Inferability

Inferability is the degree to which quantities of interest can be deduced from observed data under a specified model. It is a broader concept than interpretability, focusing on the empirical possibility of recovering parameters, latent variables, or causal effects, rather than on human-understandable explanations of a model’s behavior.

In statistics and machine learning, inferability is closely tied to identifiability. A parameter or latent structure is inferable only if it is identifiable: different values or configurations lead to distinct distributions of the observed data. When a model is unidentifiable, multiple parameter settings can explain the data equally well, making unique inference impossible. Classic examples occur in mixture models where component labels are exchangeable (label switching) or in models with insufficient data to distinguish closely related parameters.

Inferability also concerns the practicality of inference from data. Even when identifiability holds, finite data, noise, and model misspecification can limit what can be inferred with precision. Bayesian methods explicitly quantify this uncertainty via posterior distributions, while frequentist approaches use estimators and confidence intervals to summarize inferability.

In privacy and data science, inferability raises concerns about what sensitive information can be deduced from released data or models. Attack scenarios such as attribute or membership inference study the practical limits of inferability for adversaries and guide the design of defenses, including differential privacy.

Methodologically, assessing inferability involves identifiability analysis, information-theoretic measures, and experimental design. Improving inferability may require additional data, stronger modeling assumptions, regularization, or informative priors, balancing it against interpretability and robustness.

See also: Identifiability, Interpretability, Bayesian inference, Causal inference.