We perform inference under this model using Markov Chain Monte Carlo and dynamic programming .

Additionally, a computational advantage of this formalism is that the marginalized probability over all possible alignments for any two trees can be efficiently computed with a dynamic program in linear time.

We sample pairs of trees and then compute marginalized probabilities over all possible alignments using dynamic programming .

Fortunately, for any given pair of trees T1 and T2 this marginalization can be computed using a dynamic program in time O(|T1||T2|).

A dynamic program builds this table from the bottom up: For each node pair 711,712, we sum the probabilities of all local alignment configurations, each multiplied by the appro-

This algorithm is an adaptation of the dynamic program presented in (J iang et al., 1995) for finding minimum cost alignment trees (Fig.

In this paper, we propose a new Bayesian model for fully unsupervised word segmentation and an efficient blocked Gibbs sampler combined with dynamic programming for inference.

With a combination of dynamic programming and an accurate spelling model from a Bayesian perspective, our model significantly outperforms the previous reported results, and the inference is very efficient.

Instead, we propose a sentence-wise Gibbs sampler of word segmentation using efficient dynamic programming , as shown in Figure 3.

Section 4 describes an efficient blocked Gibbs sampler that leverages dynamic programming for inference.

To segment a string into “words”, we used efficient dynamic programming combined with MCMC, as described in the next section.

We next describe a dynamic programming solution for calculating p(7't | Gp(7's)).

3.3 Dynamic Programming

Thus every word generated under G0 aligns to null, and we can simplify the dynamic programming algorithm that scores a tree 7'5 under G0:

The trick is to parameterize q as a factorized distribution such that the estimation of q* and decoding using q* are both tractable through efficient dynamic programs .

(2008) effectively do take n = 00, by maintaining the whole translation string in the dynamic programming state.

Figure 4: Dynamic programming estimation of q*.