Appendix A. Proof of deterministic overconfidence (binary classification) - AWS Prescriptive Guidance

Appendix A. Proof of deterministic overconfidence (binary classification)

Consider the softmax (logistic) function binary classification:

Softmax function binary classification

The softmax function is concave for and convex for . Therefore, by Jensen's inequality:

Jensen's inequality

This implies for all . Equality is obtained when .