On Top-k Selection from m-wise Partial Rankings via Borda Counting
ISIT(2020)
摘要
We analyze the performance of Borda counting algorithm on noisy m-wise ranking data to accurately select the top-k items from a total of n items. This generalizes a previous result of a similar nature reported by Shah et al. on the noisy pairwise comparison data. We show that the associated score separation Δ
k
between the k-th item and the (k+1)-th item plays an important role: if Δ
k
is greater than a threshold depending on (n, k) and the scoring system in Borda counting, then the top-k selection is accurate asymptotically almost surely; if Δ
k
is below a threshold, then the top-k selection will not be accurate with at least a constant probability. This separation between the two thresholds depends on m and the scoring systems in the Borda counting procedure.
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关键词
m-wise partial rankings,top-k items,noisy pairwise comparison data,scoring system,Borda counting,score separation,top-k selection,noisy m-wise ranking data,constant probability
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