Efficient Agnostic Learning of Univariate Densities Under Local Differential Privacy A8C1M9BSWH

URI	`m2://res/A8C1M9BSWH`
Kind	preprint
Creators	Mohammad Afzali, Hassan Ashtiani, Sivan Sabato
Date	2026-10-15
Subjects	arxiv stat.ML, arxiv cs.CR, arxiv cs.DS, arxiv cs.IT, arxiv cs.LG, arxiv math.IT
Scope	border

Expressions

e1: version, preprint

Date	2026-10-15
Ids	arXiv 2610.21033

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
Mixture class	definition	definition 8.1	arxiv
2JPYFYZZXA	statement	theorem 3.4	arxiv
$\cA_k$-distance from CDF error	statement	lemma B.2	arxiv
LDP Agnostic Proper Learning of GMMs	statement	corollary H.3	arxiv
Discretization and polynomial approximation of mixtures	statement	lemma 8.2	arxiv
GMM Lower Bound	statement	theorem G.1	arxiv
Discretization of Bounded-Parameter Log-concave Distributions	statement	lemma 8.7	arxiv
Canonical dyadic decomposition of a prefix	statement	lemma 5.2	arxiv
Uniform discretization	definition	definition 6.2	arxiv
Efficient LDP Agnostic Learning of GMMs	statement	theorem F.2	arxiv
Local randomizer	definition	definition 2.1	arxiv
LDP synthetic dataset	statement	theorem 6.3	arxiv
9ZVZZP35EX	statement	lemma H.4	arxiv
B4R12VFT9B	statement	lemma H.2	arxiv
$L_1$ Stability of Discretization	statement	lemma C.2	arxiv
Discretization error	definition	definition 2.3	arxiv
Orthogonality of Hadamard characters, Theorem 1.5	statement	lemma C.1	arxiv
Bounded-Parameter Log-concave Distributions	definition	definition 8.4	arxiv
Discretization of Bounded-Parameter Gaussians	statement	lemma F.3	arxiv
Piece-wise polynomial approximation of Gaussians, Lemma 36	statement	lemma F.4	arxiv
HDAS600J7Q	statement	theorem 3.3	arxiv
Piece-wise polynomial approximation of log-concave distributions, Lemma 27	statement	lemma E.1	arxiv
Non-interactive local differential privacy	definition	definition 2.2	arxiv
JY1TGKX4K7	statement	theorem 3.5	arxiv
Piece-wise polynomial approximation error	definition	definition 2.5	arxiv
Piecewise polynomials	definition	definition 2.4	arxiv
Deterministic post-sampling General--Merging	statement	proposition 5.4	arxiv
Bounded Gaussians	definition	definition F.1	arxiv
Sparse distribution estimation lower bound	statement	theorem G.2	arxiv
QK1HHGMBCC	statement	theorem 3.1	arxiv
Log-concave functions	definition	definition 8.3	arxiv
Dyadic tree representation	definition	definition 5.1	arxiv
non-proper to proper learning	statement	lemma H.1	arxiv
S7XYQNYX1D	statement	theorem 7.1	arxiv
TCAVKRCB54	statement	theorem 3.2	arxiv
$\cA_k$-norm	definition	definition B.1	arxiv
Hadamard characters	definition	definition 5.3	arxiv
Piece-wise polynomial approximation of log-concave distributions	statement	lemma 8.6	arxiv
Piece-wise polynomial approximation of Gaussians	statement	lemma F.5	arxiv
Non-interactive LDP prefix oracle	statement	theorem 6.1	arxiv
Efficient LDP Agnostic Learning of Log-concave Mixtures	statement	theorem 8.5	arxiv

Catalogue records

arxiv: 2610.21033 (work)