Blessing of massive scale: spatial graphical model estimation with a total cardinality constraint approach

Xingyan Ethan Fang, Han Liu, Mengdi Wang

Research output: Contribution to journalArticle


We consider the problem of estimating high dimensional spatial graphical models with a total cardinality constraint (i.e., the ℓ 0 -constraint). Though this problem is highly nonconvex, we show that its primal-dual gap diminishes linearly with the dimensionality and provide a convex geometry justification of this “blessing of massive scale” phenomenon. Motivated by this result, we propose an efficient algorithm to solve the dual problem (which is concave) and prove that the solution achieves optimal statistical properties. Extensive numerical results are also provided.

Original languageEnglish (US)
JournalMathematical Programming
Publication statusAccepted/In press - Jan 1 2018
Externally publishedYes


ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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