The goal of this assignment is to explore the topic model -- to see how it can be implemented, applied to data, and how its hyperparameters affect the outcome of the computation.

Download and install a topic model simulator.  A few that I've been able to find are listed below, and I'm sure there are more out there.  For extra credit, 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.  Show a sample document.  Show a sample topic distribution---the 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}.

Hint:  Barber's BRML Toolkit  includes a function for drawing from a Dirichlet: dirrnd. There's other code on the web as well.

Run your topic model 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 'recovered topics' are the estimate of P(Word | Topic) that comes from sampling.  The 'true topics' are the P(Word | Topic) distributions like the one you showed in part II.

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 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.  

The Institute of Cognitive Science just purchased a subscript to a site called Sketch Engine that provides access to more than 80 corpora in dozens of languages. You can access the site via a hard-wired university computer, connected via WiFi to UCB Wireless (not as UCB Guest), or on the CU Boulder VPN.  From the landing page, click on the "IP auth" link in the upper right corner of the page. It may be fun to apply topic models to corpora in your native language, but please translate and interpret your results for the sake of the lousy American professor who can barely speak one language.
 
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.