Leave-one-out mutual information upper bound
Mathematical Methods AIMech:LeaveOneOutMutualInformationUpperBound DRAFT
Aliases: Leave-one-out variational information upper bound
An expectation-level upper bound on mutual information that compares a known conditional density for each paired sample with a mixture of conditional densities from the other independent inputs in its batch.
Identity Notes & Concept Scope
This is the leave-one-out upper bound in Poole et al., distinct from InfoNCE’s lower bound and from generic leave-one-out cross-validation. It requires evaluable normalized p(y|x), which may be the encoder defining the modeled joint distribution; an arbitrary learned critic does not supply that requirement. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 208 preceding native IDs/names/aliases. Word-delimited fixed-string searches of both full checkouts, including ignored and hidden files, returned 57 lines each: existing MINE-f component discussion, shared primary-source references, and discovery/review context. Four native neighbors and seven exact AIO nodes with scoped synonyms and outgoing relations were inspected.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
Draw K>=2 independent pairs (X_i,Y_i) from p(x)p(y|x), with evaluable normalized conditional density p(y|x). For each i form q_-i(y)=(K−1)^−1 sum_(j!=i) p(y|X_j). Then I(X;Y)<=E[K^−1 sum_i log(p(Y_i|X_i)/q_-i(Y_i))], assuming the expectations are well-defined. The mixture q_-i is independent of the held-out pair because it uses only the other inputs. Conditional on those inputs, the gap of the corresponding variational upper bound is KL(p(Y)||q_-i(Y)), a nonnegative quantity. Including the paired input in this denominator instead gives the known-conditional InfoNCE lower-bound construction, so the exclusion is essential. A finite batch computes an estimator of the upper-bound expectation rather than a guaranteed upper bound on its own.
⚠️ Curated Limitations & Negative Results
- The conditional must be normalized and evaluable for cross-sample inputs. Treating an uncalibrated score as p(y|x) invalidates the stated derivation.
- For small batches or sharply separated conditional supports, the leave-one-out mixture can be tiny or zero where the held-out conditional is positive, producing a loose or infinite upper bound.
- Independence of batch examples is part of the proof. Correlated samples or using the held-out input to construct its own denominator require a different argument.
- The expected bound does not certify a realized finite-sample number. Optimization of a noisy estimate does not guarantee monotonic true information reduction or convergence. No encoder implementation or benchmark was reproduced.
Artificial Intelligence Ontology (AIO) Grounding
Explicit AIO Snapshot Assessment: No Match
Rationale: The inspected candidates describe networks, feature-extraction tasks or self-supervised tasks, not the mathematical information bound. Shared variational terminology, an optional neural parameterization or downstream use does not establish a suitable mapping.
Search Scope: All 442 pinned AIO CLASS labels and scoped synonyms and 208 preceding native IDs/names/aliases were compared. Full fixed-string word-delimited searches of both checkouts included hidden and ignored files. Exact definitions, synonyms and outgoing relations for FeatureExtraction, VariationalAutoEncoder, AutoEncoderNetwork, RepresentationLearning, DeepNeuralNetwork, BayesianNetwork and SelfsupervisedLearning were inspected. This assessment is bounded to AIO commit 397851c547d1c4d8f06ef184f63c1d40bc86937a and this semantic neighborhood.
| Examined AIO Candidate | Rejection Reason |
|---|---|
AIO:VariationalAutoEncoder
|
A probabilistic latent autoencoder architecture is not a variational information inequality; neither implies the other. |
AIO:AutoEncoderNetwork
|
Reconstruction networks can use information objectives but do not identify this mathematical bound. |
AIO:RepresentationLearning
|
The target is a deep-network representation-learning class; it is a possible use of a bound, not the bound itself. |
AIO:DeepNeuralNetwork
|
A neural critic or decoder is one possible parameterization, not the information formula. |
AIO:FeatureExtraction
|
This preprocessing task does not specify an information estimator or bound. |
AIO:BayesianNetwork
|
Conditional distributions do not make this bound a directed graphical-model architecture. |
AIO:SelfsupervisedLearning
|
A self-generated prediction task does not specify this population information inequality. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Ben Poole, Sherjil Ozair, Aäron van den Oord, Alexander A. Alemi, George Tucker
|
primary paper
full_text
|
ID: https://proceedings.mlr.press/v97/poole19a.html
sha256:38da74b0bae6…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T09:02:43Z
Updated: 2026-10-11T09:02:43Z