Paper Citation Record · LEDGER

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition

As of 10 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2502.09047.

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

pith.paper-citation-record.v1
2502.09047 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T22:56:28.686797Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:12:12.868390Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T15:12:20.060396Z

Reference resolution

37 of 37 outbound references displayed

verified exact0
verified fuzzy20
unresolved17
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 88ab5480-4a8a-40a1-bec9-e6c02de3e01e · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:29.373389Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6d6ba060-202b-490c-9490-9bac094da17e · outbound

This paper cites For any PSD matrix M, we have E [ ˆGt⊗ ˆGt ] ◦ M≼ ψ ⟨[ O O O S ] , M ⟩[ δ2 t S δtqtS δtqtS q2 t S ].

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition For any PSD matrix M, we have E [ ˆGt⊗ ˆGt ] ◦ M≼ ψ ⟨[ O O O S ] , M ⟩[ δ2 t S δtqtS δtqtS q2 t S ]

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:29.407130Z

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Observation 5548f45e-21ac-478a-9c62-39fdbd8d887f · outbound

This paper cites C.1.3 Parameter Choice We select the parameters of ASGD using the following procedu re:.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition C.1.3 Parameter Choice We select the parameters of ASGD using the following procedu re:

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:29.391108Z

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Observation d19bc2e3-be22-4071-b0c8-7e3355ed6823 · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:29.356904Z

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Observation 095e4cb2-b0e4-4cf1-a1c7-32f45fde0644 · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:29.341083Z

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Observation cc295b02-6b16-4aa8-86f7-c0b484dc56ac · outbound

This paper cites (80) From the above procedure, we have δ≤ 1 2188ψ lnn tr S, γ ∈ [ δ, 1 2188ψ lnn∑ i>˜κλi ] , β = δ 4376ψ˜κγ lnn.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition (80) From the above procedure, we have δ≤ 1 2188ψ lnn tr S, γ ∈ [ δ, 1 2188ψ lnn∑ i>˜κλi ] , β = δ 4376ψ˜κγ lnn

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:29.325132Z

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Observation 790523b8-a3e5-4693-9bfd-b9c85f198fd5 · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:29.308826Z

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Observation edb4721d-4523-4c96-bc78-b0621fe638ab · outbound

This paper cites (83) Proof.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition (83) Proof

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:29.292173Z

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Observation 72830741-eaf1-4d26-bc42-480f714d96eb · outbound

This paper cites self- governed.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition self- governed

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:29.275021Z

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Observation 69a41e35-720b-4cd4-80ff-b5d8572a6a60 · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:29.255653Z

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Observation 2df746a7-374b-4f91-968e-3f079abc26a8 · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:29.239164Z

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Observation 0692e2cc-2986-4794-904f-4754edafa945 · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:29.222840Z

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Observation 187d2f1f-a0fb-4cc8-98bc-cb0360a44bab · outbound

This paper cites (148) Since x1x2 =c(1−δλ), we have c≤x1≤x2.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition (148) Since x1x2 =c(1−δλ), we have c≤x1≤x2

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:29.206426Z

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Observation 37e7207c-a981-4495-95b0-e076527c869c · outbound

This paper cites Let x1,2 =r(cosθ± i sinθ), we have r = √ c(1−δλ)≤ 1 and 0≤θ≤π/2 where 2r cosθ =x1 +x2 = 1 +c−qλ≥ 0 from Lemma 5.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Let x1,2 =r(cosθ± i sinθ), we have r = √ c(1−δλ)≤ 1 and 0≤θ≤π/2 where 2r cosθ =x1 +x2 = 1 +c−qλ≥ 0 from Lemma 5

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:29.189427Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0e4fb157-eade-4ea7-ad12-508a320effa6 · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:29.171034Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a9200550-0554-4fb2-ba5b-7aa999978608 · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:29.150930Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4e475559-618c-4e74-8520-1a8870825eb6 · outbound

This paper cites [2024], we have ( U(ℓ),i ) 22 = δ(ℓ) 2 + (1 +c)(q(ℓ)−δ(ℓ)) 2 ( 1−c2 +cλi(q(ℓ) +cδ(ℓ)) ) ; (175).

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition [2024], we have ( U(ℓ),i ) 22 = δ(ℓ) 2 + (1 +c)(q(ℓ)−δ(ℓ)) 2 ( 1−c2 +cλi(q(ℓ) +cδ(ℓ)) ) ; (175)

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:29.115921Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 60035656-5963-47c1-8ac4-6acda43097b8 · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:29.095984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1cea5a82-ecbc-4709-9f35-688c8085b2d4 · outbound

This paper cites [2018], we have ( U(ℓ),i ) 11 = (1− 2δ(ℓ)λi) ( U(ℓ),i ) 22 +δ2 (ℓ)λi.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition [2018], we have ( U(ℓ),i ) 11 = (1− 2δ(ℓ)λi) ( U(ℓ),i ) 22 +δ2 (ℓ)λi

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:29.079404Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation cc071115-0512-4e88-a50d-6b42a1c332ff · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:29.059059Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b017734c-3bdc-4ecf-9718-851c5cc55c7d · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:29.038827Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 473266ed-abe0-41cf-b375-e1266c915ad0 · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:29.018874Z

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Observation 4e46aca2-0cfd-4071-93f5-5d0967df28d0 · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:28.999098Z

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Observation 2fb72154-b030-4a55-bb9d-7f89e38c75ad · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:28.979384Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 602a506d-b52d-4e52-8b51-11dc44ffad93 · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:28.959378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e65b9df6-bff1-49d3-a7a5-2ed0b06a70a1 · outbound

This paper cites We assume λi ≂ i−a, λi/mi ≂ i−b and tii ≲ i−a+κ.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition We assume λi ≂ i−a, λi/mi ≂ i−b and tii ≲ i−a+κ

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:28.902384Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 70ce24ac-9de2-413c-8c98-2ad1e6493251 · outbound

This paper cites Note that distributions in r-smooth class satisﬁes the above assumption with ν = 0.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Note that distributions in r-smooth class satisﬁes the above assumption with ν = 0

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:28.875774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c21ef11f-42be-4ca4-9d91-432f0451c44d · outbound

This paper cites Then ri ≂ i−a+κ and ri/mi ≂ i−b+κ.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Then ri ≂ i−a+κ and ri/mi ≂ i−b+κ

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:28.837395Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0a3e320d-5ce2-4a62-b4d7-9e7ecdd93cd5 · outbound

This paper cites Then we have tii ≲ i−a+κ and tii/λi ≲ iκ for any integeri∈ [d], where tii denotes the i-th diagonal element of T.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Then we have tii ≲ i−a+κ and tii/λi ≲ iκ for any integeri∈ [d], where tii denotes the i-th diagonal element of T

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:28.815847Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 38e2d762-a0ec-46a7-ad83-6e7af17c7a79 · outbound

This paper cites Then we have ‖ ‖T′ i:∞,i:∞ ‖ ‖ ≲ i−b+κ for any integer i∈ [d].

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Then we have ‖ ‖T′ i:∞,i:∞ ‖ ‖ ≲ i−b+κ for any integer i∈ [d]

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:28.796780Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f5c8f008-809d-403c-b55f-c0e0206c87bf · outbound

This paper cites an unresolved cited work.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-07T22:56:28.776790Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b76bc479-5212-4c29-8a62-5ecce73cb4a0 · outbound

This paper cites From Item 1, we have ‖ ‖T′ i:∞,i:∞ ‖ ‖≤C‖diag{(λi+1/mi+1)· (i + 1)κ,..., (λd/md)·dκ}‖≤ i−b+κ.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition From Item 1, we have ‖ ‖T′ i:∞,i:∞ ‖ ‖≤C‖diag{(λi+1/mi+1)· (i + 1)κ,..., (λd/md)·dκ}‖≤ i−b+κ

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:28.756200Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ae80e897-b551-44c8-a096-d6eb8549864f · outbound

This paper cites Note that Assumption 6 implies Assumption 7.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition Note that Assumption 6 implies Assumption 7

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:28.734594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 22499c78-a357-45d1-ab1d-96d26089c963 · outbound

This paper cites (221) This form is identical to the recursion of ˜Ct if we replace 4 ‖w∗‖2 S by σ2.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition (221) This form is identical to the recursion of ˜Ct if we replace 4 ‖w∗‖2 S by σ2

Reference 109

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:28.921266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a6d06526-d50b-4808-aea9-605a7547e544 · outbound

This paper cites The following lemma characterizes U(ℓ),i and Q(ℓ),i.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition The following lemma characterizes U(ℓ),i and Q(ℓ),i

Reference 173

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:29.133359Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5a939307-d8f7-45b4-aeeb-1505d8a763d0 · outbound

This paper cites (211) Note that T≼ 2T0:k∗ + 2Tk∗:∞.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition (211) Note that T≼ 2T0:k∗ + 2Tk∗:∞

Reference 208

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:28.940789Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 77dfac1e-f9ff-4a9f-8719-5828a95b118b · outbound

This paper cites (244) We can write out the following equivalent form: min ai,τ ≥0 τ 2 π2 + d∑ i=1 σ2a2 iri nλi , s.t.∀i∈ [d], (1−ai)2ri mi ≤τ 2.

Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition (244) We can write out the following equivalent form: min ai,τ ≥0 τ 2 π2 + d∑ i=1 σ2a2 iri nλi , s.t.∀i∈ [d], (1−ai)2ri mi ≤τ 2

Reference 242

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T22:56:28.857215Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

Observation 7fbbc842-53b4-430d-9c47-7e925129935c · inbound

Dimension-adapted Momentum Outscales SGD cites this paper.

Dimension-adapted Momentum Outscales SGD Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition

Reference 66

Resolution: verified exact; local_arxiv, observed 2026-08-07T15:12:20.139288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.