Localization in 1D non-parametric latent space models from pairwise affinities
نویسندگان
چکیده
We consider the problem of estimating latent positions in a one-dimensional torus from pairwise affinities. The observed affinity between pair items is modeled as noisy observation function f(xi∗,xj∗) xi∗,xj∗ two on torus. f unknown, and it only assumed to fulfill some shape constraints ensuring that f(x,y) large when distance x y small, vice-versa. This non-parametric modeling offers good flexibility fit data. introduce an estimation procedure provably localizes all with maximum error order log(n)∕n, high-probability. rate proven be minimax optimal. A computationally efficient variant also analyzed under more restrictive assumptions. Our general results can instantiated statistical seriation, leading new bounds for ordering.
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ژورنال
عنوان ژورنال: Electronic Journal of Statistics
سال: 2023
ISSN: ['1935-7524']
DOI: https://doi.org/10.1214/23-ejs2134