& Byrne, CS&L Vol14., 2000, ``Minimum Bayes-risk automatic speech recognition’’. Kumar & Byrne, NAACL2004, ``Minimum Bayes-Risk Decoding for Statistical Machine Translation’’. , 1 4 5 , ◼ 𝑦MBR ∗ ≔ argmaxℎ∈ℋ 𝔼ො 𝑦~𝑃 𝑦|𝑥 𝑢 ℎ, ො 𝑦 ⚫ ℋ ⊂ 𝒴 𝑢: 𝒴 × 𝒴 → ℝ ⚫ 𝑃 𝑦|𝑥 𝑥 𝑦 ◼ 𝒴 ∈ 𝒴 𝑦MBR ∗ ≈ argmax ℎ∈ℋ 𝔼ො 𝑦∈ 𝒴 𝑢 ℎ, ො 𝑦 ⚫ ▶ 𝒴 ≔ ℋ ⚫ 𝑁 ≔ ℋ 𝒪 𝑁2 ▶