Statistical estimation for optimization problems on graphs

Mikhail Langovoy; Suvrit Sra

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Statistical estimation for optimization problems on graphs

Mikhail Langovoy, Suvrit Sra

Machine Learning · Submitted 29 Nov 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.90 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.04 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Large graphs abound in machine learning, data mining, and several related areas.	background 1.00	0.04	0.01	asserted 1.00
s1	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.	background 1.00	0.05	0.03	asserted 0.88
s2	These statistics provide insight into the structure of a graph, and they can help predict global properties of a graph.	background 0.95	0.06	0.04	asserted 0.68
s3	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.	contribution 0.99	0.31	0.15	asserted 0.74
s4	The general task is very difficult, if not unsolvable; so for concreteness we describe a more specific statistical estimation problem based on spanning trees.	limitation 0.67	0.26	0.08	asserted 0.76
s5	We hope that our position paper encourages others to also study other types of graphical structures for which one can prove nontrivial statistical estimates.	future work 1.00	0.06	0.11	hedged possibility 0.61

What kind of paper the classifier reports this is: position or commentary 1.00 · evidence from argument 0.98.

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arXiv listing abstract v1

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full text
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original 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.

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