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Large margin vs. large volume in transductive learning   总被引:2,自引:0,他引:2  
We consider a large volume principle for transductive learning that prioritizes the transductive equivalence classes according to the volume they occupy in hypothesis space. We approximate volume maximization using a geometric interpretation of the hypothesis space. The resulting algorithm is defined via a non-convex optimization problem that can still be solved exactly and efficiently. We provide a bound on the test error of the algorithm and compare it to transductive SVM (TSVM) using 31 datasets.  相似文献
2.
This paper concerns two fundamental but somewhat neglected issues, both related to the design and analysis of randomized on-line algorithms. Motivated by early results in game theory we define several types of randomized on-line algorithms, discuss known conditions for their equivalence, and give a natural example distinguishing between two kinds of randomizations. In particular, we show thatmixedrandomized memoryless paging algorithms can achieve strictly better competitive performance thanbehavioralrandomized algorithms. Next we summarize known—and derive new—“Yao principle” theorems for lower bounding competitive ratios of randomized on-line algorithms. This leads to four different theorems for bounded/unbounded and minimization/maximization problems.  相似文献
3.
For a complete network of n processors within which communication lines are private, we show how to achieve concurrently many Byzantine Agreements within constant expected time both on synchronous and asynchronous networks. As an immediate consequence, this provides a solution to the Interactive Consistency problem. Our algorithms tolerate up to (n-1)/3 faulty processors in both the synchronous and asynchronous cases and are therefore resilient-optimal. In terms of time complexity, our results improve a time bound of (for n concurrent agreements) which is immediately implied by the constant expected time Byzantine Agreement of Feldman and Micali (synchronous systems) and of Canetti and Rabin (asynchronous systems). In terms of resiliency, our results improve the resiliency bound of the constant time, -resilient algorithm of Ben-Or. An immediate application of our protocols is a constant expected time simulation of simultaneous broadcast channels over a network with private lines.Received: April 2001, Accepted: September 2002, Michael Ben-Or: Research supported by Israel Academy of Sciences and by United States - Israel Binational Science Foundation grant BSF-87-00082  相似文献
4.
This work is concerned with online learning from expert advice. Extensive work on this problem generated numerous expert advice algorithms whose total loss is provably bounded above in terms of the loss incurred by the best expert in hindsight. Such algorithms were devised for various problem variants corresponding to various loss functions. For some loss functions, such as the square, Hellinger and entropy losses, optimal algorithms are known. However, for two of the most widely used loss functions, namely the 0/1 and absolute loss, there are still gaps between the known lower and upper bounds.In this paper we present two new expert advice algorithms and prove for them the best known 0/1 and absolute loss bounds. Given an expert advice algorithm ALG, the goal is to form an upper bound on the regret L ALGL* of ALG, where L ALG is the loss of ALG and L* is the loss of the best expert in hindsight. Typically, regret bounds of a canonical form C · are sought where N is the number of experts and C is a constant. So far, the best known constant for the absolute loss function is C = 2.83, which is achieved by the recent IAWM algorithm of Auer et al. (2002). For the 0/1 loss function no bounds of this canonical form are known and the best known regret bound is , where C 1 = e – 2 and C 2 = 2 . This bound is achieved by a P-norm algorithm of Gentile and Littlestone (1999). Our first algorithm is a randomized extension of the guess and double algorithm of Cesa-Bianchi et al. (1997). While the guess and double algorithm achieves a canonical regret bound with C = 3.32, the expected regret of our randomized algorithm is canonically bounded with C = 2.49 for the absolute loss function. The algorithm utilizes one random choice at the start of the game. Like the deterministic guess and double algorithm, a deficiency of our algorithm is that it occasionally restarts itself and therefore forgets what it learned. Our second algorithm does not forget and enjoys the best known asymptotic performance guarantees for both the absolute and 0/1 loss functions. Specifically, in the case of the absolute loss, our algorithm is canonically bounded with C approaching and in the case of the 0/1 loss, with C approaching 3/ . In the 0/1 loss case the algorithm is randomized and the bound is on the expected regret.  相似文献
5.
We present a novel pairwise clustering method. Given a proximity matrix of pairwise relations (i.e. pairwise similarity or dissimilarity estimates) between data points, our algorithm extracts the two most prominent clusters in the data set. The algorithm, which is completely nonparametric, iteratively employs a two-step transformation on the proximity matrix. The first step of the transformation represents each point by its relation to all other data points, and the second step re-estimates the pairwise distances using a statistically motivated proximity measure on these representations. Using this transformation, the algorithm iteratively partitions the data points, until it finally converges to two clusters. Although the algorithm is simple and intuitive, it generates a complex dynamics of the proximity matrices. Based on this bipartition procedure we devise a hierarchical clustering algorithm, which employs the basic bipartition algorithm in a straightforward divisive manner. The hierarchical clustering algorithm copes with the model validation problem using a general cross-validation approach, which may be combined with various hierarchical clustering methods.We further present an experimental study of this algorithm. We examine some of the algorithm's properties and performance on some synthetic and standard data sets. The experiments demonstrate the robustness of the algorithm and indicate that it generates a good clustering partition even when the data is noisy or corrupted.  相似文献
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