This time we enter the Stack Overflow challenge, which is about predicting a status of a given question on SO. There are five possible statuses, so it’s a multi-class classification problem.

We would prefer a tool able to perform multiclass classification by itself. It can be done by hand by constructing five datasets, each with binary labels (one class against all others), and then combining predictions, but it might be a bit tricky to get right - we tried. Fortunately, nice people at Yahoo, excuse us, Microsoft, recently relased a new version of Vowpal Wabbit, and this new version supports multiclass classification.

In case you’re wondering, Vowpal Wabbit is a fast linear learner. We like the “fast” part and “linear” is OK for dealing with lots of words, as in this contest. In any case, with more than three million data points it wouldn’t be that easy to train a kernel SVM, a neural net or what have you.

VW, being a well-polished tool, has a few very convenient features. A particularly useful one is automatic hashing - it means that you don’t need to convert categorical features into sparse representations of one-hot vectors (how does it sound?) like you would in LibSVM format:

1 23:1 67:1 856:1 3372:1 4200:1 8345:1 23423:1

Instead, you just give VW the words:

1 | I'd like to have an argument, please.

Or maybe, after some pre-processing, in robot speak:

1 | id like to have an argument please

More readable than numbers, isn’t it? Here is the game plan:

pre-process CSV data convert it into VW format run learning and prediction convert output into submission format profit

If you’d like to do some tweaking, validation is a must. Therefore, there would be two additional steps: split the training set into training and validation, and at the end compute the score. A metric for this contest is multiclass logarithmic loss, which is easy enough to implement - see the code.

Ready? Let’s get pre-processing CSV files to get CSV files slightly more fitting our purposes:

extract.py train.csv train_.csv extract.py public_leaderboard.csv test_.csv

Then, converting them into Vowpal Wabbit format. We will use words (title, body, tags) as features, and also user reputation and post count. If you’re short on disk space, you can get rid of post bodies and still do OK.

csv2vw.py train_.csv train.vw csv2vw.py test_.csv test.vw

Now it’s time to train:

vw --loss_function logistic --oaa 5 -d train.vw -f model

It means: use logistic loss function, one against all classification with five classes, data from train.vw and save the resulting model in a file called model. At this point, you get some numbers:

average since example example current current current loss last counter weight label predict features 0.333333 0.333333 3 3.0 4 4 10 0.166667 0.000000 6 6.0 4 4 12 0.181818 0.200000 11 11.0 4 4 8 0.090909 0.000000 22 22.0 4 4 7 0.136364 0.181818 44 44.0 4 4 22 0.080460 0.023256 87 87.0 4 4 7 0.074713 0.068966 174 174.0 4 4 13 0.094828 0.114943 348 348.0 4 4 15 0.099138 0.103448 696 696.0 4 4 16 0.079741 0.060345 1392 1392.0 4 4 7 0.075790 0.071839 2784 2784.0 4 4 14 0.063218 0.050647 5568 5568.0 4 4 14 0.056668 0.050117 11135 11135.0 4 4 11 0.048184 0.039698 22269 22269.0 4 4 8 0.036980 0.025777 44537 44537.0 4 4 17 0.027696 0.018412 89073 89073.0 4 4 7 0.019512 0.011328 178146 178146.0 4 4 22 0.013685 0.007859 356291 356291.0 3 4 13 0.011331 0.008976 712582 712582.0 4 4 8 0.013039 0.014746 1425163 1425163.0 4 4 9 0.019277 0.025516 2850326 2850326.0 4 4 10 finished run

Probably the most important is the first column, called average loss. It shows the value of loss function as the learner goes along with example counter. Usually, the smaller the loss, the better. Here we’re getting pretty low numbers, so let’s see how it turns out. We’ll use the model to get predictions:

vw --loss_function logistic --oaa 5 -i model -t -d test.vw -r raw_predictions.txt

The switches are: -i for model file, -t means “do not train, just predict”, and -r specifies the file to output raw predictions. We need them raw because otherwise we’ll only get a predicted class. The raw predictions look as follows - first a line with values for each class, then a line with post id (we saved post id earlier):

1:-1.58226 2:-2.73852 3:-4.86114 4:2.0419 5:-4.73838 4 1:-5.56301 2:-7.46127 3:-6.26342 4:3.23339 5:-6.79117 145 1:-5.25797 2:-6.82686 3:-5.11928 4:3.65003 5:-6.38332 231

All we need now is to run these raw values through sigmoid function to obtain probabilities, and optionally normalize them so they sum up to one (Kaggle will do this automatically, but for validation the task is upon us).

sigmoid_mc.py raw_predictions.txt p.txt

4,0.150503851876,0.0536225867259,0.00678218723343,0.781431031164,0.00766034300002 145,0.00394282781518,0.0005926764116,0.00196092272855,0.992345861757,0.00115771128812 231,0.0052388258145,0.00109561525294,0.00601356189425,0.98594582605,0.00170617098785

All this takes a few minutes to run (a little longer to write from scratch) and will get you a score around 0.18. Submit and enjoy.

Update - march 2013

We re-run the model on the final data. The numbers in training look slightly worse:

(...) 0.015177 0.012582 712582 712582.0 4 4 107 0.018332 0.021487 1425163 1425163.0 4 4 87 0.022005 0.025678 2850326 2850326.0 4 4 90 finished run

But good enough for 11th place, if we did this a bit earlier:

Only recently have we learned that Marco Lui in 10th built on our approach and also shared his improvements and code.

We would like to thank Ariel Faigon and John Langford for help in understanding the workings of Vowpal Wabbit.