Index: Aleshin-Guendel 2020 - Identifiability of Latent Class MSE Models

Aleshin-Guendel 2020 - Identifiability of Latent Class MSE Models

Routing Summary

Full capture of Aleshin-Guendel (arXiv:2008.09865): identifiability of latent class models for multiple-systems estimation, standing in for Manrique-Vallier (2016). 4 notes.

• One-page summary and source map? → Aleshin-Guendel 2020 - Identifiability of Latent Class MSE Models - Overview
• $M_{th}$ model, likelihood factorisation, Definition 1? → Aleshin-Guendel 2020 - Mth Model and Identifiability Definition
• Lemma 1 and Theorem 1 (moments)? → Aleshin-Guendel 2020 - Mixed-Moments Theorem
• Theorem 2 ($2J\le K$), Table 1, LCMCR implications? → Aleshin-Guendel 2020 - Latent Class Identifiability Theorem and LCMCR

Concept Map

Concept	Note	Type	Depends On	Key Result
$M_{th}$ model	Aleshin-Guendel 2020 - Mth Model and Identifiability Definition	definition	-	latent ${\lambda }_i\sim Q$
Identifiability (Def. 1)	Aleshin-Guendel 2020 - Mth Model and Identifiability Definition	definition	likelihood	${\tilde{\pi }}_Q={\tilde{\pi }}_R\Rightarrow {\pi }_{Q,0}={\pi }_{R,0}$
Lemma 1, Theorem 1	Aleshin-Guendel 2020 - Mixed-Moments Theorem	theorem	Def. 1	proportional moments
Theorem 2	Aleshin-Guendel 2020 - Latent Class Identifiability Theorem and LCMCR	theorem	Theorem 1	identifiable iff $2J\le K$
Table 1 counterexample	Aleshin-Guendel 2020 - Latent Class Identifiability Theorem and LCMCR	example	Theorem 2	${\pi }_0=0.316$ vs $0.219$

Notes

• Aleshin-Guendel 2020 - Identifiability of Latent Class MSE Models - Overview — CONTAINS: summary, swap rationale, E109/E69 links, Source Map.
• Aleshin-Guendel 2020 - Mth Model and Identifiability Definition — CONTAINS: Eq. 1-3, Definition 1, ${\mathcal{Q}}_J$.
• Aleshin-Guendel 2020 - Mixed-Moments Theorem — CONTAINS: Lemma 1, Theorem 1 with proofs, $K=2$ check.
• Aleshin-Guendel 2020 - Latent Class Identifiability Theorem and LCMCR — CONTAINS: Theorem 2 proof sketch, counterexample, Table 1 verified, LCMCR implications.

Sources

• Aleshin-Guendel 2020 - On the Identifiability of Latent Class Models for Multiple-Systems Estimation — arXiv:2008.09865v1, 8 pp.

See Also

• Silverman 2020 - Madigan-York and Dirichlet Process Benchmarks, Concept - Latent Class and Dirichlet Process Models for Multiple Systems Estimation, Concept - Unseen Species and Latent Class Links.