By William W. Cohen (auth.), Hiroki Arimura, Sanjay Jain, Arun Sharma (eds.)
This publication constitutes the refereed complaints of the eleventh overseas convention on Algorithmic studying idea, ALT 2000, held in Sydney, Australia in December 2000.
The 22 revised complete papers awarded including 3 invited papers have been conscientiously reviewed and chosen from 39 submissions. The papers are geared up in topical sections on statistical studying, inductive good judgment programming, inductive inference, complexity, neural networks and different paradigms, aid vector machines.
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Extra info for Algorithmic Learning Theory: 11th International Conference, ALT 2000 Sydney, Australia, December 11–13, 2000 Proceedings
I have learned a lot from these talented researchers. In particular, I thank Carlos for supplying me with information on related works for preparing this manuscript. I would like to thank Professor Akahira and Professor Lynch for discussion and giving me pointers to related works. This work is supported in part by Grant-in-Aid for Scientiﬁc Research on Priority Areas (Discovery Science), 1999, the Ministry of Education, Science, Sports and Culture. References 1. J. Balcaz´ ar, a personal communication.
F. Lynch, Analysis and application of adaptive sampling, in Proc. 260–267, 1999. 28, 33 18. O. Maron and A. Moore, Hoeﬀding races: accelerating model selection search for classiﬁcation and function approximation, in Advances in Neural Information Processing Systems, Morgan Kaufmann, 59–66, 1994. 28 19. T. Scheﬀer and S. Wrobel, A sequential sampling algorithm for a general class of utility criteria, in Proc. f the 6th ACM SIGKDD Intl. Conference on Knowledge Discovery and Data Mining, ACM Press, 2000, to appear.
Problem 1 Let δ0 > 0 be any constant and ﬁxed. For a given p0 , determine (with conﬁdence > 1 − δ0 ) whether pB > p0 or not. We may assume that either pB > 3p0 /2 or pB < p0 /2 holds. That is, we would like to “approximately” compare pB with p0 . Note that we do not have to answer correctly when p0 /2 ≤ pB ≤ 3p0 /2 holds. First we use our sample size bound (2) for Approximation Goal 1. It is easy to see that the requirement of the problem is satisﬁed if we run Batch Sampling algorithm with sample size n1 computed by using = p0 /2 and δ = δ0 , and compare the obtained pB with p0 .