Paper Citation Record · LEDGER

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations

As of 15 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 2 inbound Pith citation observations for arXiv:1908.10935.

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

pith.paper-citation-record.v1
1908.10935 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T10:39:53.611050Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-31T03:15:47.958266Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-12T00:31:18.035990Z

Reference resolution

36 of 36 outbound references displayed

verified exact4
verified fuzzy20
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6ae85262-90c5-44a1-af86-84dfd966e2af · outbound

This paper cites Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate gaussian mixture models.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate gaussian mixture models

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:54.041669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6eb913c6-b5b9-4828-bc6b-97e81519fb72 · outbound

This paper cites Statistical guarantees for the EM algorithm: From population to sample-based analysis.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Statistical guarantees for the EM algorithm: From population to sample-based analysis

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-14T10:39:53.479158Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 63f8fdc7-0588-482a-abb4-9ca434473b79 · outbound

This paper cites Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:54.021680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2b408e5f-bb66-44d0-893a-a3d2e46fdac2 · outbound

This paper cites Trust region methods , volume 1.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Trust region methods , volume 1

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:54.010705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 708b1de1-d72e-4be3-bca2-d0745ecc1e76 · outbound

This paper cites Cai, Zongming Ma, and Yihong Wu.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Cai, Zongming Ma, and Yihong Wu

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.999473Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f4532618-8cd2-482a-9d01-d6b4f2cf3137 · outbound

This paper cites Singularity, Misspecification, and the Convergence Rate of EM.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Singularity, Misspecification, and the Convergence Rate of EM

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-14T10:39:53.495790Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 978e8a92-bed7-49f3-8b9d-d372266fd9f3 · outbound

This paper cites Sharp Analysis of Expectation-Maximization for Weakly Identifiable Models.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Sharp Analysis of Expectation-Maximization for Weakly Identifiable Models

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-14T10:39:53.715023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3076b55f-569a-4fdd-b523-1114555776e7 · outbound

This paper cites Maximum likelihood from incomplete data via the EM algorithm.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Maximum likelihood from incomplete data via the EM algorithm

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.988454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8b208a99-bcad-4451-8dc6-27c9402796dd · outbound

This paper cites Local operator theory, random matrices and B anach spaces.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Local operator theory, random matrices and B anach spaces

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.977135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 663a9914-9177-4a5d-b93c-1f33c65e780e · outbound

This paper cites Ten steps of EM suffice for mixtures of two G aussians.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Ten steps of EM suffice for mixtures of two G aussians

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.966124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ce337b71-bfc9-4e20-8632-f6ea39db6835 · outbound

This paper cites an unresolved cited work.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:39:53.954416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 553c4508-213e-476d-a713-16816c24c695 · outbound

This paper cites On the rate of convergence in wasserstein distance of the empirical measure.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations On the rate of convergence in wasserstein distance of the empirical measure

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.942705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a3974d9d-2e18-4ccf-abbd-6bcd7a882988 · outbound

This paper cites an unresolved cited work.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:39:53.931195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 57f1c1c8-7555-4900-a33c-8d86d3b2d357 · outbound

This paper cites Optimal rates for finite mixture estimation.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Optimal rates for finite mixture estimation

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-14T10:39:53.699346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ea5e5bf0-7bf3-42f9-9469-e4dfef82f078 · outbound

This paper cites Convergence rates of parameter estimation for some weakly identifiable finite mixtures.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Convergence rates of parameter estimation for some weakly identifiable finite mixtures

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.919742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2fb4b4d9-8faa-4200-9bd0-0688a12b6fef · outbound

This paper cites Ingster and I.A.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Ingster and I.A

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.908171Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation defc50cc-c371-4cc5-b739-a096f07d306f · outbound

This paper cites Local maxima in the likelihood of G aussian mixture models: Structural results and algorithmic consequences.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Local maxima in the likelihood of G aussian mixture models: Structural results and algorithmic consequences

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-14T10:39:53.536603Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 110d422b-13c5-48e1-88ff-1b3c3c4fa743 · outbound

This paper cites Global Convergence of EM Algorithm for Mixtures of Two Component Linear Regression.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Global Convergence of EM Algorithm for Mixtures of Two Component Linear Regression

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-14T10:39:53.540945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b5fd964a-47a7-425d-8bb6-954924f55a19 · outbound

This paper cites Choosing initial values for the EM algorithm for finite mixtures.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Choosing initial values for the EM algorithm for finite mixtures

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.890465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 22115801-4bdb-48d1-a5aa-7e15b663af58 · outbound

This paper cites Laurent and P.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Laurent and P

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.878362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation df4de3a5-b62a-4438-a9b2-9dde80ec66a1 · outbound

This paper cites Statistical and Computational Guarantees of Lloyd's Algorithm and its Variants.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Statistical and Computational Guarantees of Lloyd's Algorithm and its Variants

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-14T10:39:53.551650Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a4d94b6-af11-471f-976f-8984fe3f80a5 · outbound

This paper cites The landscape of empirical risk for nonconvex losses.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations The landscape of empirical risk for nonconvex losses

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.866005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3cae0bc5-1ab1-4cd6-b2f2-51c038c7a617 · outbound

This paper cites Sharp optimal recovery in the two-component Gaussian Mixture Model.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Sharp optimal recovery in the two-component Gaussian Mixture Model

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-14T10:39:53.664058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 604576eb-96fc-42d5-9c28-a13ce85ff118 · outbound

This paper cites Dissipation of information in channels with input constraints.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Dissipation of information in channels with input constraints

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.854232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cbbb5f2b-5a96-412c-ac00-61e061ddb796 · outbound

This paper cites Mixture densities, maximum likelihood and the EM algorithm.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Mixture densities, maximum likelihood and the EM algorithm

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.842977Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 94fb9ce1-54f4-4004-ad1c-b37967fc94d9 · outbound

This paper cites An introduction to maximum-likelihood methods in cryo- EM.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations An introduction to maximum-likelihood methods in cryo- EM

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.831193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5e6e3bef-0760-4f0c-aa47-512db1b5ee5a · outbound

This paper cites Empirical processes with applications to statistics.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Empirical processes with applications to statistics

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.820157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b583e619-ff3c-41d5-9575-ce097cb918ac · outbound

This paper cites The transportation cost from the uniform measure to the empirical measure in dimension 3.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations The transportation cost from the uniform measure to the empirical measure in dimension 3

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.801385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 47d222b1-4e71-4f7b-9f30-689bea01c4ef · outbound

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

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations High-Dimensional Probability: An Introduction with Applications in Data Science

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-14T10:39:53.585726Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c4a23db-ddca-4191-a642-3737df396802 · outbound

This paper cites an unresolved cited work.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:39:53.784580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 312945d6-88ef-4f78-a9d9-3daf0f477c55 · outbound

This paper cites Functional properties of MMSE and mutual information.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Functional properties of MMSE and mutual information

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.773303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation abaff8d2-1431-4c83-a70b-c353dd2a2cdf · outbound

This paper cites Optimal estimation of Gaussian mixtures via denoised method of moments.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Optimal estimation of Gaussian mixtures via denoised method of moments

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-08-14T10:39:53.648042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8985ad75-6f5f-48e8-a058-c921631d979c · outbound

This paper cites an unresolved cited work.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:39:53.762008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b9691851-2dbf-4b6a-acf4-738644073d4e · outbound

This paper cites Global analysis of expectation maximization for mixtures of two G aussians.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Global analysis of expectation maximization for mixtures of two G aussians

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-14T10:39:53.603098Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f84b550f-ac2f-4cee-88a4-005ed1db263c · outbound

This paper cites On convergence properties of the EM algorithm for G aussian mixtures.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations On convergence properties of the EM algorithm for G aussian mixtures

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-14T10:39:53.606445Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41956d32-976f-4c53-9605-77cbb4bff0cd · outbound

This paper cites Yang and A.

Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations Yang and A

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:39:53.736779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

Observation 4a29b0fc-cd24-4f5c-81ba-f00b520a34d8 · inbound

On Model-Based Clustering With Entropic Optimal Transport cites this paper.

On Model-Based Clustering With Entropic Optimal Transport Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations

Reference 68

Resolution: verified exact; arxiv_id, observed 2026-05-12T00:31:18.038945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ade24c57-94cf-4757-8840-5d45bc5d2f2b · inbound

Transfer Learning in High-Dimensional Clustering: Minimax Thresholds and Applications in Single-Cell Data cites this paper.

Transfer Learning in High-Dimensional Clustering: Minimax Thresholds and Applications in Single-Cell Data Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in $O(\sqrt{n})$ iterations

Reference 56

Resolution: unresolved; no resolver link, observed 2026-07-31T03:15:47.958266Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.