# The Perceptron Algorithm vs. Winnow: Linear vs. Logarithmic Mistake Bounds when few Input Variables are Relevant

@inproceedings{Kivinen1995ThePA, title={The Perceptron Algorithm vs. Winnow: Linear vs. Logarithmic Mistake Bounds when few Input Variables are Relevant}, author={Jyrki Kivinen and Manfred K. Warmuth}, booktitle={COLT}, year={1995} }

- Published in COLT 1995
DOI:10.1145/225298.225333

We give an adversary strategy that forces the Perceptron algorithm to make (N-k+1)/2 mistakes when learning k-literal disjunctions over N variables. Experimentally we see that even for simple random data, the number of mistakes made by the Perceptron algorithm grows almost linearly with N, even if the number k of relevant variable remains a small constant. In contrast, Littlestone''s algorithm Winnow makes at most O(k log N) mistakes for the same problem. Both algorithms use thresholded linear… CONTINUE READING

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