These numbers come from my solution. It's entirely possible there's some kind of stupid bug in it, so if you have questions about a specific point, please let me know. Otherwise, I'm going to assume your numbers should look similar to these.
Once I get a chance to look over the assignments, I'll let you know if your solution needs more work. If you don't get an email from me by Thursday evening, you can assume you have full credit. If you do get an email, it will tell you what you need to do to get credit.
My solution uses an end marker in both the unigram and bigram case, and when ranking, divides by the length of the original sentence (without the end marker).
Lots of people computed different variants of the log probability of the correct translation, like the average log probability of a sentence, or the average of the ranking function (normalized by length). These are all equivalent, of course, but the tradition in this area is to report either the total log probability of the corpus or the perplexity, which is 2 to the entropy of the random variable w_i.
| Model | Alpha | Beta | Total LogP | Avg LogP | Total Normalized LogP | Avg Normalized LogP | Avg Error |
| Random Baseline | - | - | - | - | - | - | 4.604 |
| Unigrams | 1 | - | -144681 | -114 | -9015 | -7.11 | 5.85 |
| Unigrams | 1.593 | - | -144660 | -114 | -9016 | -7.11 | 5.86 |
| Bigrams | 1 | 1 | -122079 | -96 | -7041 | -5.55 | 2.70 |
| Bigrams | 1.593 | 1 | -121799 | -96 | -7024 | -5.54 | 2.69 |
| Bigrams | 1.593 | 113 | -112267 | -88 | -6590 | -5.20 | 2.98 |
| Model | Alpha | Beta | Total LogP | Avg LogP | Total Normalized LogP | Avg Normalized LogP | Avg Error |
| Random Baseline | - | - | - | - | - | - | 5.056 |
| Unigrams | 1 | - | -151362 | -128 | -8427 | -7.14 | 6.46 |
| Unigrams | 1.593 | - | -151326 | -128 | -8423 | -7.14 | 6.45 |
| Bigrams | 1 | 1 | -136881 | -116 | -7264 | -6.16 | 3.40 |
| Bigrams | 1.593 | 1 | -136592 | -115 | -7246 | -6.14 | 3.38 |
| Bigrams | 1.593 | 113 | -123916 | -105 | -6641 | -5.63 | 3.67 |