latent-identifiability

Latent Identifiability

Turn a research mechanism into a defensible identification result, or establish precisely why the requested result does not follow. Write the mathematical argument when requested; do not stop at a proof plan. Keep population identifiability, estimation consistency, optimization, individual latent recovery, and causal identification separate.

Start from the research state

Use the user's model, notes, equations, code, and requested destination. Ask only for information that changes the mathematical problem and cannot be inferred. With an incomplete model, work on an explicitly labeled provisional formulation and identify the missing decisions. Do not fabricate biological mechanisms or silently add identifying information.

Enter at the appropriate stage: informal idea -> formal specification; specified model -> symmetry search; candidate theorem -> proof or attack; existing proof -> line-by-line audit. An empirical performance question does not need to become a theorem task.

This workflow is self-contained. Enter at the stage required by the mathematical question; no external router or delegation is required.

1. Define what the data can identify

Create a compact model specification:

• Observed variables, latent blocks, covariates, graph/time/view structure, and sampling unit.
• The exact observable law: P(X), P(X|U), a multi-view joint law, or the full graph law. Specify whether the graph/design is fixed, random, or observed. Node marginals do not determine a graph joint law.
• Generative factorization, noise kernel, nuisance parameters, parameter class, supports, latent dimensions, and required regularity.
• Which objects are known, observed, learned, or unobserved. A recovered latent block is not an observed auxiliary variable until its recovery has been justified.
• Target: parameters, latent blocks, sufficient statistics, posterior laws, a subspace, or a downstream functional.

Define the admissible class before comparing equivalent fits. Audit normalizers that depend on latent values; support restrictions; positive definiteness; conditional independence; and whether the global model actually induces the claimed local law. Use an explicit valid example to show the assumptions are jointly satisfiable when their compatibility is uncertain.