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Abstract: We give an adversary strategy that forces the Perceptron algorithm to make \Omega\Gamma kN ) mistakes in learning monotone disjunctions over N variables with at most k literals. In contrast, Littlestone's algorithm Winnow makes at most O(k log N ) mistakes for the same problem. Both algorithms use thresholded linear functions as their hypotheses. However, Winnow does multiplicative updates to its weight vector instead of the additive updates of the Perceptron algorithm. The Perceptron algorithm ... (Update)
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BibTeX entry: (Update)
@techreport{ kivinen95perceptron,
author = "Jyrki Kivinen and Manfred Warmuth",
title = "{THE} {PERCEPTRON} {ALGORITHM} {VS} {WINNOW}: {LINEAR} {VS} {LOGARITHMIC} {MISTAKE} {BOUNDS} {WHEN} {FEW} {INPUT} {VARIABLES} {ARE} {RELEVANT}",
number = "UCSC-CRL-95-44",
year = "1995",
url = "citeseer.ist.psu.edu/kivinen97perceptron.html" }
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