Poisson square root graphical model

⚠️ Curated Limitations & Negative Results

• The factorial base measure is essential to the unrestricted finite-parameter normalization result. Removing it or changing support requires a new validity analysis. No statement about infinite graphs or unbounded parameter limits follows.
• The conditional normalizer is generally an infinite sum, and existence alone does not certify any cutoff or numerical approximation. exp(eta_i) is not its general conditional mean.
• The direct factorial-domination argument avoids treating the paper’s directional summations as a complete change-of-measure proof. It is a curator derivation consistent with the stated finite-parameter model, not an empirical reproduction.
• The graph is finite and Phi is symmetric; an off-diagonal matrix entry contributes twice in the quadratic form. Separately estimated node regressions need not agree on one symmetric joint parameterization.
• The node conditionals usually have two sufficient statistics and differ from the original univariate base family. A base-family name is not a claim about every conditional or marginal distribution, and an edge parameter is not a universal marginal-correlation or causal-effect statement.
• The printed radial formulas omit the Jacobian needed to interpret x=z*v as a change of continuous coordinates. In p dimensions the L1-radius transformation contributes z^(p-1); a bare ray kernel is not generally the radius distribution. Discrete directions require a counting-measure treatment. The normalization arguments stated here use direct joint domination instead.
• The paper proposes nodewise l1-penalized fitting, numerical conditional partitions and annealed importance sampling. Model existence does not establish finite-data graph recovery, sampler mixing, numerical accuracy or optimizer convergence; no author code, empirical fitting or benchmark was reproduced.
• Reported synthetic and airport-delay experiments are contextual. The paper’s synthetic description prints a positive diagonal while calling the matrix negative definite, an inconsistent sign convention that must be resolved before reproducing that generator. Airport associations and fitted likelihoods do not establish causal effects or held-out predictive performance.