Institute Homepage DE Sign In

Back

Empirical Inference Conference Paper 2011

Statistical estimation for optimization problems on graphs

Thumb ticker sm thumb suvrit sra
Empirical Inference
Suvrit Sra
no image
Empirical Inference
Mikhail Langovoy

Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics — e.g., or the expected length of a shortest path between two nodes, or the expected weight of a minimum spanning tree of the graph, etc. These statistics provide insight into the structure of a graph, and they can help predict global properties of a graph. Motivated thus, we propose to study statistical properties of structured subgraphs (of a given graph), in particular, to estimate the expected objective function value of a combinatorial optimization problem over these subgraphs. The general task is very difficult, if not unsolvable; so for concreteness we describe a more specific statistical estimation problem based on spanning trees. We hope that our position paper encourages others to also study other types of graphical structures for which one can prove nontrivial statistical estimates.

Author(s): Langovoy, M. and Sra, S.
Pages: 1-6
Year: 2011
Month: December
Day: 0
Bibtex Type: Conference Paper (inproceedings)
Event Name: NIPS Workshop on Discrete Optimization in Machine Learning (DISCML) 2011: Uncertainty, Generalization and Feedback
Digital: 0
Electronic Archiving: grant_archive
Links:

BibTex 

@inproceedings{LangovoyS2011,
  title = {Statistical estimation for optimization problems on graphs},
  abstract = {Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics  — e.g., or the expected length of a shortest path between two nodes, or the expected weight of a minimum spanning tree of the graph, etc. These statistics provide insight into the structure of a graph, and they can help predict global
  properties of a graph. Motivated thus, we propose to study statistical properties of structured subgraphs (of a given graph), in particular, to estimate the expected objective function value of a combinatorial optimization problem over these subgraphs. The general task is very difficult, if not unsolvable; so for concreteness we describe a more specific statistical estimation problem based on spanning trees.
  We hope that our position paper encourages others to also study other types of graphical structures for which one can prove nontrivial statistical estimates.},
  pages = {1-6},
  month = dec,
  year = {2011},
  slug = {langovoys2011},
  author = {Langovoy, M. and Sra, S.},
  month_numeric = {12}
}