Noisy-OR belief network
Architectures AIMech:NoisyORBeliefNetwork DRAFT
A directed acyclic binary probabilistic network that models a node’s inactivity as the product of a leak-failure factor and failure factors for its active parents.
Identity Notes & Concept Scope
The core record denotes the noisy-OR conditional model described by Neal, with zero/one variables and failure factors between zero and one. It is a probabilistic conditional family, not additive input noise, a deterministic OR gate or a sigmoid function. Neal also studies a signed-weight exponential extension; its distinct validity condition and loss of an individual failure-probability interpretation are stated explicitly rather than silently treating negative weights as ordinary noisy-OR failures. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 346 preceding native IDs/names/aliases. Full-checkout fixed-string searches included ignored and hidden files in worktree and main, returning 23 and 23 lines respectively. All 17 unique matched line contents were inspected in full: SBN source metadata, NADE and DARN scope distinctions, their saved review and the carried noisy-OR discovery lead, not existing candidate records. Exact checkout counts and differences are retained in the ledger. Seventeen exact AIO CLASS nodes with scoped synonyms/comments and outgoing edges and six full native neighboring records were inspected. Absence is bounded to this snapshot and semantic neighborhood.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
For node i, let q_i0 be the failure probability for an always-on bias or leak source and q_ij the failure probability associated with active parent j. Set P(s_i=0|parents)=q_i0 times the product of q_ij over parents with state1, and set P(s_i=1|parents) to its complement. This corresponds to independently failing activation contributions; it does not require the parent variables themselves to be independent. Multiply normalized node factors in a topological order to obtain the joint model and sample it ancestrally. For strictly positive failure factors, define w_ij=-log(q_ij), including the bias; then P(s_i=1|parents)=1-exp(-a_i), with a_i=w_i0+sum_j w_ij s_j and nonnegative standard weights. Neal’s separate signed-weight extension retains this exponential formula if a_i is nonnegative for every binary parent configuration, equivalently w_i0+sum_(j:w_ij<0) w_ij>=0. Negative weights in that extension need not correspond to failure probabilities in[0,1]. Parameter updates must preserve validity; the architecture itself does not specify a unique learning algorithm.
⚠️ Curated Limitations & Negative Results
- A negative weighted input gives an invalid negative activation probability. The signed extension therefore needs explicit constraints and is not an unconstrained sigmoid parameterization.
- Zero failure probabilities yield deterministic activation contributions and infinite log-failure weights; the probability-product form still defines the boundary, but the finite-weight reparameterization excludes those endpoints.
- The independent-failure interpretation concerns contributions conditional on parent states, not a proof that the parent variables are independent or that the model’s edges identify interventions in real data.
- Local normalization and ancestral generation do not remove hidden-variable marginalization or guarantee Gibbs mixing. Boundary zero probabilities can also obstruct positivity conditions used by sampling arguments.
- Neal’s constraint-projection and learning discussion was inspected, but its appendix proofs and executable implementations were not audited. No projection-optimality theorem, general convergence or empirical advantage is certified.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:BayesianNetwork
Bayesian Network
|
broad_match | The AIO target denotes the broader directed acyclic probabilistic network class. The native noisy-OR family narrows its binary conditional factors to the stated failure-product form; its explicitly qualified signed extension retains an acyclic normalized factor model only under its validity constraint. Neither noisy input layers nor causal graph terminology establishes this identity. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Radford M. Neal
|
primary paper
full_text
|
ID: doi:10.1016/0004-3702(92)90065-6
sha256:4e4f40a92dce…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T17:36:54Z
Updated: 2026-10-11T17:36:54Z
Source File:
data/curated/NoisyORBeliefNetwork.yaml