L7-05 · Identifiability before quantum causal learning

Learn¶

A flexible learner can match observed probabilities while representing the wrong intervention behavior. This is a fundamental identification problem rather than an optimizer defect. Define the observational or operational equivalence class before choosing a model architecture. The target must be constant across that class to be identifiable.

For quantum processes, restricted instruments can make distinct channels or graphs indistinguishable. Hidden environments can enlarge the equivalence class. An expressive quantum or classical learner cannot create information absent from the data. A prior can choose an answer but must be disclosed as an additional assumption.

Use a constructive test. Find two allowed models with identical accessible predictions but different target values. Such a pair disproves identification for that design. To repair the study, add an informative intervention, narrow the justified model class, or report bounds instead of a point claim.

Practice¶

Check your understanding¶

What disproves target identification?

• A. A low training loss

• B. Two data-equivalent models with different target values

• C. A larger neural model

Sources¶

This lesson draws on Costa & Shrapnel, 2016Barrett et al., 2019Allen et al., 2017.

Next: L7-06 · Sample complexity and resource accounting