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

Xingyuan Fang, Han Liu, Mengdi Wang

Research output: Contribution to journalArticle

Abstract

We consider the problem of estimating high dimensional spatial graphical models with a total cardinality constraint (i.e., the ℓ-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)
Pages (from-to)175-205
Number of pages31
JournalMathematical Programming
Volume176
Issue number1-2
DOIs
StatePublished - Jul 1 2019

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Cardinality Constraints
Spatial Model
Graphical Models
Convex Geometry
Geometry
Primal-dual
Dual Problem
Justification
Statistical property
Dimensionality
High-dimensional
Efficient Algorithms
Optimal Solution
Linearly
Numerical Results

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

Cite this

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Blessing of massive scale : spatial graphical model estimation with a total cardinality constraint approach. / Fang, Xingyuan; Liu, Han; Wang, Mengdi.

In: Mathematical Programming, Vol. 176, No. 1-2, 01.07.2019, p. 175-205.

Research output: Contribution to journalArticle

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