On Obtaining Stable Rankings
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We often have to rank items with multiple attributes in a dataset. A typical method to achieve this is to compute a goodness score for each item as a weighted sum of its attribute values, and then to rank by sorting on this score. Clearly, the ranking obtained depends on the weights used for this summation. Ideally, we would want the ranked order not to change if the weights are changed slightly. We call this property stability of the ranking. A consumer of a ranked list may trust the ranking more if it has high stability. A producer of a ranked list prefers to choose weights that result in a stable ranking, both to earn the trust of potential consumers and because a stable ranking is intrinsically likely to be more meaningful. In this paper, we develop a framework that can be used to assess the stability of a provided ranking and to obtain a stable ranking within an "acceptable" range of weight values (called "the region of interest"). We address the case where the user cares about the rank order of the entire set of items, and also the case where the user cares only about the top-k items. Using a geometric interpretation, we propose the algorithms for producing the stable rankings. We also propose a randomized algorithm that uses Monte-Carlo estimation. To do so, we first propose an unbiased sampler for sampling the rankings (or top-k results) uniformly at random from the region of interest. In addition to the theoretical analyses, we conduct extensive experiments on real datasets that validate our proposal.
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