# Valid Confidence Sets in Multiclass and Multilabel Prediction

Ask for valid confidence:

- “Valid”: validate for test data, train data, or the generating process?
- “Confidence”: $P(Y \notin C(X)) \le \alpha$

To avoid too much attention on data based validation, a framework called conformal inference was proposed by Vovk et al. in 2005,

- $n$ observations,
- desired confidence level $1-\alpha$,
- construct confidence sets $C(x)$ using conform methods so that the sets capture the underlying the distribution
- a new pair $(X_{n+1}, Y_{n+1})$ from the same distribution,
- $P(Y_{n+1}\in C(X_{n+1})) \le 1-\alpha$

Planted:
by L Ma;

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