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The capacity of majority rule

✍ Scribed by Shao C. Fang; Santosh S. Venkatesh

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
274 KB
Volume
12
Category
Article
ISSN
1042-9832

No coin nor oath required. For personal study only.

✦ Synopsis

Let ‫ނ‬ s y1, 1 denote the vertices of the n-dimensional cube. Let U m be a random m-element subset of ‫ނ‬ n and suppose w g ‫ނ‬ n is a vertex closest to the centroid of Ε½ . U m . Using a large deviation, multivariate local limit theorem due to Richter, we show that Ε½ . nr log n is a threshold function for the property that the convex hull of U m is contained in the positive half-space determined by w.

The decision problem considered here is an instance of binary integer programming, and Ε½ . the algorithm selecting w as the vertex closest to the centroid of U m has been previously dubbed majority rule in the context of learning binary weights for a perceptron.

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