Localization in 1D non-parametric latent space models from pairwise affinities - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2021

Localization in 1D non-parametric latent space models from pairwise affinities

Abstract

We consider the problem of estimating latent positions in a one-dimensional torus from pairwise affinities. The observed affinity between a pair of items is modeled as a noisy observation of a function f (x * i , x * j) of the latent positions x * i , x * j of the two items on the torus. The affinity function f is unknown, and it is only assumed to fulfill some shape constraints ensuring that f (x, y) is large when the distance between x and y is small, and vice-versa. This non-parametric modeling offers a good flexibility to fit data. We introduce an estimation procedure that provably localizes all the latent positions with a maximum error of the order of log(n)/n, with highprobability. This rate is proven to be minimax optimal. A computationally efficient variant of the procedure is also analyzed under some more restrictive assumptions. Our general results can be instantiated to the problem of statistical seriation, leading to new bounds for the maximum error in the ordering.
Fichier principal
Vignette du fichier
seriation_main.pdf (840.51 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03317631 , version 1 (06-08-2021)

Identifiers

  • HAL Id : hal-03317631 , version 1

Cite

Christophe Giraud, Yann Issartel, Nicolas Verzelen. Localization in 1D non-parametric latent space models from pairwise affinities. 2021. ⟨hal-03317631⟩
52 View
40 Download

Share

Gmail Mastodon Facebook X LinkedIn More