Dirichlet compound multinomial latent Dirichlet allocation
Model Families AIMech:DirichletCompoundMultinomialLDA DRAFT
Aliases: DCM-LDA
A topic-model family for grouped documents in which each group draws its own topic-word distributions from corpus-shared topic-specific Dirichlet distributions, while individual documents mix those group-specific topics.
Identity Notes & Concept Scope
Scoped to Mimno and McCallum's JCDL2007 DCM-LDA model for pages within books. Corpus topic identity is shared through fitted Dirichlet parameters beta_t, whereas topic-word vectors phi_bt are book-specific and document/page topic mixtures are local. This differs from standard LDA with corpus-shared word vectors and from merely replacing a symmetric LDA prior by an asymmetric one. The reported clustering and restricted-topic fitting procedure is distinguished from the fixed-parameter probability model. DCM-LDA is the source acronym. No normalized candidate identity matched all 442 pinned AIO IDs, labels and scoped synonyms or 441 preceding native IDs, names and aliases. Full-checkout searches included ignored and hidden files in both checkouts; twelve matching lines per checkout came from five unique prior discovery-ledger contents and the existing GCA mapping rationale. All matching excerpts were read. All 205 semantic label/synonym hits and 21 annotated AIO nodes with outgoing edges were byte-verified against prior readings. Thirty contextual YAMLs comprise 27 unchanged prior readings, two fully read final native targets verified against saved review inputs, and a fully read Metropolis-Hastings record. No candidate record is present within this bounded pinned-snapshot and maintained-corpus search.
Claims & Grounded Evidence
3 Claims
Mechanism
#group-local-emissions
Each corpus topic has a shared Dirichlet parameter vector over words. Each book draws a separate word-probability vector for that topic, and each page draws its own topic mixture. Tokens select a topic from the page mixture and a word from the corresponding book/topic vector. Integrating those vectors yields Dirichlet-multinomial reinforcement within a book/topic group. With fixed shared Dirichlet parameters, different books can be processed independently; a fully Bayesian treatment of uncertain shared parameters would introduce additional dependence.
Mechanism
#collapsed-local-counts
Conditional on fixed topic subsets and valid hyperparameters, a collapsed token update multiplies a leave-token-out page-topic predictive factor by a book/topic-word predictive factor. Emission counts pool across pages of the same book, not directly across all books. Other books can affect predictions through refitted corpus Dirichlet parameters. With a uniform two-word prior and one topic, two identical words have integrated probability 1/3 when sharing one book emission vector versus 1/4 across independent book vectors. The construction is exchangeable within its groups rather than a word-order or phrase model.
Mechanism
#cluster-and-refit-procedure
The reported stochastic-EM-style procedure first fits topic assignments independently within books, clusters the resulting local topic word distributions, estimates a corpus Dirichlet vector for each cluster using a cited fixed-point method, then retrains book models with selected cluster priors. The demonstrated clustering is hard greedy agglomeration using Jensen-Shannon divergence. A shared-support expression accelerates pairwise divergence calculation; its disjoint-support constant of one assumes base-two logs. After a Gibbs round, each book retains its most-used topics, with the topic-count heuristic ten plus page count divided by ten. These topic-selection and clustering choices are part of the reported approximation, not an exact-posterior or likelihood-monotonicity guarantee.
⚠️ Curated Limitations & Negative Results
- The source does not fully specify agglomerative linkage updates, stopping, count-rule rounding or every empty-vector/Dirichlet-estimation edge case. A restricted book topic subset changes available assignments; it is not automatically an exact sampler over all corpus topics.
- The model supplies faceted topics rather than an ontology subsumption hierarchy. Selected virtual shelves and topic/Library-of-Congress-heading mutual information do not establish complete semantic accuracy or a validated retrieval benchmark; new retrieval evaluation is identified as future work.
- The large-corpus timing uses particular preprocessing, hardware and two major training stages. The much longer standard-LDA estimate is extrapolated, not a matched full-corpus run. An inconsistent smaller subcollection count in related work is not silently reconciled with the reported 42000-book experiment.
- Finite checks cover 160 fixed-parameter collapsed conditionals, group sharing and the shared-support Jensen-Shannon identity. No author software, full clustering pipeline or empirical benchmark was executed.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:Model
Model
|
broad_match | The source-defined probabilistic model family is narrower than the pinned Model class. |
AIO:ProbabilisticTopicModel
Probabilistic Topic Model
|
related_match | The construction supports probabilistic topic modeling; the pinned target is task-scoped rather than this particular model or inference procedure. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
David Mimno, Andrew McCallum
|
primary paper
full_text
|
sha256:20cb383fd474…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-12T01:01:32Z
Updated: 2026-10-12T01:01:32Z
Source File:
data/curated/DirichletCompoundMultinomialLDA.yaml