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Admixture of Poisson Markov random fields

Model Families AIMech:AdmixtureOfPoissonMarkovRandomFields DRAFT

Aliases: Admixture of Poisson MRFs, APM

A probabilistic topic-model family that draws each document from a proper Poisson-MRF base distribution whose canonical unary and interaction parameters are convex combinations of topic parameters under document-specific simplex weights.

Identity Notes & Concept Scope APM denotes the Poisson-MRF admixture construction in this source. It mixes parameters within one document-specific distribution, rather than choosing one topic for the entire document or summing independently drawn fixed-total topic vectors. Its narrow canonical-space form differs from LDA probability-space mixing and from the broader transformed-parameter admixture framework in the same paper. Shared words such as sparse, graphical or softmax do not identify it with SAGE, Replicated Softmax or a neural output layer. No normalized identity match was found across all 442 pinned AIO labels and all scoped synonyms and 415 preceding native IDs, names and aliases. Full-checkout fixed-string searches included ignored and hidden files in worktree and main, yielding six and three matched lines; all five unique contents were read and describe existing frontier references, not records of these identities. The three-character APM acronym was checked in normalized identities but omitted from broad text search; the longer LPMRF acronym was included. Preparation included the three final GRM records before their merge; their inspected bytes are unchanged. All 188 semantic label/synonym hits were read. Fifty-one fully annotated exact CLASS nodes and outgoing edges were inspected: 46 byte-verified against prior reading and five fully read here. Seventy-eight full contextual YAMLs comprise 51 generated and 27 native records: six were fully read during this preparation and 72 byte-verified after prior full reading. Absence is bounded to the pinned snapshot, maintained corpus and inspected semantic neighborhood.

Claims & Grounded Evidence

2 Claims

Mechanism #method

For k topics sharing a specified proper Poisson-MRF exponential-family base, sufficient statistics and count support, let topic natural parameters be (theta_j,Theta_j). Draw document weights w from Dirichlet(alpha), alpha_j>0, and form theta_bar=sum_j w_j*theta_j and Theta_bar=sum_j w_j*Theta_j. Draw x from the normalized base law at these averaged canonical parameters. The paper also proposes priors on topic parameters; this construction requires those priors to be proper on an admissible parameter domain. Convex combinations of finite natural parameters of the same exponential family remain in its finite-partition domain by Holder’s inequality. In the raw-count, unbounded, zero-diagonal PMRF case, symmetric off-diagonal interactions must be nonpositive. The paper states that its positive-interaction implementation instead uses modified sufficient statistics from Yang et al. 2013 while retaining abbreviated raw-PMRF notation. Those modifications must be specified consistently; averaging invalid positive raw-count parameters does not make them proper. In the raw-count Poisson case with all interactions zero, canonical mixing averages log rates and hence geometrically mixes rates. A modified sufficient statistic need not give an ordinary independent Poisson law. LDA mixes word probabilities arithmetically for the same weights; the Poisson-total/multinomial identity alone does not equate these document-weight parameterizations.

supports Source: Admixture of Poisson MRFs: A Topic Model with Word Dependencies · Locator: Section 2.1, PDF p. 2, normalization restriction and modified-statistic qualification; Sections 2.2–3, pp. 3–4, Poisson–multinomial identity, proposed prior and transformed admixtures; Section 4, p. 4, Equation (3), canonical APM; Sections 5–6, pp. 5–7, approximate fitting and experiments
context Source: Fixed-Length Poisson MRF: Adding Dependencies to the Multinomial · Locator: Introduction, PDF/printed p. 3; Section 3, p. 5, canonical-parameter APM versus summed fixed-length topic distributions and LDA reduction
context Source: Admixture of Poisson MRFs — Supplementary Material · Locator: Supplemental PDF p. 1, Figure 6; p. 2, Tables 1–2, qualitative graphs and topic-word/coherence context

Limitation #followup-estimator-boundary

The NIPS 2014 follow-up relaxes symmetry to fit independent nodewise regression coefficients, alternating topic parameters with document simplex weights. Its Appendix C describes OR/AND edge selection and coefficient averaging as post-processing. In the inspected public v0.9.1 source, raw counts enter exponentiated linear predictors with zero self coefficients and unrestricted directed interaction estimates. Returned coefficient arrays are not constrained to be compatible conditionals of a normalized joint law. Neither averaging directed coefficients nor numerically capping rates supplies the modified-statistic base required for a proper positive-edge APM. This separates the probability-model definition from the released fitting surrogate; it does not identify that release with every experiment in either paper.

supports Source: Capturing Semantically Meaningful Word Dependencies with an Admixture of Poisson MRFs · Locator: Section 2, PDF/printed p.3, positive-edge qualification; Section 3, pp.3-4, symmetry footnote and alternating objective
supports Source: Capturing Semantically Meaningful Word Dependencies with an Admixture of Poisson MRFs — Supplementary Material · Locator: Appendix C, printed p.11 / PDF p.2, asymmetry and OR/AND rules; Appendix D, p.12 / PDF p.3, fitting algorithms
supports Source: APM MATLAB implementation, version 0.9.1 · Locator: apm.m input transformation and evalObj/initVars; pmrfs.m pmrfsingle, computegamvec and phi2theta; admixweights.m and utils/APMNums.m; v0.9.1 at commit 1001dd0ab9ecfab6d02d79f2297df3daf6561301

⚠️ Curated Limitations & Negative Results

Topic components must share the same statistics, support and reference measure before averaging their natural parameters. Unrestricted positive raw-count Poisson interactions are not normalizable; positive-edge plots do not remove that restriction.
The original source describes modified sufficient statistics for positive interactions. The NIPS 2014 follow-up and public v0.9.1 release have now been inspected: the release instead fits raw-count asymmetric nodewise regressions without a sufficient-statistic transformation or joint admissibility constraints. This code does not certify the source-described proper positive-edge model. Other historical implementations and experimental runs are not inferred from this release.
The proposed prior’s claimed beta->beta+x posterior closure is not generally valid for its interaction coefficient: beta*beta^T+x*x^T differs from (beta+x)*(beta+x)^T. Its Gamma analogy also depends on the reference measure, gamma and the quadratic penalty. No exact conjugacy or calibrated posterior claim is adopted.
The displayed approximate-posterior expression is a sum of log-like terms despite being labeled as a posterior. Pseudolikelihood, l1 regularization and FISTA-like proximal updates are approximate fitting machinery; their availability does not make the jointly coupled topic/weight objective globally convex.
Canonical mixing generally differs from LDA arithmetic probability mixing. The 2015 fixed-length paper explicitly treats APM as an indirect relaxation and its summed-topic construction as a different model. Neither a single-document Poisson identity nor a coherence comparison proves equality of the full Bayesian models.
The preliminary 20 Newsgroup experiment used only 200 words and reported final APM fits with no interaction edges. Those coherence scores do not validate recovered dependency structure. Grolier graph illustrations were manually filtered and are qualitative, not causal or held-out performance evidence. No author code, fitting or benchmark was reproduced.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:Model` Model	broad_match	This is a specified family of probability distributions, within the broader mathematical representations described by Model. Its fitting procedure or application does not replace its distributional identity.
`AIO:ProbabilisticTopicModel` Probabilistic Topic Model	related_match	The primary source explicitly defines a probabilistic topic-model construction for document counts. The pinned AIO topic-model target lies under MachineLearningTask, so related_match records that modeling context without treating a model family as a task or equating different topic constructions.

Evidence Sources & Primary Literature

6 Sources

Source ID	Publication / Document	Type / Access	Reference & Checksum
`method-source`	Admixture of Poisson MRFs: A Topic Model with Word Dependencies David I. Inouye, Pradeep Ravikumar, Inderjit S. Dhillon	primary paper full_text	sha256:38ba6916cfa0…
`comparison`	Fixed-Length Poisson MRF: Adding Dependencies to the Multinomial David I. Inouye, Pradeep Ravikumar, Inderjit S. Dhillon	primary paper full_text	sha256:3b60adcf8ab2…
`supplement`	Admixture of Poisson MRFs — Supplementary Material David I. Inouye, Pradeep Ravikumar, Inderjit S. Dhillon	primary paper full_text	sha256:3a49790ce255…
`followup-method`	Capturing Semantically Meaningful Word Dependencies with an Admixture of Poisson MRFs David I. Inouye, Pradeep Ravikumar, Inderjit S. Dhillon	primary paper full_text	sha256:f38e28540906…
`followup-supplement`	Capturing Semantically Meaningful Word Dependencies with an Admixture of Poisson MRFs — Supplementary Material David I. Inouye, Pradeep Ravikumar, Inderjit S. Dhillon	primary paper full_text	sha256:97c115b77a70…
`followup-code`	APM MATLAB implementation, version 0.9.1 David I. Inouye	official documentation documentation	ID: https://github.com/davidinouye/apm/tree/1001dd0ab9ecfab6d02d79f2297df3daf6561301 sha256:62cc4a2a9741…

Curation Provenance

Curator: Codex

Method: ai_assisted

Model: GPT-6

Created: 2026-10-11T23:06:04Z

Updated: 2026-10-11T23:32:13Z

Source File: data/curated/AdmixtureOfPoissonMarkovRandomFields.yaml