Information Lattice Learning as Probabilistic Graphical Model Structure Learning

• URL: http://arxiv.org/abs/2606.19366v1
• Date: Thu, 11 Jun 2026 03:42:57 GMT
• Title: Information Lattice Learning as Probabilistic Graphical Model Structure Learning
• Abstract summary: Information lattice learning (ILL) learns interpretable rules of a signal by alternately projecting the signal onto a partition lattice.<n>A partition in ILL induces a deterministic quotient variable, and a rule is the marginal law of that quotient variable.<n>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.
• Score: 14.431607564729427
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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