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- W4386555400 abstract "Given pairwise comparisons between multiple items, how to rank them so that the ranking matches the observations? This problem, known as rank aggregation, has found many applications in sports, recommendation systems, and other web applications. As it is generally NP-hard to find a global ranking that minimizes the mismatch (known as the Kemeny optimization), we focus on the Erdos-R'enyi outliers (ERO) model for this ranking problem. Here, each pairwise comparison is a corrupted copy of the true score difference. We investigate spectral ranking algorithms that are based on unnormalized and normalized data matrices. The key is to understand their performance in recovering the underlying scores of each item from the observed data. This reduces to deriving an entry-wise perturbation error bound between the top eigenvectors of the unnormalized/normalized data matrix and its population counterpart. By using the leave-one-out technique, we provide a sharper $ell_{infty}$-norm perturbation bound of the eigenvectors and also derive an error bound on the maximum displacement for each item, with only $Omega(nlog n)$ samples. Our theoretical analysis improves upon the state-of-the-art results in terms of sample complexity, and our numerical experiments confirm these theoretical findings." @default.
- W4386555400 created "2023-09-09" @default.
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- W4386555400 date "2023-09-07" @default.
- W4386555400 modified "2023-09-29" @default.
- W4386555400 title "Improved theoretical guarantee for rank aggregation via spectral method" @default.
- W4386555400 doi "https://doi.org/10.48550/arxiv.2309.03808" @default.
- W4386555400 hasPublicationYear "2023" @default.
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