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Weakly monotone functions

โœ Scribed by Juan J. Manfredi


Book ID
112937674
Publisher
Springer-Verlag
Year
1994
Tongue
English
Weight
353 KB
Volume
4
Category
Article
ISSN
1050-6926

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๐Ÿ“œ SIMILAR VOLUMES


Nontrivial monotone weakly symmetric Boo
โœ Gao Sui-Xiang; Hu Xiao-Dong; Wu Weili ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 268 KB

A Boolean function \_/+I,. . ,x,,) is elusive if every decision tree evaluating f must examine all n variables in the worst case. Rivest and Vuillemin conjectured that every nontrivial monotone weakly symmetric Boolean function is elusive. In this note, we show that this conjecture is true for n = 6

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We construct an adaptive estimate for the value of a function at a given point assuming that the function is monotone. This estimate has maximum risk within a constant factor of the minimax risk over Lipschitz classes.

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