Paper Citation Record · LEDGER

PCA of probability measures: Sparse and Dense sampling regimes

As of 8 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2602.02190.

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

pith.paper-citation-record.v1
2602.02190 v2

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T05:34:54.062787Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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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

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verified fuzzy0
unresolved35
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malformed identifier1
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External citation measurements

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Outbound references

Observation 35fec569-ad57-4a54-bca4-5ffc62337fa0 · outbound

This paper cites Stability Bounds for Smooth Optimal Transport Maps and their Statistical Implications.

PCA of probability measures: Sparse and Dense sampling regimes Stability Bounds for Smooth Optimal Transport Maps and their Statistical Implications

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:49.402714Z

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Observation da59c8cb-621c-4a7c-9ee4-756f74c0bb2c · outbound

This paper cites Minimax estimation of functional principal components from noisy discretized functional data.Scandinavian Journal of Statistics, 52(1):38– 80, 2025.

PCA of probability measures: Sparse and Dense sampling regimes Minimax estimation of functional principal components from noisy discretized functional data.Scandinavian Journal of Statistics, 52(1):38– 80, 2025

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:49.475993Z

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Observation 64963b80-3740-479b-aef8-3208fff5b618 · outbound

This paper cites Springer Science & Business Media, 2011.

PCA of probability measures: Sparse and Dense sampling regimes Springer Science & Business Media, 2011

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:49.566435Z

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Observation 2b17d70f-da3b-438d-9e7d-a9a474acf118 · outbound

This paper cites Geodesic pca in the wasserstein space by convex pca.

PCA of probability measures: Sparse and Dense sampling regimes Geodesic pca in the wasserstein space by convex pca

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:49.678179Z

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Observation 41b7ed44-89bc-4b80-aaee-a3a94ca76aa1 · outbound

This paper cites Chapman and Hall/CRC, 2019.

PCA of probability measures: Sparse and Dense sampling regimes Chapman and Hall/CRC, 2019

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:49.764060Z

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Observation 3e07d768-778b-420c-ac6c-ea0945fad2d1 · outbound

This paper cites Polar factorization and monotone rearrangement of vector-valued functions.Communica- tions on pure and applied mathematics, 44(4):375–417, 1991.

PCA of probability measures: Sparse and Dense sampling regimes Polar factorization and monotone rearrangement of vector-valued functions.Communica- tions on pure and applied mathematics, 44(4):375–417, 1991

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:49.900865Z

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Observation a9031359-bc4d-4068-bbc4-2e8f6cd0ec34 · outbound

This paper cites Computational resources for high- dimensional immune analysis from the human immunology project consortium.Nature biotechnology, 32(2):146–148, 2014.

PCA of probability measures: Sparse and Dense sampling regimes Computational resources for high- dimensional immune analysis from the human immunology project consortium.Nature biotechnology, 32(2):146–148, 2014

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:49.956128Z

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Observation 8605ba39-17ed-4720-a9fd-2695cee9c6b1 · outbound

This paper cites Statistical optimal transport.

PCA of probability measures: Sparse and Dense sampling regimes Statistical optimal transport

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:50.023924Z

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Observation 9eee7b57-a86d-4a59-9fbe-4622aa706514 · outbound

This paper cites Conway.A Course in Functional Analysis.

PCA of probability measures: Sparse and Dense sampling regimes Conway.A Course in Functional Analysis

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:50.154150Z

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Observation 4de87c34-7d7a-4193-9c72-ee0472edb015 · outbound

This paper cites Sinkhorn distances: Lightspeed computation of optimal transport.Advances in neural information processing systems, 26, 2013.

PCA of probability measures: Sparse and Dense sampling regimes Sinkhorn distances: Lightspeed computation of optimal transport.Advances in neural information processing systems, 26, 2013

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:50.306626Z

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Observation 2c6325cf-2d8a-4265-b3ff-d27f4624647d · outbound

This paper cites Rates of estimation of optimal transport maps using plug-in estimators via barycentric projections.Advances in Neural Information Processing Systems, 34:29736–29753, 2021.

PCA of probability measures: Sparse and Dense sampling regimes Rates of estimation of optimal transport maps using plug-in estimators via barycentric projections.Advances in Neural Information Processing Systems, 34:29736–29753, 2021

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:50.491192Z

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Observation 64bb7f47-e565-4f8b-a4f8-bc2baf4d62cf · outbound

This paper cites On the rate of convergence in wasserstein distance of the empirical measure.Probability Theory and Related Fields, 162(3-4):707–738, 2015.

PCA of probability measures: Sparse and Dense sampling regimes On the rate of convergence in wasserstein distance of the empirical measure.Probability Theory and Related Fields, 162(3-4):707–738, 2015

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:50.571617Z

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Observation 59541972-4f06-464f-a2c6-eb0fd56f20b9 · outbound

This paper cites Generalized procrustes analysis.Psychometrika, 40(1):33–51, 1975.

PCA of probability measures: Sparse and Dense sampling regimes Generalized procrustes analysis.Psychometrika, 40(1):33–51, 1975

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:50.655678Z

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Observation 65fe9acd-2474-4fe9-ae79-23524744e4dd · outbound

This paper cites Properties of principal component methods for functional and longitudinal data analysis.Annals of Statistics, 34(3):1493–1517, 2006.

PCA of probability measures: Sparse and Dense sampling regimes Properties of principal component methods for functional and longitudinal data analysis.Annals of Statistics, 34(3):1493–1517, 2006

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:50.755188Z

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Observation 958aa878-84ac-4958-8568-0e6593d16be1 · outbound

This paper cites Minimax estimation of smooth optimal transport maps.

PCA of probability measures: Sparse and Dense sampling regimes Minimax estimation of smooth optimal transport maps

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:50.871059Z

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Observation 98060938-11c0-48fd-a649-fdd12313414a · outbound

This paper cites On the translocation of masses.

PCA of probability measures: Sparse and Dense sampling regimes On the translocation of masses

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:51.035179Z

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Observation d300b993-6dfe-4a64-9cc0-98409fd12b91 · outbound

This paper cites Scalable optimal transport methods in machine learning: A contemporary survey.IEEE transactions on pattern analysis and machine intelligence, 2024.

PCA of probability measures: Sparse and Dense sampling regimes Scalable optimal transport methods in machine learning: A contemporary survey.IEEE transactions on pattern analysis and machine intelligence, 2024

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:51.138312Z

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Observation 032ceefb-51aa-466b-b2a0-3e616c34be35 · outbound

This paper cites Optimal mass transport: Signal processing and machine-learning applications.IEEE signal processing magazine, 34(4):43–59, 2017.

PCA of probability measures: Sparse and Dense sampling regimes Optimal mass transport: Signal processing and machine-learning applications.IEEE signal processing magazine, 34(4):43–59, 2017

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:51.288097Z

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Observation 3f3d9593-4156-4e74-9f48-bc1cdb6dcac0 · outbound

This paper cites Concentration inequalities and moment bounds for sample covariance operators.Bernoulli, pages 110–133, 2017.

PCA of probability measures: Sparse and Dense sampling regimes Concentration inequalities and moment bounds for sample covariance operators.Bernoulli, pages 110–133, 2017

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:51.444862Z

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Observation 2968ee17-9010-44c4-ba7d-821c43b9aa35 · outbound

This paper cites Plugin estimation of smooth optimal transport maps.The Annals of Statistics, 52(3):966–998, 2024.

PCA of probability measures: Sparse and Dense sampling regimes Plugin estimation of smooth optimal transport maps.The Annals of Statistics, 52(3):966–998, 2024

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:51.590179Z

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Observation 47763b38-0d82-47fa-9126-98bd4c9366d6 · outbound

This paper cites Mémoire sur la théorie des déblais et des remblais.Mem.

PCA of probability measures: Sparse and Dense sampling regimes Mémoire sur la théorie des déblais et des remblais.Mem

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:51.725469Z

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Observation 327b9ee7-ffdc-4dfb-a197-7cd33dccb5be · outbound

This paper cites Recent advances in optimal transport for machine learning.IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024.

PCA of probability measures: Sparse and Dense sampling regimes Recent advances in optimal transport for machine learning.IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:51.931443Z

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Observation c6326cde-f13a-4c96-8be7-1c545078694b · outbound

This paper cites Kernel mean embedding of distributions: A review and beyond.Foundations and Trends®in Machine Learning, 10(1-2):1–141, 2017.

PCA of probability measures: Sparse and Dense sampling regimes Kernel mean embedding of distributions: A review and beyond.Foundations and Trends®in Machine Learning, 10(1-2):1–141, 2017

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:52.062216Z

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Observation 701e4f97-db69-4a63-895e-274e6fe7ecf7 · outbound

This paper cites Springer Nature, 2020.

PCA of probability measures: Sparse and Dense sampling regimes Springer Nature, 2020

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:52.221276Z

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Observation 804a54db-f2c9-4875-b1c4-c90a00c309ef · outbound

This paper cites Computational optimal transport: With applications to data science.

PCA of probability measures: Sparse and Dense sampling regimes Computational optimal transport: With applications to data science

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:52.439773Z

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Observation 8fcff4d7-6e97-4975-b649-80462fe23823 · outbound

This paper cites Minimax estimation of discontinu- ous optimal transport maps: The semi-discrete case.

PCA of probability measures: Sparse and Dense sampling regimes Minimax estimation of discontinu- ous optimal transport maps: The semi-discrete case

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:52.620754Z

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Observation ac74a830-613d-444c-84d9-2d3a3584263a · outbound

This paper cites Wasserstein barycenter and its application to texture mixing.

PCA of probability measures: Sparse and Dense sampling regimes Wasserstein barycenter and its application to texture mixing

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:52.702354Z

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Observation 63924bf5-75af-4ca1-92ad-9ba459f33b1f · outbound

This paper cites Elsevier, 1978.

PCA of probability measures: Sparse and Dense sampling regimes Elsevier, 1978

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:52.832675Z

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Observation 49e10630-fe60-4d81-9e4a-9b5e88729ded · outbound

This paper cites Nonasymptotic upper bounds for the reconstruction error of pca.The Annals of Statistics, 48(2):1098–1123, 2020.

PCA of probability measures: Sparse and Dense sampling regimes Nonasymptotic upper bounds for the reconstruction error of pca.The Annals of Statistics, 48(2):1098–1123, 2020

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:52.944380Z

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Observation b8c9495a-fd51-4559-a1eb-f5205cc1276d · outbound

This paper cites Principal geodesic analysis for probability measures under the optimal transport metric.Advances in Neural Information Processing Systems, 28, 2015.

PCA of probability measures: Sparse and Dense sampling regimes Principal geodesic analysis for probability measures under the optimal transport metric.Advances in Neural Information Processing Systems, 28, 2015

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:53.111152Z

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Observation 17a72aa4-8b4a-4e38-aa41-b1a3ddee69ee · outbound

This paper cites Springer Science & Business Media, 2003.

PCA of probability measures: Sparse and Dense sampling regimes Springer Science & Business Media, 2003

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:53.268797Z

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Observation dcf91036-3ea9-4967-a3e6-42bed5da11ea · outbound

This paper cites On the Wasserstein Geodesic Principal Component Analysis of probability measures.

PCA of probability measures: Sparse and Dense sampling regimes On the Wasserstein Geodesic Principal Component Analysis of probability measures

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:53.419120Z

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Observation 275d0836-c2ce-4673-b039-8dc1d697fb07 · outbound

This paper cites Springer, 2008.

PCA of probability measures: Sparse and Dense sampling regimes Springer, 2008

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:53.601378Z

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Observation 7783f047-96f8-4485-9d32-6ad25f7a3c7e · outbound

This paper cites A linear optimal transportation framework for quantifying and visualizing variations in sets of images.International journal of computer vision, 101(2):254–269, 2013.

PCA of probability measures: Sparse and Dense sampling regimes A linear optimal transportation framework for quantifying and visualizing variations in sets of images.International journal of computer vision, 101(2):254–269, 2013

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:53.766265Z

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Observation 52c9e1bb-c916-45ce-9b4f-f051d75fcc84 · outbound

This paper cites 3d shapenets: A deep representation for volumetric shapes.

PCA of probability measures: Sparse and Dense sampling regimes 3d shapenets: A deep representation for volumetric shapes

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:53.906217Z

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Observation 51fe92b6-d7ee-470c-9aa4-7169f2013240 · outbound

This paper cites Functional data analysis for sparse longitudinal data.Journal of the American Statistical Association, 100(470):577–590, 2005.

PCA of probability measures: Sparse and Dense sampling regimes Functional data analysis for sparse longitudinal data.Journal of the American Statistical Association, 100(470):577–590, 2005

Reference 36

Resolution: malformed identifier; no resolver link, observed 2026-08-03T05:34:54.062787Z

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