Leading strategies in competitive on-line prediction

We start from a simple asymptotic result for the problem of on-line regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a "leading prediction strategy", which not only asymptotically performs at least as well as any continuous limited-memory strategy but also satisfies the property that the excess loss of any continuous limited-memory strategy is determined by how closely it imitates the leading strategy. More specifically, for any class of prediction strategies constituting a reproducing kernel Hilbert space we construct a leading strategy, in the sense that the loss of any prediction strategy whose norm is not too large is determined by how closely it imitates the leading strategy. This result is extended to the loss functions given by Bregman divergences and by strictly proper scoring rules.Comment: 20 pages; a conference version is to appear in the ALT'2006 proceeding

7th Drug hypersensitivity meeting: part two

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Clustering with Lower Bound on Similarity ⋆

Abstract. We propose a new method, called SimClus, for clustering with lower bound on similarity. Instead of accepting k the number of clusters to find, the alternative similarity-based approach imposes a lower bound on the similarity between an object and its corresponding cluster representative (with one representative per cluster). SimClus achieves a O(log n) approximation bound on the number of clusters, whereas for the best previous algorithm the bound can be as poor as O(n). Experiments on real and synthetic datasets show that our algorithm produces more than 40 % fewer representative objects, yet offers the same or better clustering quality. We also propose a dynamic variant of the algorithm, which can be effectively used in an on-line setting.

Loss bounds for online category ranking

Abstract. Category ranking is the task of ordering labels with respect to their relevance to an input instance. In this paper we describe and analyze several algorithms for online category ranking where the instances are revealed in a sequential manner. We describe additive and multiplicative updates which constitute the core of the learning algorithms. The updates are derived by casting a constrained optimization problem for each new instance. We derive loss bounds for the algorithms by using the properties of the dual solution while imposing additional constraints on the dual form. Finally, we outline and analyze the convergence of a general update that can be employed with any Bregman divergence.