Paper Citation Record · LEDGER

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm

As of 13 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 3 inbound Pith citation observations for arXiv:2411.15660.

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

pith.paper-citation-record.v1
2411.15660 v1

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T14:08:58.209121Z

measured 23 of 23 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 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T19:02:27.699052Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-20T07:18:06.907497Z

Reference resolution

20 of 20 outbound references displayed

verified exact1
verified fuzzy11
unresolved8
parse uncertain0
malformed identifier0
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External citation measurements

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Outbound references

Observation 54b14cae-3ed0-4707-9639-2bd2788b8639 · outbound

This paper cites Upper bound forJ (p).

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm Upper bound forJ (p)

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:08:58.730004Z

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 e628546f-d664-48b6-a831-bae84a42f917 · outbound

This paper cites (40) Meanwhile (see Appendix C.2), ∇ψ(Θ)∗ : Rp×p → Rp×r is given by ∇ψ(Θ)∗(M ) = ¯Θ⊥ ¯Θ⊤ ⊥(M + M ⊤) ¯ΘW −1/2.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm (40) Meanwhile (see Appendix C.2), ∇ψ(Θ)∗ : Rp×p → Rp×r is given by ∇ψ(Θ)∗(M ) = ¯Θ⊥ ¯Θ⊤ ⊥(M + M ⊤) ¯ΘW −1/2

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:08:58.753860Z

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Observation 36e6d8de-0526-4be7-9557-ebc4f79fa6b7 · outbound

This paper cites Local privacy and statistical minimax rates.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm Local privacy and statistical minimax rates

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:08:58.833075Z

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Observation b08046b7-10b3-4ee6-9475-b636601bb866 · outbound

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

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm Calibrating noise to sensitivity in private data analysis

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:08:58.821873Z

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

Observation 9828e6b4-689d-478d-acb3-bfed0405b914 · outbound

This paper cites Asymptotics and concentration bounds for bilinear forms of spectral projectors of sample covariance.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm Asymptotics and concentration bounds for bilinear forms of spectral projectors of sample covariance

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:08:58.791077Z

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 78f04332-de90-430e-aa4d-37a555fd9b98 · outbound

This paper cites URL https://doi.org/10.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm URL https://doi.org/10

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-12T14:08:57.887222Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0be0d1c5-ecdb-40fb-96f9-c669f9f6fa51 · outbound

This paper cites John Novembre and Matthew Stephens.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm John Novembre and Matthew Stephens

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-12T14:08:57.903106Z

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Observation a489bf57-c58f-47a2-9041-9dd05476fb19 · outbound

This paper cites Using these facts, we have E X j1,··· ,jl∈[m] wj1 · · ·wjltr(U ⊤M (s1)M (s1)⊤∆j1M (s2) · · ·M (sl)⊤∆jlM (sl+1)M (sl+1)⊤U ) · 1(E) ≤ r · X j∈I2(s) uj1 · · ·ujl.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm Using these facts, we have E X j1,··· ,jl∈[m] wj1 · · ·wjltr(U ⊤M (s1)M (s1)⊤∆j1M (s2) · · ·M (sl)⊤∆jlM (sl+1)M (sl+1)⊤U ) · 1(E) ≤ r · X j∈I2(s) uj1 · · ·ujl

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:08:58.766061Z

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 7c06f8a3-f9f2-4b50-b98a-bdd5561340cb · outbound

This paper cites Recall G(j) 1 = E⟨∇ψ(Θ)(∇ log p(Dj; Θ| bUj)), ∇ψ(Θ)(∇ log p(X (j) 1 ; Θ| bUj))⟩.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm Recall G(j) 1 = E⟨∇ψ(Θ)(∇ log p(Dj; Θ| bUj)), ∇ψ(Θ)(∇ log p(X (j) 1 ; Θ| bUj))⟩

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:08:58.670536Z

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 26c4d52c-652b-4a2f-b215-d5d3257ae60f · outbound

This paper cites The term Etr(W −4) can be computed using the Theorem 4.1 of Von Rosen (1988), which implies Etr(W −4) · e−c1p/2 ≤ p−2.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm The term Etr(W −4) can be computed using the Theorem 4.1 of Von Rosen (1988), which implies Etr(W −4) · e−c1p/2 ≤ p−2

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:08:58.556106Z

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 6e41e1cb-a1c3-41b3-9966-afd584cb06ec · outbound

This paper cites Lemma 5 (Koltchinskii and Lounici (2017)).

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm Lemma 5 (Koltchinskii and Lounici (2017))

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:08:58.469200Z

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

Observation df397a00-a683-4cf2-8c19-81e126354f07 · outbound

This paper cites Principal component analysis: a review and recent developments.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm Principal component analysis: a review and recent developments

Reference 2001

Resolution: unresolved; no resolver link, observed 2026-08-12T14:08:57.878684Z

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Observation 4142b718-0141-4a8d-8f90-b90c7e2bb3fd · outbound

This paper cites The algorithmic foundations of differential privacy.Foundations and Trends® in Theoretical Computer Science , 9(3–4):211–407, 2014a.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm The algorithmic foundations of differential privacy.Foundations and Trends® in Theoretical Computer Science , 9(3–4):211–407, 2014a

Reference 2006

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:08:58.810770Z

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 b4b0a4a8-7702-4f70-90b8-b48f4750274b · outbound

This paper cites URL https://doi.org/10.1214/ 08-AOS600.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm URL https://doi.org/10.1214/ 08-AOS600

Reference 2008

Resolution: unresolved; no resolver link, observed 2026-08-12T14:08:57.592724Z

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Observation 6d8f54a9-194d-492a-b301-10ce84e4205c · outbound

This paper cites URL https://doi.org/10.1214/09-AOS752.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm URL https://doi.org/10.1214/09-AOS752

Reference 2010

Resolution: verified exact; doi, observed 2026-08-12T14:08:58.297225Z

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 5b387a57-34c8-4098-9e46-93eaf5455c87 · outbound

This paper cites URL https: //doi.org/10.1214/13-AOS1178.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm URL https: //doi.org/10.1214/13-AOS1178

Reference 2013

Resolution: unresolved; no resolver link, observed 2026-08-12T14:08:57.745799Z

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Observation 703904cc-aff5-475a-ade3-4630d36bdcee · outbound

This paper cites ISBN 9781450329576.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm ISBN 9781450329576

Reference 2014

Resolution: unresolved; no resolver link, observed 2026-08-12T14:08:57.874868Z

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Observation 1ef41d7c-c9a1-45da-b7b4-50e92d59a7f3 · outbound

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

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm Optimal Federated Learning for Nonparametric Regression with Heterogeneous Distributed Differential Privacy Constraints

Reference 2016

Resolution: unresolved; no resolver link, observed 2026-08-12T14:08:57.795048Z

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Observation ccf6a1d2-4d03-4520-a3df-02a475bef6e0 · outbound

This paper cites URL https://doi.org/10.1214/17-AOS1541.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm URL https://doi.org/10.1214/17-AOS1541

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-12T14:08:57.634351Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d98ff82c-6562-4419-9d3b-14c1bdc8efe3 · outbound

This paper cites In the proof, we set λmax = λ1 and λmin = λr.

Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm In the proof, we set λmax = λ1 and λmin = λr

Reference 2022

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:08:58.777425Z

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

Observation 43c6e754-da5f-4c6f-914b-bbc591a90e1e · inbound

Spectral Joint Subspace Estimation for Heterogeneous Multi-View Data: Geometry and Reweighting cites this paper.

Spectral Joint Subspace Estimation for Heterogeneous Multi-View Data: Geometry and Reweighting Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm

Reference 2013

Resolution: unresolved; no resolver link, observed 2026-08-03T19:02:27.699052Z

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Observation 960e43da-43c9-41a8-bfee-3222d42f5020 · inbound

A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning cites this paper.

A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm

Reference 35

Resolution: verified exact; arxiv_id, observed 2026-05-20T07:18:06.909041Z

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 edbdec41-56ca-4ba1-a1da-de4aeb2d8acd · inbound

A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning cites this paper.

A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm

Reference 35

Resolution: unresolved; no resolver link, observed 2026-07-12T16:29:28.243675Z

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