Paper Citation Record · LEDGER

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints

As of 13 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2412.18992.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.18992 v2

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T01:07:29.855150Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

36 of 36 outbound references displayed

verified exact1
verified fuzzy31
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 05c6ece9-7335-48b4-98f0-8bf882e225e9 · outbound

This paper cites Op- timal rates for nonparametric density estimation under communication constraints.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Op- timal rates for nonparametric density estimation under communication constraints

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.392104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation bbf465da-392c-4c9b-8980-46b0723ff543 · outbound

This paper cites Unified lower bounds for interactive high-dimensional estimation under information constraints.Advances in Neural Information Processing Systems , 36, 2024.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Unified lower bounds for interactive high-dimensional estimation under information constraints.Advances in Neural Information Processing Systems , 36, 2024

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.377499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cd42cb45-4026-4e66-9a1a-a588e6b8ad3f · outbound

This paper cites Discrete distribution estimation under user-level local differential privacy.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Discrete distribution estimation under user-level local differential privacy

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.363808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4f85a6a5-2caa-4033-bb14-dbe26e06e312 · outbound

This paper cites Differentially private assouad, fano, and le cam.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Differentially private assouad, fano, and le cam

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.349620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 494fa719-e191-4a2a-8ca5-1cf16a8635a0 · outbound

This paper cites Fisher information under local differential privacy.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Fisher information under local differential privacy

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.333392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 148e02f4-6812-4a75-986e-a98b1b54d316 · outbound

This paper cites Federated Learning for Emoji Prediction in a Mobile Keyboard.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Federated Learning for Emoji Prediction in a Mobile Keyboard

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-11T01:07:29.729355Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8fe46bdd-ea43-4519-981f-c6437618a3e7 · outbound

This paper cites Tony Cai, Abhinav Chakraborty, and Lasse Vuursteen.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Tony Cai, Abhinav Chakraborty, and Lasse Vuursteen

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.318855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c691cc48-6fcc-4089-9cd6-4e3ed298d9fc · outbound

This paper cites Optimal Federated Learning for Nonparametric Regression with Heterogeneous Distributed Differential Privacy Constraints.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Optimal Federated Learning for Nonparametric Regression with Heterogeneous Distributed Differential Privacy Constraints

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T01:07:29.738850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48c42499-f8d3-40f3-a0f4-7a9b70f3ae71 · outbound

This paper cites Tony Cai and Ming Yuan.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Tony Cai and Ming Yuan

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.304247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 06939813-4098-4828-83d2-1c3c837b45e5 · outbound

This paper cites Private distribution testing with heterogeneous constraints: Your epsilon might not be mine.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Private distribution testing with heterogeneous constraints: Your epsilon might not be mine

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.290286Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2607bbfa-d931-4858-9d28-a0a0ceab33b6 · outbound

This paper cites Jordan, Xuelin Yang, Lydia Zakynthinou, and Nikita Zhivotovskiy.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Jordan, Xuelin Yang, Lydia Zakynthinou, and Nikita Zhivotovskiy

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.275860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 249af64d-2ad4-40f7-9ba6-20ad85d0abf9 · outbound

This paper cites Ten lectures on wavelets.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Ten lectures on wavelets

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-11T01:07:29.755390Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e82fa8e-16fe-4caa-ae97-267d62de3eb0 · outbound

This paper cites Constructive Approximation.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Constructive Approximation

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.252870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 602a2e66-8030-40d9-9bfd-c2d0f4f90bbb · outbound

This paper cites Calibrating noise to sensitivity in private data analysis.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Calibrating noise to sensitivity in private data analysis

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.238898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 62d19d96-feb4-49d3-9451-4bf5d15a1b12 · outbound

This paper cites The algorithmic foundations of differential privacy.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints The algorithmic foundations of differential privacy

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-11T01:07:29.768283Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b1f3f37-744a-4a7d-9e1d-36df22e93910 · outbound

This paper cites Springer Science & Business Media, Berlin, Heidelberg, 2006.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Springer Science & Business Media, Berlin, Heidelberg, 2006

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.215469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation be914649-a241-4728-b497-5caaf12f1348 · outbound

This paper cites Applications of the van trees inequality: a bayesian cram´ er-rao bound.Bernoulli, pages 59–79, 1995.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Applications of the van trees inequality: a bayesian cram´ er-rao bound.Bernoulli, pages 59–79, 1995

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.202115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7da6c9ea-ba3f-4f11-b1c0-3f1044fd41b4 · outbound

This paper cites Differential privacy for functions and functional data.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Differential privacy for functions and functional data

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.189128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 82250166-96d9-48e0-a5f7-f96f924743c4 · outbound

This paper cites Wavelets, approximation, and statistical applications, volume 129.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Wavelets, approximation, and statistical applications, volume 129

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.176188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d19d8d0d-a594-43ab-87af-11e3137fbc4b · outbound

This paper cites Sampling depth trade-off in function estimation under a two-level design.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Sampling depth trade-off in function estimation under a two-level design

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-11T01:07:29.899188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d05cef73-9796-43fe-8afc-204ef55130e4 · outbound

This paper cites Function Estimation and Gaussian Sequence Models.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Function Estimation and Gaussian Sequence Models

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.163290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b6528fbb-81c6-462e-afaa-63dae0bd04d1 · outbound

This paper cites On the statistical complexity of estimation and testing under privacy constraints.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints On the statistical complexity of estimation and testing under privacy constraints

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.150321Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 56bc7e7a-f9cd-46c7-91d1-79adeda2b752 · outbound

This paper cites Learning with user-level privacy.Advances in Neural Information Processing Systems, 34:12466–12479, 2021.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Learning with user-level privacy.Advances in Neural Information Processing Systems, 34:12466–12479, 2021

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.137415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation de4d99d5-1bb7-4abc-a966-012281ca555a · outbound

This paper cites Learning discrete distributions: user vs item-level privacy.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Learning discrete distributions: user vs item-level privacy

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.123604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a3be369d-1c9b-48f2-a1f6-8005ef55c643 · outbound

This paper cites Formal privacy for func- tional data with gaussian perturbations.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Formal privacy for func- tional data with gaussian perturbations

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.109427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5e5bb02b-f14b-44f1-9b55-a201646fae9c · outbound

This paper cites Tight and robust private mean estimation with few users.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Tight and robust private mean estimation with few users

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.094090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation dc0a2a95-5f6e-449e-b2ea-46d8b743450b · outbound

This paper cites Principal components analysis for functional data.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Principal components analysis for functional data

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.080015Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a9dd9692-201a-47d6-b431-488204c9e547 · outbound

This paper cites Estimating the mean and covariance structure nonparametrically when the data are curves.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Estimating the mean and covariance structure nonparametrically when the data are curves

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.065844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 82718901-34f6-4a8b-9420-280f25919341 · outbound

This paper cites Tsybakov.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Tsybakov

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.050995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0bb97f7c-f922-47a2-84e7-a7c33b822d92 · outbound

This paper cites Tsybakov.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Tsybakov

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.036418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b1f3196f-bc3b-4c74-b298-83664adea79c · outbound

This paper cites High-Dimensional Probability: An Introduction with Applications in Data Science.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints High-Dimensional Probability: An Introduction with Applications in Data Science

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.021434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ebc8254d-4e64-4851-b800-690c9995bd36 · outbound

This paper cites Functional data analysis.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Functional data analysis

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:30.005613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b411bfde-a777-4531-842b-edb08512c2a7 · outbound

This paper cites Optimal estimation in private distributed functional data analysis.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Optimal estimation in private distributed functional data analysis

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:29.991798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9c805d81-92eb-466a-9140-94ea052110da · outbound

This paper cites ∇fL log dPT f dµ′ !#.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints ∇fL log dPT f dµ′ !#

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:29.976711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9289a4dd-080d-4e25-a331-0171e3ff0b16 · outbound

This paper cites Lemma 14.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints Lemma 14

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:29.961842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 1a68a3e4-d34c-4ad0-80d1-78c61832a4bf · outbound

This paper cites exp t SY (s) 1 f 2 2 ! exp 1 2 t2 c2 ϕ ms (ns − 1) 2L SY (s) 1 f 2 2 !# = 2 Ef.

Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints exp t SY (s) 1 f 2 2 ! exp 1 2 t2 c2 ϕ ms (ns − 1) 2L SY (s) 1 f 2 2 !# = 2 Ef

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:07:29.947462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

No inbound Pith citation observations are available.