Partially specified models
Concrete Problems in AI Safety — inherited
A family of approaches, developed mainly in econometrics, that make assumptions about only some aspects of a data distribution rather than requiring a fully well-specified model.
Econometricians learned long ago to commit to only part of a model, assuming a few things about a distribution and staying agnostic about the rest. Partially specified models name that family of approaches, which Concrete Problems in AI Safety (2016) borrows as a way to survive distribution shift on weaker assumptions.
After a section on specifying only part of a distribution, the prose introduces the techniques this family gave rise to, and the retreat from a fully specified model that motivates them both.
Specifying only part of a distribution
Partially specified models are a family of statistical approaches, developed mainly in econometrics well before Concrete Problems was written, that assume something about only some aspects of a data-generating distribution rather than committing to a fully specified model family. The paper introduces the idea through a single worked example: a linear regression $y = \langle w^*, x \rangle + v$ where the only assumption made about the noise $v$ is that $\mathbb{E}[v \mid x] = 0$, with no further claim about its distributional form. This partial commitment is already enough to identify the true parameter $w^*$, and the resulting estimator still minimizes squared prediction error even if the distribution over $x$ shifts between training and test — because the identifying condition, $\mathbb{E}[v \mid x] = 0$, never referenced the marginal distribution of $x$ in the first place (concrete-problems, §"Partially specified models: method of moments, unsupervised risk estimation, causal identification, and limited-information maximum likelihood.", p. 17). This generalizes into a large econometric toolkit including Generalized method of moments, limited-information maximum likelihood, and instrumental-variables estimation.
A family with two children and one motivating retreat
This concept functions as a genuine hub in the paper's distributional-shift response. The edge Covariate shift assumption — untestability motivates retreat to → Partially specified models frames it as a direct response to a specific weakness of Covariate shift assumption: covariate shift's single, sweeping invariant is "very strong and also untestable," so partial specification trades the scope of the guarantee for the ability to check, in principle, whether the (smaller) assumption underlying it actually held. Two children instantiate the family toward different ends. Generalized method of moments generalizes the founding regression example into full machinery for parameter identification, per Generalized method of moments — generalizes the founding example of → Partially specified models; Unsupervised risk estimation instead partially specifies the distribution of a model's errors, per Unsupervised risk estimation — partially specifies error not parameters → Partially specified models, answering "how wrong is this model" rather than "what is the true model." A companion edge, Generalized method of moments — diverges in target from → Unsupervised risk estimation, notes the paper treats parameter identification and risk estimation as genuinely separate problems that happen to admit the same partial-specification strategy, rather than one subsuming the other. The paper's own summary is candid about the family's immaturity for ML: it calls partially specified models "potentially promising" but currently underdeveloped outside econometrics, with an open question of whether they can scale past simple, conservative cases (concrete-problems, §"A unifying view: counterfactual reasoning and machine learning with contracts.", p. 19). The concept is a child of Robustness to distributional shift, anchors the Weakening statistical assumptions to survive distribution shift theme, sits in the Borrowed machinery that doesn't fully transfer, and says so and One umbrella idea, aimed at different targets each time it's used connective themes, and belongs to the Distributional shift: relax the statistics, or rewrite the contract supertheme.