What is the significance of feature importance in AI Explainability, and how can it be determined?

Instruction: Discuss the concept of feature importance in the context of AI Explainability and describe methods to determine it. Use a fixed held-out scoring metric and explain why a low permutation importance need not make a feature irrelevant.

Context:

A fixed trained classifier scores 0.80 F1 on a held-out sample. After repeatedly permuting one feature in that sample, its mean score is 0.70. No retraining is done.

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The way I'd explain it in an interview is this: Feature importance matters because it gives a first view into which inputs are influencing the model most strongly...

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