MIT Press

Table 4:

Configurations for y⁺ and y⁻ for weakly supervised MT adaptation. ŷ is the highest-probability model output. π_w(y|x) is the probability of y under the model. The arg max_y is taken over the k-best list 𝒦(x). α is a scaling factor regulating the influence of the metric compared to the model probability. δ₁ and δ₂ are metrics defined with respect to relevant and irrelevant documents d⁺ and d⁻ (see Eq. 8 and 9).

Loss	y⁺	y⁻
RAMP	arg max_yπ_w(y\|x) − α(1 − δ₁(y,d⁺))	arg max_yπ_w(y\|x) + α(1 − δ₁(y,d⁺))
RAMP⁻	arg max_yπ_w(y\|x) − α(1 − δ₁(y,d⁺))	arg max_yπ_w(y\|x) − α(1 − δ₁(y,d⁻))
RAMP1⁻	ŷ	arg max_yπ_w(y\|x) − α(1 − δ₁(y,d⁻))
RAMP2	arg max_yπ_w(y\|x) − α(1 − δ₁(y,d⁺))	ŷ
RAMP_δ₂	arg max_yπ_w(y\|x) − α(1 − δ₂(y,d⁺,d⁻))	arg max_yπ_w(y\|x) + α(1 − δ₂(y,d⁺,d⁻))

Loss	y⁺	y⁻
RAMP	arg max_yπ_w(y\|x) − α(1 − δ₁(y,d⁺))	arg max_yπ_w(y\|x) + α(1 − δ₁(y,d⁺))
RAMP⁻	arg max_yπ_w(y\|x) − α(1 − δ₁(y,d⁺))	arg max_yπ_w(y\|x) − α(1 − δ₁(y,d⁻))
RAMP1⁻	ŷ	arg max_yπ_w(y\|x) − α(1 − δ₁(y,d⁻))
RAMP2	arg max_yπ_w(y\|x) − α(1 − δ₁(y,d⁺))	ŷ
RAMP_δ₂	arg max_yπ_w(y\|x) − α(1 − δ₂(y,d⁺,d⁻))	arg max_yπ_w(y\|x) + α(1 − δ₂(y,d⁺,d⁻))

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