[2606.19366] Information Lattice Learning as Probabilistic Graphical Model Structure Learning
[Submitted on 11 Jun 2026]
Title:Information Lattice Learning as Probabilistic Graphical Model Structure Learning
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Abstract:Information lattice learning (ILL) learns interpretable rules of a signal by alternately projecting the signal onto a partition lattice that encodes a hierarchy of abstractions and lifting selected rules back to the signal domain. When the signal is a probability mass function, we show the probabilistic rules learned by ILL admit a natural probabilistic graphical model (PGM) interpretation and develop this interpretation in detail. A partition in ILL induces a deterministic quotient variable, and a rule is the marginal law of that quotient variable. A rule set is therefore a collection of marginal constraints over interpretable abstractions. General lifting is the feasible family of all joint distributions satisfying those constraints, while special lifting chooses a maximum-ignorance reconstruction, implemented in ILL by an L2 uniformity principle closely related to maximum entropy. Under a Shannon-entropy lifting, the same constraints yield a log-linear factor graph whose factors are indexed by learned abstractions. The information lattice itself, however, is not a Bayesian network: its edges encode refinement and coarsening of abstractions, not conditional dependence. Thus ILL is best viewed as structure learning for interpretable constraint-based factor graphs over quotient variables. This view clarifies how ILL relates to graphical models and maximum entropy models, while suggesting new directions for inference, identifiability, and hybrid symbolic-probabilistic learning.
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Signal Processing (eess.SP)
Cite as: arXiv:2606.19366 [cs.LG]
(or arXiv:2606.19366v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.19366
arXiv-issued DOI via DataCite
Submission history
From: Lav Varshney [view email] [v1] Thu, 11 Jun 2026 03:42:57 UTC (12 KB)
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