As an example, while our probabilistic HR-SCFG maintains a separate joint phrase-pair emission distribution per nonterminal, the smoothing features (a) above assess the conditional translation of surface phrases irrespective of any notion of recursive translation structure.

As Hiero uses a single nonterminal and concentrates on overcoming translation lexicon sparsity, it barely explores the recursive nature of translation past the lexical level.

By advancing from structures which mimic linguistic syntax, to learning linguistically aware latent recursive structures targeting translation, we achieve significant improvements in translation quality for 4 different language pairs in comparison with a strong hierarchical translation baseline.

Figure 2: Recursive Reordering Grammar rule categories; A, B, C non—terminals; oz, fl source and target strings respectively.

structural part and their associated probabilities define a model 19(0) over the latent variable 0 determining the recursive , reordering and phrase-pair segmenting structure of translation, as in Figure 4.

We aim to induce a recursive translation structure explaining the joint generation of the source and target

each model parameter over sentence Wl in document d in the training corpus D. For the WORD-PREDICTOR and the SEMANTIZER, the number of possible semantic annotation sequences is exponential, we use forward-backward recursive formulas that are similar to those in hidden Markov models to compute the expected counts.

In M-step, the recursive linear interpolation scheme (Jelinek and Mercer, 1981) is used to obtain a smooth probability estimate for each model component, WORD-PREDICTOR, TAGGER, and CONSTRUCTOR.

The recursive mixing scheme is the standard one among relative frequency estimates of different orders k = 0, - - - ,n as explained in (Chelba and J elinek, 2000).