Download Algorithmic Learning Theory: 11th International Conference, by William W. Cohen (auth.), Hiroki Arimura, Sanjay Jain, Arun PDF

By William W. Cohen (auth.), Hiroki Arimura, Sanjay Jain, Arun Sharma (eds.)

This ebook constitutes the refereed lawsuits of the eleventh foreign convention on Algorithmic studying idea, ALT 2000, held in Sydney, Australia in December 2000.
The 22 revised complete papers provided including 3 invited papers have been rigorously reviewed and chosen from 39 submissions. The papers are geared up in topical sections on statistical studying, inductive common sense 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

Example text

Note that t is a random variable that varies depending on the examples drawn from D. Let mt and pt denote the value m and m/n when the algorithm halts at the tth step. Since the while-condition breaks at the tth step, it holds that A ≤ mt . On the other hand, mt < A + 1 holds because the while-condition holds before the tth step. Hence we have A/t ≤ pt < (A + 1)/t. Here in order to simplify our discussion, we assume that pt ≈ A/t. In fact, we will see below that t is larger than 1/(ε2 pB ) with high probability; thus, the difference (A + 1)/t − A/t (= 1/t) is negligible compared with the error bound εpB .

493–509, 1952. 29 3. C. Dominogo, Faster near-optimal reinforcement learning: adding adaptiveness to the E3 algorithm, in Proc. 241– 251, 1999. 28, 32 4. C. Domingo and O. Watanabe, Scaling up a boosting-based learner via adaptive sampling, in Proc. 317–328, 2000. 28 5. C. Domingo and O. Watanabe, MadaBoost: a modification of AdaBoost, in Proc. 180–189, 2000. 28 6. C. Domingo, R. Gavald` a, and O. Watanabe, Practical algorithms for on-line selection, in Proc. f the First Intl. 150–161, 1998. 27, 38 7.

Our estimation problem is completely specified by fixing an “approximation goal” that defines the notion of “good approximation”. We consider the following one for our first approximation goal. t. ) Approximation Goal 1 (Absolute Error Bound) For given δ > 0 and , 0 < < 1, the goal is to have Pr[ |pB − pB | ≤ ] > 1 − δ. (1) As mentioned above, the simplest sampling algorithm for estimating pB is to pick up instances of D randomly and estimate the probability pB on these selected instances. Figure 1 gives the precise description of this simplest sampling algorithm, which we call Batch Sampling algorithm.

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