The weak aggregating algorithm and weak mixability

Kalnishkan, Yuri; Vyugin, Michael V.

doi:10.1016/j.jcss.2007.08.003

Cited by 46 publications

(33 citation statements)

References 8 publications

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“…The game of prediction is being played repeatedly by a learner that has access to decisions made by a pool of experts, which leads to the following prediction protocol: Here L N is the cumulative loss of the learner at a time step N , and L k N is the cumulative loss of kth expert at this step. There are a lot of well-developed algorithms for the learner, probably the most known are Weighted Average Algorithm [8], Strong Aggregating Algorithm [11,12], Weak Aggregating Algorithm [7], Hedge Algorithm [4], and Tracking the Best Expert [6]. The basic idea behind these algorithms is to assign weights to experts and then use their predictions in the correspondence with their weights in a way that minimizes the learner's loss.…”

Section: Online Prediction Framework and Aggregating Algorithmmentioning

confidence: 99%

Online Prediction of Ovarian Cancer

Zhdanov

Vovk

Burford

et al. 2009

Artificial Intelligence in Medicine

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Abstract. In this paper we apply computer learning methods to diagnosing ovarian cancer using the level of the standard biomarker CA125 in conjunction with information provided by mass-spectrometry. We are working with a new data set collected over a period of 7 years. Using the level of CA125 and mass-spectrometry peaks, our algorithm gives probability predictions for the disease. To estimate classification accuracy we convert probability predictions into strict predictions. Our algorithm makes fewer errors than almost any linear combination of the CA125 level and one peak's intensity (taken on the log scale). To check the power of our algorithm we use it to test the hypothesis that CA125 and the peaks do not contain useful information for the prediction of the disease at a particular time before the diagnosis. Our algorithm produces p-values that are better than those produced by the algorithm that has been previously applied to this data set. Our conclusion is that the proposed algorithm is more reliable for prediction on new data.

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Section: Online Prediction Framework and Aggregating Algorithmmentioning

confidence: 99%

Online Prediction of Ovarian Cancer

Zhdanov

Vovk

Burford

et al. 2009

Artificial Intelligence in Medicine

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“…This subsection will introduce the main technical tool used in this paper, an aggregating algorithm (in fact intermediate between the strong aggregating algorithm of [42] and the weak aggregating algorithm of [23]). For future use in §5, we will allow the observations to belong to the Euclidean space R m (in fact, we will only be interested in the cases m = 1 and m = 2).…”

Section: Aggregating Algorithmmentioning

confidence: 99%

Leading Strategies in Competitive On-Line Prediction

Vovk

2006

Lecture Notes in Computer Science

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Competitive on-line prediction (also known as universal prediction of individual sequences) is a strand of learning theory avoiding making any stochastic assumptions about the way the observations are generated. The predictor's goal is to compete with a benchmark class of prediction rules, which is often a proper Banach function space. Metric entropy provides a unifying framework for competitive on-line prediction: the numerous known upper bounds on the metric entropy of various compact sets in function spaces readily imply bounds on the performance of on-line prediction strategies. This paper discusses strengths and limitations of the direct approach to competitive on-line prediction via metric entropy, including comparisons to other approaches.

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“…In Section 2, we propose a generalization of the Aggregating Algorithm [20] and prove the same bound as in [20] but for the discounted loss. In Section 3, we consider convex loss functions and propose an algorithm similar to the Weak Aggregating Algotihm [14] and the exponentially weighted average forecaster with time-varying learning rate [2, § 2.3], with a similar loss bound. In Section 4, we consider the use of prediction with expert advice for the regression problem and adapt the Aggregating Algorithm for Regression [22] (applied to spaces of linear functions and to reproducing kernel Hilbert spaces) to the discounted square loss.…”

Section: Introductionmentioning

confidence: 99%