Writing Exercise

Writing is an essential part of science. How will anyone know or care about your results if you don’t communicate them? As part of your homework assignments, we expect you to turn in a report describing what models you designed and experimented with. Since we have already given you a concrete problem and dataset, you do not need describe these as if you were writing a full scientific paper. So, you should focus on an accurate technical description of these things:

Motivation: why did you choose the model you experimented with?
Description of Model or Algorithm: describe mathematically or algorithmically what you did. Your description should be clear enough that someone else in the class could implement it. What is your model? How did you optimize it? How did you align with it? What were the values of any fixed parameters you used?
Results: You most likely experimented with various settings of any models you implemented. We want to know how you decided on the final model that you submitted for us to grade. What parameters did you try, and what were the results? If you evaluated any qualities of the results other than AER, even if you evaluated them qualitatively, how did you do it? Most importantly: what did you learn?

To help calibrate you for what to expect, we ask you to first read and evaluate the example writeups below. They are real examples from others who have implemented good solutions for Assignment 1, and if you can reimplement one of these, you are likely to get very good results. You should read these critically, as if you were reviewing for a scientific conference. Ask yourself the following questions:

Do you understand the motivation behind the method?
Do you understand the method itself?
Do you understand the results?
Could you implement this method yourself, based on the description in the paper?
Is it mathematically sound?
Are the heuristics and approximations justified?
Are you convinced by the results? Why or why not?
Are there other obvious questions that aren’t answered?
Are there any easy additional experiments to do?
What did I learn from reading this?

Focus on clarity rather than novelty. It is fine if the reports describe models and algorithms that first appeared somewhere else in the scientific literature. In fact, we expect that to be the case for most of the reports. Your sole objective is to decide how clear the paper is. Once you start to internalize the idea of clear scientific writing, you can start to apply it to your own writing.

Writing Sample 1

I implemented IBM2 (seeded with IBM1 probability), trained it both ways on the data. Kept all matches, kept match that was reversed in other, and kept 40% of the (top) alignments [not counting the others].

I also other things, but the only thing that helped the score was training a word stem distribution between IBM1 and IBM2 models, but I kept running out of ram when running it on the full data set.

Other things I tried:

out of vocab word
distributions on stem and suffixes
priority queue for selecting the most probable alignments
training word length distribution (helped a little if trained after IBM2)

Writing Sample 2

Our model combines three basic insights about word alignment:

Words are more likely to be translations of each other if they cooccur frequently.
Words at similar positions in each sentence are more likely to be translations of each other.
Correspondences tend to be one-to-one.

To model these effects, we use ideas from:

Model 1.
A simple reparameterization of Model 2 (Dyer et al. 2013).
Alignment by agreement (Liang et al. 2006).

The basic model follows the form of Model 1. Given a French sentence ${\bf f} = f_1...f_n$ and English sentence ${\bf e} = e_1...e_m$ , we model alignments of the form ${\bf a} = a_1...a_n$ , where each $a_i$ takes a value from 1 to $m$ , denoting the index of the English word to which the $i$ th French word is aligned. We do not model null alignment. The probability of a particular alignment and the English, given the French, is then:

$$p({\bf f},{\bf a}|{\bf e}) = \prod_{i=1}^n p(a_i=j|i,j,m,n) \times p(f_i|e_{a_i})$$

We define $p(a_i|i,j,m,n)$ as $\frac{1}{Z_{i,m,n}} e^{\lambda h(i,j,m,n)}$ , where $Z_{i,m,n}$ is a normalization term, $\lambda$ is a parameter that we tune on the development data, and $h(i,j,m,n) = -|\frac{i}{n}-\frac{j}{m}|$ . We used $\lambda=1$ in our submission (Dyer et al. learn this parameter along with the others using a stochastic gradient step in EM). As $\lambda$ increases the model prefers alignments that are closer to the diagonal. Under this model, the $a_i$ ’s are conditionally independent, and the posterior probability that $f_i$ aligns to $e_j$ is just:

$$p(a_i=j|{\bf f},{\bf e}) = \frac{p(a_i=j|i,j,m,n) \times p(f_i|e_{a_i})}{\sum_{j'\in[1,m]} p(a_i=j'|i,j',m,n) \times p(f_i|e_{a_i})}$$

We can then use this posterior as usual in the expectation maximization algorithm.

This model enforces that each French word is aligned to exactly one English word, but there is no similar constraint on the English words, which can align to arbitrarily many French words. If we enforced a similar constraint on the English words, inference would be intractable. One approximation is to learn translation models $p_{\theta_1}({\bf f}|{\bf e})$ and $p_{\theta_2}({\bf e}|{\bf f})$ —parameterized by $\theta_1$ and $\theta_2$ respectively—and combine their predictions. We do this at decoding time by taking the intersection of the most probable alignments given by each model. We can take it a step further by learning the two models together, modifying the posteriors so that, in expectation, they reflect a preference for one-to-one alignments. Denote the event that $f_i$ aligns to $e_j$ by $x_{ij}=1$ . Then the posterior probability under both models is proportional to:

$$p(x_{ij}|{\bf f},{\bf e}) \propto p_{\theta_1}(a_i=j|{\bf f},{\bf e}) \times p_{\theta_2}(a_j=i|{\bf e},{\bf f})$$

Liang et al. 2006 show that this can be viewed as a heuristic approximation to a model that enforces one-to-one alignment on both English and French words. We simply use this value in the computation of the posterior probability for both alignment models.

We implemented these models in 92 lines of python code, and tested several combinations on the development set with 1000 sentences of training.

Model	AER
Dice	0.68
Model 1 p(f\|e)	0.51
Model 1 p(e\|f)	0.45
Model 1 intersection	0.38
Model 1 joint train	0.44
Model 1 joint train + intersection	0.32
Model 2 p(f\|e)	0.45
Model 2 p(e\|f)	0.36
Model 2 intersection	0.33
Model 2 joint train	0.37
Model 2 joint train + intersection	0.27

Our final AER on the development set with all training data is 0.177.

Writing Sample 3

Here is my algorithm:

Create a new data set as follows:
- Loop over aligned sentence pairs
- For each token in the french sentence identify a “corresponding window” of 9 tokens in the english sentence.
- The index at the center of the “corresponding window” is just the index of the french token times the ratio of the length of the english sentence to the length of the french sentence.
- For each token in that english window, add a new pair of one token “sentences” (the english token and the original french token) to the new dataset.
Compute dice’s coefficient on the new dataset

Note: I didn’t really think of the algorithm this way, and I actually do the counting as I create the dataset.

Decoding, loop over sentence pairs:
- Tentatively align each token in the french sentence with the English token that has the highest Dice’s coefficient as computed above.
- Break ties in Dice score based on distance from french index to “corresponding” English index (same calculation as above).
- Repeat the process in the other direction and report only those alignments which are chosen in both directions.

Writing Sample 4

Implemented solution

I implemented the model described in Dyer et al. 2013, in addition to model 1.

A diagonal prior is imposed on the alignment links, and a mean-field approximation is used in the E step to estimate the posterior translation distribution with a Dirichlet prior.

Then, I applied several pre-processing steps to improve alignments: - lowercase the data - stem German and English with the Snowball stemmer (see stem-corpus.py) - split the compounds in German using cdec (see csplit.py and uncsplit.py)

Finally, I tuned the hyperparameters of the systems (diagonal tension, null alignment probability and Dirichlet prior strength) on the dev set to minimize AER using the simplex method.

Results summary (dev corpus)

Model	AER	Δ
Baseline	0.792556
Model 1	0.421544	0.37
+ diagonal prior	0.290222	0.13
+ Dirichlet prior	0.269823	0.02
+ compound split	0.257015	0.01
+ stem	0.243009	0.01
+ tune	0.233541	0.01

Usage

Run the following command to replicate the experiments: