Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:45:58.257921Z
Paper Citation Record · LEDGER
Minimax Optimal Rates for Regression on Manifolds and Distributions
As of 19 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 1 inbound Pith citation observation for arXiv:2506.07504.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-01T20:21:45.303967Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
51 of 51 outbound references displayed
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- verified fuzzy17
- unresolved33
- parse uncertain0
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External citation measurements
No source-named external measurement is stored.
Outbound references
Observation e1992c7b-28ef-458e-b0bf-902a31e626c4 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 1
- Resolution
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 89107439-0ada-4feb-939f-66f0202a79c4 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 2
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 8baf70ef-2905-4f28-8b16-dfe353f7b5f9 · outbound
This paper cites Using the partition of unity, one can glue constructions in the local charts to form a global construc- tion on the manifold.
Minimax Optimal Rates for Regression on Manifolds and Distributions Using the partition of unity, one can glue constructions in the local charts to form a global construc- tion on the manifold
Reference 3
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- raw_fallback, observed 2026-08-07T05:45:59.265806Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 389b5276-2a9e-4154-9f46-3f710d3db668 · outbound
This paper cites The proof of Lemma 7 is provided in Appendix E.1.
Minimax Optimal Rates for Regression on Manifolds and Distributions The proof of Lemma 7 is provided in Appendix E.1
Reference 4
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- raw_fallback, observed 2026-08-07T05:45:59.072345Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 200426a8-8d25-4273-bd88-bfa9d0abe5e7 · outbound
This paper cites 35 A.2 Smooth submanifold family and smooth conditional distributions Firstly we recall the definition of(β Y , βX )-smooth manifold family defined in Definition 4 of the main text.
Minimax Optimal Rates for Regression on Manifolds and Distributions 35 A.2 Smooth submanifold family and smooth conditional distributions Firstly we recall the definition of(β Y , βX )-smooth manifold family defined in Definition 4 of the main text
Reference 8
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- raw_fallback, observed 2026-08-07T05:45:59.220327Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d641b07e-aae7-4a47-b5c7-0797a88637bd · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 9
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- unresolved
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 545f720f-4371-4c75-87ab-d2e7093c25a4 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 10
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- unresolved
- raw_fallback, observed 2026-08-07T05:45:59.192036Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b072e901-28c9-4e38-af80-34ddbb25875e · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 11
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- unresolved
- raw_fallback, observed 2026-08-07T05:45:59.178227Z
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 63aa5de2-a233-4f98-aa65-29892cd59bb4 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:45:59.164065Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a83f2e52-ef1c-4d31-8fb1-f9eac1b23dc3 · outbound
This paper cites Then there existsL′ so that{µ ∗ Y|x }x∈MX ∈C βY ,βX ,αY ,αX τ,τ1,L′ (dY , DY ,M X ).
Minimax Optimal Rates for Regression on Manifolds and Distributions Then there existsL′ so that{µ ∗ Y|x }x∈MX ∈C βY ,βX ,αY ,αX τ,τ1,L′ (dY , DY ,M X )
Reference 13
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- raw_fallback, observed 2026-08-07T05:45:59.149358Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 0291a98f-708a-435c-8557-751165a03ae1 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 14
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- unresolved
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Observation 34456ac7-e6b6-4ddd-ab6d-2455b82a905b · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 15
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- raw_fallback, observed 2026-08-07T05:45:59.118867Z
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7f9d9652-f933-42b1-b4f0-057411e7b56c · outbound
This paper cites 38 (d) for anyj≥1andx∈R d, {ψ∈ Ψ d j :I ψ ∩B Rd(x,2 −(j−1))̸=∅} ≤C ‡ L.
Minimax Optimal Rates for Regression on Manifolds and Distributions 38 (d) for anyj≥1andx∈R d, {ψ∈ Ψ d j :I ψ ∩B Rd(x,2 −(j−1))̸=∅} ≤C ‡ L
Reference 16
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Observation 717d9667-f1a1-4ccc-9251-ac7870b9ef0f · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 17
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Observation b84fb188-f146-4906-b60f-42036e5f9c88 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 19
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 9b8ca4a9-dd40-479f-a60a-4ee11bb89b97 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 20
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Observation cb7b791e-b201-47ed-b12d-6f0fb3bf419b · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 21
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Observation 440c811e-d610-43f5-bd0e-ef67bf09f681 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 22
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- raw_fallback, observed 2026-08-07T05:45:59.011783Z
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Observation 7ce7f15c-0d06-4eaf-ba9e-70b1c252f8ea · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 23
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Observation ca70f7cc-bda5-4328-87d9-89481e950f43 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 24
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Observation 6b82633e-0ebd-4fa5-a6cb-e122eed72119 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 25
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- unresolved
- raw_fallback, observed 2026-08-07T05:45:58.935642Z
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 4fdf9c67-a8d7-4494-9806-367bfd8a457a · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 26
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- raw_fallback, observed 2026-08-07T05:45:58.912175Z
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 9c42f7a7-80d8-4240-9fa3-a3426853c9be · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 27
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Observation 40d58c41-7668-4657-8fda-036801a5a5c2 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 28
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- raw_fallback, observed 2026-08-07T05:45:58.881432Z
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation db119071-3ac5-4f8f-88a9-6131708d52c7 · outbound
This paper cites Moreover, since for anyk∈[K]\ bK, it holds that 1 n X i∈I1 ρ[k](Xi, Yi)≤ 1 n X i∈I1 1(∥(Xi, Yi)−(x k, yk)∥ ≤ √ 2τ2) = 0.
Minimax Optimal Rates for Regression on Manifolds and Distributions Moreover, since for anyk∈[K]\ bK, it holds that 1 n X i∈I1 ρ[k](Xi, Yi)≤ 1 n X i∈I1 1(∥(Xi, Yi)−(x k, yk)∥ ≤ √ 2τ2) = 0
Reference 29
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- raw_fallback, observed 2026-08-07T05:45:58.866147Z
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 1c7468e3-9d28-4f3c-84d9-19eab2f301a5 · outbound
This paper cites For eachω∈ {0,1}mdY 1 ×mdX 2 , define¯ω= 1−ωin the element-wise manner.
Minimax Optimal Rates for Regression on Manifolds and Distributions For eachω∈ {0,1}mdY 1 ×mdX 2 , define¯ω= 1−ωin the element-wise manner
Reference 30
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- raw_fallback, observed 2026-08-07T05:45:58.850544Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation cdfddbd8-deab-4539-88e5-531abc5e2d0b · outbound
This paper cites Consequently, we have for anyx∈ M X, 1 c4 f(·, x)∈ Hγ 1 (RD Y )(recall that we only considerγ <1).
Minimax Optimal Rates for Regression on Manifolds and Distributions Consequently, we have for anyx∈ M X, 1 c4 f(·, x)∈ Hγ 1 (RD Y )(recall that we only considerγ <1)
Reference 31
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- raw_fallback, observed 2026-08-07T05:45:58.834940Z
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Observation a309d367-039e-459f-9003-dba4da66a4f4 · outbound
This paper cites Consider anyγ 1 ∈(0,1]and denoteN(G, d γ1 ∞, ε)as theε-covering number of Gwith respect to thed γ1 ∞ distance, whered γ1 ∞(G1, G2) = sup z∈RdY ,x∈RDX ∥G1(z, x)−G2(z, x)∥γ1.
Minimax Optimal Rates for Regression on Manifolds and Distributions Consider anyγ 1 ∈(0,1]and denoteN(G, d γ1 ∞, ε)as theε-covering number of Gwith respect to thed γ1 ∞ distance, whered γ1 ∞(G1, G2) = sup z∈RdY ,x∈RDX ∥G1(z, x)−G2(z, x)∥γ1
Reference 32
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- raw_fallback, observed 2026-08-07T05:45:58.818213Z
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Observation f983690f-5ecc-4448-b97b-0f0a3d304b92 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 33
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- raw_fallback, observed 2026-08-07T05:45:58.801670Z
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Observation 4b005d91-4fd3-4e37-97b8-e29e68ec5b9d · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:45:58.647350Z
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 9716a5b1-9534-42ab-86ce-2d1be350951e · outbound
This paper cites LetN z c2 −j be ac2 −j-covering set ofB RdY (0, τ1), contained withinB RdY (0, τ1), wherecis a small enough positive constant.
Minimax Optimal Rates for Regression on Manifolds and Distributions LetN z c2 −j be ac2 −j-covering set ofB RdY (0, τ1), contained withinB RdY (0, τ1), wherecis a small enough positive constant
Reference 35
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- raw_fallback, observed 2026-08-07T05:45:58.630776Z
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 5f6266e1-2ee1-4c4b-9005-1c0e2e19adb4 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 36
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- raw_fallback, observed 2026-08-07T05:45:58.612590Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation cae4e089-57e2-444e-b250-58bc09e07a49 · outbound
This paper cites The proof of Lemma 19 is provided in Appendix D.14.
Minimax Optimal Rates for Regression on Manifolds and Distributions The proof of Lemma 19 is provided in Appendix D.14
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:45:58.594829Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation caad69de-15ec-4dad-b78e-63148304bce8 · outbound
This paper cites Hencesup x∈Rd P ψ∈Ψd j 1(x∈I ψ)≤C ′ L.
Minimax Optimal Rates for Regression on Manifolds and Distributions Hencesup x∈Rd P ψ∈Ψd j 1(x∈I ψ)≤C ′ L
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:45:58.576151Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a733031d-ee5b-42f1-9fb8-bb047ffccd5c · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 39
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:45:58.560808Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 94447610-2f27-4172-9190-df92beda1754 · outbound
This paper cites 116 For the last statement.
Minimax Optimal Rates for Regression on Manifolds and Distributions 116 For the last statement
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:45:58.544279Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation aabc45be-6132-47c7-9620-ebb2141586fe · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 41
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:45:58.528994Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3717858e-0d14-4d4d-a356-255de293c18e · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 42
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:45:58.512268Z
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 214a88ca-0441-49e9-b89f-5f000d0b1a3d · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 43
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:45:58.496527Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ee220c95-05dd-4446-a168-9662bd27d042 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 44
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:45:58.479877Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 1b90515d-1474-4d28-ba1d-db19c56f0023 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 45
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:45:58.463277Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 2ea0a67a-91fb-446f-99b7-c10a51e7cada · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 46
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:45:58.446170Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3348066f-09cd-4382-94cd-d862e7917846 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 47
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:45:58.428209Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 0cb82a27-3dc7-4121-aab2-98990acd6a0f · outbound
This paper cites • if∥z−z 0∥<1, then |G(ej +j1,j2) [k] (z, x)−G(ej +j1,j2) [k] (z0, x)| ≤ p dY L∥z−z 0∥ ≤ p dY L∥z−z 0∥αY −|j1|− αY αX |j2|.
Minimax Optimal Rates for Regression on Manifolds and Distributions • if∥z−z 0∥<1, then |G(ej +j1,j2) [k] (z, x)−G(ej +j1,j2) [k] (z0, x)| ≤ p dY L∥z−z 0∥ ≤ p dY L∥z−z 0∥αY −|j1|− αY αX |j2|
Reference 48
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:45:58.409738Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 50524221-e1f6-4159-977c-95061cac46e1 · outbound
This paper cites • if∥z−z 0∥<1, then |G(ej +j1,j2) [k] (z, x)−G(ej +j1,j2) [k] (z0, x)| ≤L∥z−z0∥βY −|j1|−1− βY βX |j2| ≤L∥z−z 0∥αY −|j1|− αY αX |j2|.
Minimax Optimal Rates for Regression on Manifolds and Distributions • if∥z−z 0∥<1, then |G(ej +j1,j2) [k] (z, x)−G(ej +j1,j2) [k] (z0, x)| ≤L∥z−z0∥βY −|j1|−1− βY βX |j2| ≤L∥z−z 0∥αY −|j1|− αY αX |j2|
Reference 49
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:45:58.393007Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 9ad7a178-f59a-461e-9169-1ade79081841 · outbound
This paper cites an unresolved cited work.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 50
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:45:58.376083Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation aacec020-7d7a-448f-9f08-e8980663ed0e · outbound
This paper cites Z rn 0 r Wn log 4Tnρ ε2 dε # = C4√n Eµ∗,⊗n.
Minimax Optimal Rates for Regression on Manifolds and Distributions Z rn 0 r Wn log 4Tnρ ε2 dε # = C4√n Eµ∗,⊗n
Reference 51
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:45:58.358235Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7a77737c-a993-49b5-bee0-4e863394a0f3 · outbound
This paper cites Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory.
Minimax Optimal Rates for Regression on Manifolds and Distributions Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory
Reference 2013
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T05:45:57.994758Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8e5d2508-6888-4f6b-88d0-b84eaf19986e · outbound
This paper cites Conditional Generative Adversarial Nets.
Minimax Optimal Rates for Regression on Manifolds and Distributions Conditional Generative Adversarial Nets
Reference 2018
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T05:45:58.002606Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 54a2ed4a-6a03-460d-a877-e6ecf25deb25 · outbound
This paper cites Minimax Optimal Rates for Regression on Manifolds and Distributions.
Minimax Optimal Rates for Regression on Manifolds and Distributions Minimax Optimal Rates for Regression on Manifolds and Distributions
Reference 2019
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:45:59.281501Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation bcba965b-2753-430c-bd71-34e0aec5429b · outbound
This paper cites Wasserstein Auto-Encoders.
Minimax Optimal Rates for Regression on Manifolds and Distributions Wasserstein Auto-Encoders
Reference 2021
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T05:45:58.008164Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
Observation b545a0df-3538-4765-9e9b-de8138b951a7 · inbound
Semi-Supervised Conditional Diffusion via Label Augmentation cites this paper.
Semi-Supervised Conditional Diffusion via Label Augmentation Minimax Optimal Rates for Regression on Manifolds and Distributions
Reference 37
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T20:21:45.303967Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.