Fixed-length Poisson MRF topic model

⚠️ Curated Limitations & Negative Results

• The hierarchy defines the model; the alternating hard/MAP allocation and surrogate-parameter updates are approximations. They do not by themselves guarantee exact posterior inference, marginal likelihood or monotone ascent of the true likelihood.
• The displayed negative-log-posterior objective on p. 6 prints Pr rather than log Pr in its data term. Its topic-transfer expression adds a to the second total’s partition index even though that topic loses a counts; the required total is m_q-a. These displayed expressions are not copied as verified algorithms.
• Zero topic allocations, the chosen length distribution and the per-topic normalization must be handled explicitly. The proposed prior evaluated at topic proportions does not automatically supply the exact posterior implied by the generative hierarchy.
• Finite fixed-total support ensures normalization, but does not make partition computation or parameter estimation trivial. Adding a length distribution requires the correctly normalized conditional distribution at each total; one normalizer cannot be reused across lengths.
• The source reuses nodewise Poisson regression from an unbounded model as a surrogate estimator. A fixed-total count coordinate is deterministic given all other count coordinates, so this is not its exact count-coordinate pseudolikelihood. Graph-recovery guarantees for a different Cartesian-support model do not automatically transfer.
• For a general symmetric Phi, a token-label Gibbs update has log weight theta_s+2*(Phi*x_minus)_s+Phi_ss. The printed sampler omits Phi_ss and needs zero/equal diagonals or a specified reparameterization. The printed eigenvalue bound using L^2*lambda_max also needs lambda_max>=0; for arbitrary symmetric matrices a safe loose bound uses its nonnegative part. These are curator qualifications of displayed formulas, not reproduced code defects.
• The length-dependent interaction weighting and curve fitted above AIS estimates are modeling and numerical choices. A curve above finitely many estimated log partitions is not a certified upper bound on every exact partition value. No AIS convergence, likelihood accuracy or author implementation was validated.
• The reported topic-model perplexities use MAP latent assignments, as the source explicitly notes, rather than exact marginalization over all topic allocations. Qualitative word pairs and historical timing curves do not establish causal relations, generic superiority or current performance. No author fit or benchmark was reproduced.