# A general theory of identification

arXiv: https://arxiv.org/abs/2002.06041 · HTML: https://mlsanity.com/paper/2002.06041/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2020.

## Built on by (most cited first, 4 of 4)

- [Impossibility Results in AI: A Survey](https://mlsanity.com/paper/2109.00484/) (2021)
- [Statistical Decision Theory with Counterfactual Loss](https://mlsanity.com/paper/2505.08908/) (2025)
- [A Fiber Criterion for Representation Identifiability in Supervised Learning](https://mlsanity.com/paper/2606.01092/) (2026)
- [Identifiable Latent Bandits: Leveraging observational data for personalized decision-making](https://mlsanity.com/paper/2407.16239/) (2024)

## Abstract (arXiv)

What does it mean to say that a quantity is identifiable from the data? Statisticians seem to agree on a definition in the context of parametric statistical models --- roughly, a parameter θ in a model P = Pθ: θ ∈ Theta is identifiable if the mapping θ mapsto Pθ is injective. This definition raises important questions: Are parameters the only quantities that can be identified? Is the concept of identification meaningful outside of parametric statistics? Does it even require the notion of a statistical model? Partial and idiosyncratic answers to these questions have been discussed in econometrics, biological modeling, and in some subfields of statistics like causal inference. This paper proposes a unifying theory of identification that incorporates existing definitions for parametric and nonparametric models and formalizes the process of identification analysis. The applicability of this framework is illustrated through a series of examples and two extended case studies.