Advanced computation of sparse precision matrices for big data

Abdelkader Baggag, Halima Bensmail, Jaideep Srivastava

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


The precision matrix is the inverse of the covariance matrix. Estimating large sparse precision matrices is an interesting and a challenging problem in many fields of sciences, engineering, humanities and machine learning problems in general. Recent applications often encounter high dimensionality with a limited number of data points leading to a number of covariance parameters that greatly exceeds the number of observations, and hence the singularity of the covariance matrix. Several methods have been proposed to deal with this challenging problem, but there is no guarantee that the obtained estimator is positive definite. Furthermore, in many cases, one needs to capture some additional information on the setting of the problem. In this paper, we introduce a criterion that ensures the positive definiteness of the precision matrix and we propose the inner-outer alternating direction method of multipliers as an efficient method for estimating it. We show that the convergence of the algorithm is ensured with a sufficiently relaxed stopping criterion in the inner iteration. We also show that the proposed method converges, is robust, accurate and scalable as it lends itself to an efficient implementation on parallel computers.

Original languageEnglish (US)
Title of host publicationAdvances in Knowledge Discovery and Data Mining - 21st Pacific-Asia Conference, PAKDD 2017, Proceedings
EditorsLongbing Cao, Kyuseok Shim, Jae-Gil Lee, Jinho Kim, Yang-Sae Moon, Xuemin Lin
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783319575285
StatePublished - 2017
Externally publishedYes
Event21st Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2017 - Jeju, Korea, Republic of
Duration: May 23 2017May 26 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10235 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other21st Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2017
Country/TerritoryKorea, Republic of


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