These methods define a context-sensitive fallback probability α(w i−1 i−n+1 ) for order n models, and recursively calculate the probability of the higher order models from the lower order models: (3) To express this as a linear mixture, we convert α(w i−1 i−n+1 ) into the appropriate value for λ n (w i−1 i−N +1 ).
the probability assigned to each P M L (w i |w i−1 i−n+1 ) is set to the product of the fallbacks α for all higher orders and the probability of not falling back (1 − α) at the current level: Discounting: The widely used technique of discounting (Ney et al., 1994) defines a fixed discount d and subtracts it from the count of each word before calculating probabilities: .