariance or correlation matrix as input. Instead, a PGRF takes as input a set of p (dimension, dimension) pairs for which the user suspects there might be a strong correlation or anti-correlation. This set of pairs defines the graphical structure of the model, with a simple Gaussian factor associated with each of the p (dimension, dimension) pairs. Using this structure, it is easy to perform simultaneous inference and imputation of the model. The key benefit of the approach is that the time required for the PGRF to perform inference is approximately linear with respect to p, where p will typically be much smaller than the number of entries in a m×m covariance or precision matrix.
Sponsorship	Toshiba
Starting Page	61
Ending Page	70
File Size	345459
Page Count	10
File Format	PDF
ISBN	9780769551081
ISSN	15504786
DOI	10.1109/ICDM.2013.149
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-12-07
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Covariance matrices Correlation Data models Gaussian distribution Markov processes Computational modeling Monte Carlo methods imputation classification
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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