By William W. Cohen (auth.), Hiroki Arimura, Sanjay Jain, Arun Sharma (eds.)
This booklet constitutes the refereed lawsuits of the eleventh foreign convention on Algorithmic studying thought, ALT 2000, held in Sydney, Australia in December 2000.
The 22 revised complete papers provided 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 common sense programming, inductive inference, complexity, neural networks and different paradigms, aid vector machines.
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Extra resources for Algorithmic Learning Theory: 11th International Conference, ALT 2000 Sydney, Australia, December 11–13, 2000 Proceedings
Then the probabilistic mutual information is the relative entropy between the joint distribution and the product distribution : 1 log = x y X Y p x y p y I X Y p x XX I X Y p x p y p x y p x y p x p y : Every function of a data sample |like the sample mean or the sample variance|is called a statistic of . A. edu. The paper was partly written during this author's visit at CWI. Address: CWI, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands. nl ? H . A rimura, S .
42 Pe t e r G´ac s e t al. models, say a family of probability mass functions ff g indexed by , together with a distribution over . A statistic T D is called su cient if the probabilistic mutual information I D = I T D 2 for all distributions of . Hence, the mutual information between parameter and data sample is invariant under taking su cient statistics and vice versa. That is to say, a statistic T D is called su cient for if it contains all the information in D about . For example, consider n tosses of a coin with unknown bias with outcome D = d1 d2 : : : dn where di 2 f0 1g 1 i n.
A natural strategy that we can take in such a situation is random sampling. That is, we pick up some instances of D randomly and estimate the probability pB on these selected instances. Without seeing all instances, we cannot hope for computing the exact value of pB . Also due to the “randomness nature”, we cannot always obtain a desired answer. Therefore, we must be satisﬁed if our sampling algorithm yields a good approximation of pB with reasonable probability. In this paper, we will discuss this type of approximate estimation problem.
Algorithmic Learning Theory: 11th International Conference, ALT 2000 Sydney, Australia, December 11–13, 2000 Proceedings by William W. Cohen (auth.), Hiroki Arimura, Sanjay Jain, Arun Sharma (eds.)