By Imre Csiszár (auth.), Yoav Freund, László Györfi, György Turán, Thomas Zeugmann (eds.)
This ebook constitutes the refereed lawsuits of the nineteenth foreign convention on Algorithmic studying concept, ALT 2008, held in Budapest, Hungary, in October 2008, co-located with the eleventh foreign convention on Discovery technology, DS 2008.
The 31 revised complete papers awarded including the abstracts of five invited talks have been rigorously reviewed and chosen from forty six submissions. The papers are devoted to the theoretical foundations of laptop studying; they handle issues akin to statistical studying; likelihood and stochastic procedures; boosting and specialists; energetic and question studying; and inductive inference.
Read or Download Algorithmic Learning Theory: 19th International Conference, ALT 2008, Budapest, Hungary, October 13-16, 2008. Proceedings PDF
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Additional info for Algorithmic Learning Theory: 19th International Conference, ALT 2008, Budapest, Hungary, October 13-16, 2008. Proceedings
For any scoring function s, deﬁne the AUC as: 1 AUC(s) = ROC(s, α) dα , 0 and set AUC∗ = AUC(η). We then have: d1 (s∗ , s) = AUC∗ − AUC(s). When it comes to ﬁnding a scoring function, based on empirical data, which will perform well with respect to the AUC criterion, various strategies can be considered. A possible angle is the plug-in approach ([DGL96]). The idea of plugin consists in using an estimate ηˆ of the regression function as a scoring function. It is expected that, whenever ηˆ is close to η in a certain sense, then ROC(ˆ η , ·) and ROC∗ are also close.
As the ROC curve provides a performance measure of functional nature, the approximation can be conceived in a variety of ways depending on the topology equipping the space of ROC curves. For instance, the AUC is related to the L1 distance but we will also consider convergence to the optimal ROC curve in a stronger sense described by the L∞ -distance. A recursive implementation of the approximation procedure naturally leads to a tree-like structure for underlying scoring functions. We suggest that such a tree-based ranker could serve as a weak learner and feed a boosting-type algorithm such as RankBoost ([FISS03]).
We assume that we are given a class C of subsets of X . TreeRank Algorithm 1. Initialization. Set C0,0 = X . 2. Iterations. For d = 0, . . , D − 1 and for k = 0, . . ) Set the entropy measure: ˆ − (βd,k+1 − βd,k )α(C). ˆ Λd,k+1 (C) = (αd,k+1 − αd,k )β(C) Find the best subset Cd+1,2k of rectangle Cd,k in the AUC sense: Cd+1,2k = arg max Λd,k+1 (C) . C∈C, C⊂Cd,k Then, set Cd+1,2k+1 = Cd,k \ Cd+1,2k . ) Set ˆ d+1,2k ) ˆ (Cd+1,2k ) and βd+1,2k+1 = βd,k + β(C αd+1,2k+1 = αd,k + α as well as αd+1,2k+2 = αd,k+1 and βd+1,2k+2 = βd,k+1 .