Tracking Linear-Threshold Concepts with Winnow
In this paper, we give a mistake-bound for learning arbitrary linear-threshold concepts that are allowed to change over time in the on-line model of learning. We use a standard variation of the Winnow algorithm and show that the bounds for learning shifting linear-threshold functions have many of the same advantages that the traditional Winnow algorithm has on fixed concepts. These benefits include a weak dependence on the number of irrelevant attributes, inexpensive runtime, and robust behavior against noise. In fact, we show that the bound for the tracking version of Winnow has even better performance with respect to irrelevant attributes. Let X ∈ [0,1] n be an instance of the learning problem. In the traditional algorithm, the bound depends on ln n. In this paper, the shifting concept bound depends approximately on max ln (‖X‖1).
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- Littlestone, N.: Mistake bounds and linear-threshold learning algorithms. PhD thesis, University of California, Santa Cruz (1989) Technical Report UCSC-CRL-89-11.Google Scholar
- Littlestone, N.: Learning quickly when irrelevant attributes abound: A new linear-threshold algorithm. Machine Learning 2 (1988) 285–318Google Scholar
- Blum, A., Hellerstein, L., Littlestone, N.: Learning in the presence of finitely or infinitely many irrelevant attributes. In: COLT-91. (1991) 157–166Google Scholar
- Kuh, A., Petsche, T., Rivest, R. L.: Learning time-varying concepts. In: NIPS-3, Morgan Kaufmann Publishers, Inc. (1991) 183–189Google Scholar
- Littlestone, N.: Redundant noisy attributes, attribute errors, and linear-threshold learning using winnow. In: COLT-91. (1991) 147–156Google Scholar
- Grove, A. J., Littlestone, N., Schuurmans, D.: General convergence results for linear discriminant updates. In: COLT-97. (1997) 171–183Google Scholar
- Littlestone, N.: (1998) Unpublished research that generalizes Winnow algorithm.Google Scholar
- Mesterharm, C.: A multi-class linear learning algorithm related to winnow. In: NIPS-12, MIT Press (2000) 519–525Google Scholar