Papers โบ As you like it: Localization via paired comparisons
As you like it: Localization via paired comparisons
Andrew K. Massimino, Mark A. Davenport
Suppose that we wish to estimate a vector ๐ฑ from a set of binary paired comparisons of the form "๐ฑ is closer to ๐ฉ than to ๐ช" for various choices of vectors ๐ฉ and ๐ช. The problem of estimating ๐ฑ from this type of observation arises in a variety of contexts, including nonmetric multidimensional scaling, "unfolding," and ranking problems, often because it provides a powerful and flexible model of preference. We describe theoretical bounds for how well we can expect to estimate ๐ฑ under a randomized model for ๐ฉ and ๐ช. We also present results for the case where the comparisons are noisy and subject to some degree of error. Additionally, we show that under a randomized model for ๐ฉ and ๐ช, a suitable number of binary paired comparisons yield a stable embedding of the space of target vectors. Finally, we also show that we can achieve significant gains by adaptively changing the distribution for choosing ๐ฉ and ๐ช.
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