Decoding is the problem of taking an input sentence in a foreign language:
honorables sénateurs , que se est - il passé ici , mardi dernier ?
and finding the best translation into a target language, according to a model:
honourable senators , what happened here on Tuesday ?
Your task is to find the most probable translation, given the foreign input, the translation likelihood model, and the English language model. We assume the traditional noisy channel decomposition:
We also assume that the distribution over all segmentations and all alignments is uniform. This means that there is no distortion model or segmentation model.
ssh in to
Once you’ve logged in, run this command:
git clone https://github.com/2016-Spring-UIUC-LING506/YOUR_GITHUB_USERNAME_GOES_HERE-decoding.git
In your github repository, you will find a Python program called
decode, which is an implementation of a simple stack decoder.
The decoder translates monotonically — that is, without reordering the
English phrases — and by default it also uses very strict pruning limits,
which you can vary on the command line.
The provided decoder solves the search problem, but makes two assumptions, the first of which is that
This approximation means that you can use the dynamic programming Viterbi algorithm to find the best translation.
The second assumption is that there is no reordering of phrases during translation, therefore the reordering of source words can only be accomplished if the reordering is part of a memorized phrase pair. If word-for-word translations are all that are available for some sentence, the translations will always be in the source language order.
In the starter kit there is also the
data directory which contains a translation model,
a language model, and a set of input sentences to translate. Run the decoder using this
decode > output
This loads the models and decodes the input sentences, storing the result in output. You can see the translations simply by looking at the file. To calculate their true model score, run the command:
grade < output
This command computes the probability of the output sentences according to the model. It works by summing over all possible ways that the model could have generated the English from the French. In general this is intractable, but because the phrase dictionary is fixed and sparse, the specific instances here can be computed in a few minutes. It is still easier to do this exactly than it is to find the optimal translation. In fact, if you look at the grade script you may get some hints about how to do the assignment!
Improving the search algorithm in the decoder — for instance by enabling it to search over permutations of English phrases — should permit you to find more probable translations of the input French sentences than the ones found by the baseline system.
The grade program will tell you the probability of your output.
Your task for this assignment is to find the English sentence with the highest possible probability. Formally, this means your goal is to solve the problem:
where is a French sentence and is an English sentence. In the model we have provided you,
We will make the simplifying assumption that segmentation and reordering probabilities are uniform across all sentences, and hence constant. This results in a model whose probability density function does not sum to one. But from a practical perspective, it slightly simplifies the implementation without substantially harming empirical accuracy. This means that you only need consider the product of the phrase translation probabilities
where and index phrases in and , respectively.
Unfortunately, even with all of these simplifications, finding the most probable English sentence is completely intractable! To compute it exactly, for each English sentence you would need to compute as a sum over all possible alignments with the French sentence: . A nearly universal approximation is to instead search for the English string together with a single alignment, . This is the approach taken by the monotone default decoder.
Since this involves multiplying together many small probabilities, it is helpful to work in logspace to avoid numerical underflow. We instead solve for that maximizes:
The default decoder already works with log probabilities, so it is
not necessary for you to perform any additional conversion; you can simply work
with the sum of the scores that the model provides for you. Note that
since probabilities are always less than or equal to one, their equivalent
values in logspace will always be negative or zero, respectively (you may
grade sometimes reports positive translation model
scores; this is because the sum it computes does not include
the large negative constant associated
with the log probabilities of segmentation and reordering). Hence your
translations will always have negative scores, and you will be looking for
the one with the smallest absolute value. In other words, we have
transformed the problem of finding the most probable translation into a
problem of finding the shortest path through a large graph of possible
Under the phrase-based model we’ve given you, the goal is to find a phrase segmentation, translation of each resulting phrase, and permutation of those phrases such that the product of the phrase translation probabilities and the language model score of the resulting sentence is as high as possible. Arbitrary permutations of the English phrases are allowed, provided that the phrase translations are one-to-one and exactly cover the input sentence. Even with all of the simplifications we have made, this problem is still NP-Complete, so we recommend that you solve it using an approximate method like stack decoding, discussed in Chapter 6 of the textbook. In fact, the baseline score you must beat was achieved using stack decoding with reordering. You can trade efficiency for search effectiveness by implementing histogram pruning or threshold pruning, or by playing around with reordering limits as described in the textbook. Or, you might consider implementing other approaches to solving the search problem:
Several techniques used for the IBM Models (which have very similar search problems as phrase-based models) could also be adapted:
Also consider marginalizing over the different alignments:
But the sky’s the limit! There are many, many ways to try to solve the decoding problem, and you can try anything you want as long as you follow the ground rules:
If you have any questions or you’re confused about anything, just ask.