Truncated Poisson graphical model

⚠️ Curated Limitations & Negative Results

• Positive interactions and large neighboring counts can concentrate conditional mass at the cutoff. R changes the model, and a cutoff selected as the observed maximum does not guarantee that future counts will lie within its support.
• The unbounded limit cannot retain arbitrary positive pairwise coefficients while preserving the classical Poisson joint law. Finite-support normalizability is not evidence of unbounded-model validity.
• The source Theorem 1 is worded as a universal impossibility result for Winsorized conditionals, but independent constant-parameter Winsorized variables form a valid joint product. Its supplemental contradiction assumes nonzero interaction. Original calculations preserve that exception and separately show incompatibility of one symmetric log-mean interacting specification; the blanket impossibility statement is not adopted.
• The finite graph and the symmetric once-counted edge parameters must be specified. Independently fitted node regressions do not automatically agree on a compatible joint parameterization. Model definition, numerical estimation and graph selection are distinct.
• The source sketches l1-penalized neighborhood fitting, but explicitly leaves extensions of statistical graph-recovery guarantees to future work. A model existence result is not a sparsistency theorem or a guarantee that a chosen approximate optimizer finds the intended fit.
• The reported network experiments are contextual evidence, not a universal performance guarantee. The processed breast-cancer microRNA data and cited biological associations do not establish causal regulation or clinical predictive validity. No author implementation, empirical fit or benchmark was reproduced.