论文信息 - On-line learning of linear functions

On-line learning of linear functions

We present an algorithm for the on-line learning of linear functions which is optimal to within a constant factor with respect to bounds on the sum of squared errors for a worst case sequence of trials. The bounds are logarithmic in the number of variables. Furthermore, the algorithm is shown to be optimally robust with respect to noise in the data (again to within a constant factor).

Philip M. Long | Manfred K. Warmuth | Nick Littlestone

[1] Ethan Bernstein. Absolute error bounds for learning linear functions online , 1992, COLT '92.

[2] J. Mycielski. A learning theorem for linear operators , 1988 .

[3] Leonard Pitt,et al. Prediction-Preserving Reducibility , 1990, J. Comput. Syst. Sci..

[4] Manfred K. Warmuth,et al. The Weighted Majority Algorithm , 1994, Inf. Comput..

[5] N. Littlestone. Mistake bounds and logarithmic linear-threshold learning algorithms , 1990 .

[6] N. Littlestone. Learning Quickly When Irrelevant Attributes Abound: A New Linear-Threshold Algorithm , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[7] S. Kullback,et al. A lower bound for discrimination information in terms of variation (Corresp.) , 1967, IEEE Trans. Inf. Theory.

[8] David Haussler,et al. Learning Conjunctive Concepts in Structural Domains , 1989, Machine Learning.

[9] N. Littlestone,et al. Learning in the presence of finitely or infinitely many irrelevant attributes , 1991, COLT '91.

[10] Leslie G. Valiant,et al. On the learnability of Boolean formulae , 1987, STOC.

[11] Richard O. Duda,et al. Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[12] Philip M. Long,et al. Worst-case quadratic loss bounds for a generalization of the Widrow-Hoff rule , 1993, COLT '93.