Growing Alphabets in Canonical Shuffle Experiments: Likelihood-Ratio Laws, Estimation Bounds, and Low-Budget Equivariant Design
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911654054199296 |
|---|---|
| author | Shvets, Alex |
| author_facet | Shvets, Alex |
| contents | We study canonical one-step neighboring shuffle experiments for finite-output epsilon_0-LDP d-ary channels along growing alphabets, with frequency estimation and mechanism design under a pairwise chi-squared budget. The pairwise likelihood-ratio law nu_{ab,d} (pushforward of the row ratio under the null row) is the governing invariant: the canonical shuffled histogram experiment is exactly equivalent to the quotient multinomial experiment generated by nu_{ab,d}. Alphabet growth improves canonical shuffled privacy iff the worst pairwise law collapses to delta_1. We prove a sharp pure-LDP endpoint principle for the pairwise chi-squared, construct full-support obstruction families saturating it, and establish a diluting/persistent dichotomy with explicit finite-n hockey-stick bounds. The worst-case pairwise budget chi_*(W) governs a two-regime Assouad lower bound for arbitrary estimators in the i.i.d. multinomial model. Symmetrization reduces the uniform-point Fisher criterion to permutation-equivariant channels. Calibrated GRR is not optimal; in the low-budget regime, augmented GRR is optimal among permutation-equivariant channels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18080 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Growing Alphabets in Canonical Shuffle Experiments: Likelihood-Ratio Laws, Estimation Bounds, and Low-Budget Equivariant Design Shvets, Alex Information Theory 62B15, 68P27, 60F05 We study canonical one-step neighboring shuffle experiments for finite-output epsilon_0-LDP d-ary channels along growing alphabets, with frequency estimation and mechanism design under a pairwise chi-squared budget. The pairwise likelihood-ratio law nu_{ab,d} (pushforward of the row ratio under the null row) is the governing invariant: the canonical shuffled histogram experiment is exactly equivalent to the quotient multinomial experiment generated by nu_{ab,d}. Alphabet growth improves canonical shuffled privacy iff the worst pairwise law collapses to delta_1. We prove a sharp pure-LDP endpoint principle for the pairwise chi-squared, construct full-support obstruction families saturating it, and establish a diluting/persistent dichotomy with explicit finite-n hockey-stick bounds. The worst-case pairwise budget chi_*(W) governs a two-regime Assouad lower bound for arbitrary estimators in the i.i.d. multinomial model. Symmetrization reduces the uniform-point Fisher criterion to permutation-equivariant channels. Calibrated GRR is not optimal; in the low-budget regime, augmented GRR is optimal among permutation-equivariant channels. |
| title | Growing Alphabets in Canonical Shuffle Experiments: Likelihood-Ratio Laws, Estimation Bounds, and Low-Budget Equivariant Design |
| topic | Information Theory 62B15, 68P27, 60F05 |
| url | https://arxiv.org/abs/2603.18080 |