Case context: A team is building an image classifier and wants to combine a large set of internet images with a smaller set of mobile-app images from their actual users. They assume that combining the two datasets is fine because both datasets contain the same object categories.

Question: Based on the shared label mapping concept, what is missing from the team's justification for combining the two datasets, and what additional condition should they verify?

Sample answer: Having the same object categories in both datasets is not sufficient justification for combining them. The key condition the team should verify is whether there exists a single x-to-y mapping that works well for both internet and mobile-app images, meaning a system could reliably predict the correct label from either type of image without knowing its source. If the visual characteristics of internet images (e.g., professionally taken, well-lit) differ enough from mobile-app images (e.g., casual, variable lighting) that no single mapping predicts labels well for both, then combining the data may not be justified even though the categories match.

Key points:

• Matching label categories alone does not justify combining datasets
• The critical condition is the existence of a shared x-to-y mapping
• This mapping must reliably predict labels for both image sources
• The system should not need to know the image's source to predict correctly

Rubric: Full credit for identifying that matching categories alone does not justify combining data, and that the team must verify a shared x-to-y mapping predicts labels reliably for both sources without knowing the source. Partial credit for only noting the category-matching gap or only describing the shared mapping requirement.