The goal of this assignment is to explore topic models -- to see how they are applied to data and how model hyperparameters affect the outcome of the computation.

Select a topic modeling package, or for extra credit, write your own. I'm guessing that most of you will want to use the LDA class that is available in scikit learn.  It estimates posteriors with variational Bayes, not with Gibbs sampling. It also has the capability for doing online training. "Online training" means that it processes the data in small batches, which is the only way to train if you have a really huge data set and can't sweep through all the data at once. For this assignment, using batch training will be fine. The variational Bayes algorithm used for training this version of LDA is described in this paper.  You'll need to take a look at the paper to figure out how the notation we've discussed maps to the notation in the scikit learn documentation. (One big hint: the parameter we have called α has the same name but the parameter we have called β is renamed η, and β is confusingly used instead for the topic-conditional word distribution.) 

Here are a few additional topic modeling packages I've seen.


You can even write your own.  The amount of code needed is pretty minimal to do Gibbs sampling, and all the equations are specified in my class notes or in the text. Some of the packages will have default values for parameters (α, β) and sampling procedure (# burn in iterations, # data collection iterations).  Make sure you pick a package that gives you enough flexibility for the rest of the assignment; that is, you will need to estimate P(T|D) and P(W|T) from the topic assignments.

Write code for and run a generative topic model that produces synthetic data.  For this small scale example, generate 200 documents each with 50 word tokens from a dictionary of 20 word types and 3 topics.  Use α=.1, β=.01.  [I am using the notation we discussed in class.]

Show a sample document.  Show a sample topic distribution---a probability table over the 20 word types representing P(Word|Topic) for some topic. To use consistent notation across the class, label your words A-T (the first 20 letters of the alphabet), so that a document will be a string of 50 letters drawn from {A, ..., T}. When you generate output, make sure it is in a format that can be read by the topic modeling package you downloaded (see Part II).

Hint:  Barber's BRML Toolkit  includes a function for drawing from a Dirichlet: dirrnd. numpy.random.dirichlet works if you're using python. There's other code on the web as well.

Run your topic modelling package with T=3, α=.1, β=.01 on your synthetic data set.  Compare the true topics (in your generative model) to the recovered topics.  The 'true topics' are the P(Word | Topic) distributions like the one you showed in part I. The 'recovered topics' are the estimate of P(Word | Topic) that comes from your model.  You should decide on a sensible means of comparing the distributions.

The bias α=.1 encourages sparse topic distributions and the bias β=.01 encourages sparse distributions over words. Change one of these biases and find out how robust the results are to having chosen parameters that match the underlying generative process.  You may wish to quanitfy how changing these parameters affects the results in terms of an entropy measure.  For example, if you modify α, then you might want to compare the mean entropy of topic distributions:
This is a measure of how focused the distribution of topics is on average across documents. As you increase α, this entropy should increase.  If you modify β, you can evaluate the consequence via the mean entropy of the word distribution:

Run the topic model, with parameters you select, on a larger, interesting data set. Data sets are abundant on the web.  I only ask that it be an English language data set so that other members of the class can see and understand your results. The UCI Matlab Topic Modeling Toolbox includes a variety of data sets.  There's also a corpus of 2246 articles from the Associated Press available from Blei at Princeton. Jim Martin has a corpus of 54k abstracts from medical journals in his information retrieval class (no fair using this if you've taken the IR class already; play with a different data set). Or be creative: use your own email corpus.  Or phone text message corpus.  Just be sure that whatever data set you choose is large enough that you have something interesting to experiment with.  

Be sure to choose a large enough number of topics that your results will give you well delineated topics.  Find a few interpretable topics and present them by showing the highest probability words (10-20) within the topic, and give a label to the topic.  You may decide that P(W|T) isn't the best measure for interpreting a topic, since high frequency words will have high probability in every topic.  Instead, you may prefer a discriminative measure such as P(W|T)P(T|W).  (I just made up this measure.  It's a total hack, but it combines how well a word predicts a topic and how well a topic predicts a word.)

Note: Depending on the number of word types in your collection, you may want to use a β < .01 to obtain sparser topics.