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Fully visible sigmoid belief network

Architectures AIMech:FullyVisibleSigmoidBeliefNetwork DRAFT

Aliases: FVSBN, Logistic autoregressive Bayesian network

A fully observed binary autoregressive probabilistic model whose conditional probability at each position is a logistic function of a bias and a weighted sum of preceding visible variables.

Identity Notes & Concept Scope This is the fully visible sigmoid model discussed by Larochelle and Murray, with no stochastic hidden variables. Frey and colleagues call their binary logistic special case a fully visible belief network; that local usage does not make all fully visible Bayesian networks synonyms of the sigmoid family. The record specializes the broader sigmoid-belief-network family and is distinct from NADE’s nonlinear deterministic hidden features and DARN’s stochastic latent architecture. 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

Fix an ordering of D binary visible variables. Parameterize P(x_i=1|x_<i)=sigmoid(b_i+sum_(j<i) w_ij x_j). Multiply the corresponding Bernoulli probabilities over positions to evaluate the normalized observed joint. All variables in that product are visible, so complete-data likelihood evaluation has no hidden-state marginalization or recognition-model posterior approximation. Its negative log likelihood is the sum of the positionwise binary logistic losses. Generate a sample by drawing each bit from the conditional determined by already drawn predecessors. Full connectivity makes all earlier visible variables available as parents; zero coefficients can remove particular dependencies. A fixed-order conditional’s log odds are affine in its predecessors, unlike the more general nonlinear neural conditional used by NADE.

supports Source: The Neural Autoregressive Distribution Estimator · Locator: Section3, Equations(3)–(4), PDFp.2 / printedp.30; Figure1, PDFp.3 / printedp.31; related-work description, PDFp.4 / printedp.32
supports Source: Does the Wake-sleep Algorithm Produce Good Density Estimators? · Locator: Binary logistic generative setup, PDFp.1 / printedp.661; Section2 competitor Fully Visible Belief Network, PDFp.3 / printedp.663
supports Source: Connectionist learning of belief networks · Locator: Section4.1, Equations(11)–(16), PDFpp.9–10 / printedpp.79–80; Section6.1–6.2, PDFpp.15–16 / printedpp.85–86

⚠️ Curated Limitations & Negative Results

The chain-rule factorization is general, but restricting each conditional to a logistic-linear function limits the distribution family. A given fixed-order conditional table with a nonzero logit interaction cannot be represented by that affine logit; this is not a claim about every alternative ordering or latent extension.
Exact complete-observation likelihood and forward generation do not provide arbitrary missing-variable posteriors for free. Conditioning on a suffix while earlier variables are unknown still requires inference or summation.
Changing the variable order changes the restricted model family and can affect fitting. The absence of stochastic latent variables is part of this specialization, not a property of all sigmoid belief networks.
The source’s FVBN label is interpreted within its binary logistic model setting. No assertion that every fully visible Bayesian model uses logistic factors, no universal performance ranking and no trained-model result is included.

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes

AIO Target Class	Mapping Relation	Mapping Rationale
`AIO:BayesianNetwork` Bayesian Network	broad_match	The pinned AIO target is broader than this fully visible binary logistic family. Ordered visible variables and normalized forward conditional factors form a directed acyclic probabilistic network; the local identity adds logistic-linear parameterization and absence of latent random variables.

Evidence Sources & Primary Literature

3 Sources

Source ID	Publication / Document	Type / Access	Reference & Checksum
`method-source`	The Neural Autoregressive Distribution Estimator Hugo Larochelle, Iain Murray	primary paper full_text	ID: pmlr-v15-larochelle11a sha256:b1fe502ea1b3…
`fvbn-source`	Does the Wake-sleep Algorithm Produce Good Density Estimators? Brendan J. Frey, Geoffrey E. Hinton, Peter Dayan	primary paper full_text	ID: https://proceedings.neurips.cc/paper_files/paper/1995/file/55b1927fdafef39c48e5b73b5d61ea60-Paper.pdf sha256:cb6d748c6816…
`sigmoid-source`	Connectionist learning of belief networks 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/FullyVisibleSigmoidBeliefNetwork.yaml