Fast rates for noisy clustering
type: Dataset
description: The effect of errors in variables in empirical minimization is investigated. Given a loss $l$ and a set of decision rules $\mathcal{G}$, we prove a general upper bound for an empirical minimization based on a deconvolution kernel and a noisy sample $Z_i=X_i+\epsilon_i,i=1,\ldots,n$. We apply this general upper bound to give the rate of convergence for the expected excess risk in noisy clustering. A recent bound from \citet{levrard} proves that this rate is $\mathcal{O}(1/n)$ in the direct case, under Pollard's regularity assumptions. Here the effect of noisy measurements gives a rate of the form $\mathcal{O}(1/n^{\frac{\gamma}{\gamma+2\beta}})$, where $\gamma$ is the Hölder regularity of the density of $X$ whereas $\beta$ is the degree of illposedness.
issued: 2026-05-19T16:52:48.190134
language: en
modified: 2026-05-19T16:52:48.190140
contact point: Organization
  fn: CCSD
keyword: clustering
keyword: deconvolution
keyword: empirical-minimization
keyword: fast-rates
keyword: infoeu-reposemanticspreprint
keyword: infoinfo-lgcomputer-science-csmachine-learning-cslg
keyword: inverse-problem
keyword: mathmath-stmathematics-mathstatistics-mathst
keyword: preprints-working-papers-
keyword: statthstatistics-statstatistics-theory-statth
landing page: https://hal.science/hal-00695258

Fast rates for noisy clustering
type: Distribution
format: HTML
issued: 2026-05-19T16:52:48.212960
modified: 2026-05-19T16:52:48.160765
access URL: https://hal.science/hal-00695258

test_moissonnage_selune
type: Agent