function GibbsSamplerAT

Runs the AT Gibbs sampler for the Author-Topic model.

[ WP , AT, Z, X ] = GibbsSamplerAT( WD,AD,T,N,ALPHA,BETA,SEED,OUTPUT ) will run the Gibbs sampler for the AT model on a bag of words sparse count matrix WD of size W x D (W=vocabulary size, D=number of documents) and a author document sparse matrix AD of size A x D (A=number of authors). WD(i,j) contains the frequency of word i in document j. AD(i,j) contains binary values indicating the presence and absence of author i on document j. The first output is matrix WP, a W x T matrix, where WP(i,j) contains the number of times word i has been assigned to topic j. T is the number of topics. The second output is matrix AT, a matrix of size A x T, where AT(i,j) contains the number of times a word in a document with author i has been assigned to topic j. The outputs Z and X are vectors that contain the topic and author assignments respectively.

[ WP , AT, Z, X ] = GibbsSamplerAT( WD,AD,T,N,ALPHA,BETA,SEED,OUTPUT,ZIN,XIN ) will run the sampler from starting state ZIN, and XIN where ZIN(k) contains the topic assignment for token k, and XIN(k) contains the author assignment for token k, saved from a previous sample

Notes

WD and AD should be sparse matrices in double precision

N determines the number of iterations to run the Gibbs sampler

ALPHA and BETA are the hyperparameters on the Dirichlet priors for the topic distributions (theta) and the topic-word distributions (phi) respectively

SEED sets the seed for the random number generator

OUTPUT determines the screen output by the sampler 0 = no output provided 1 = show the iteration number only 2 = show all output

The time to complete the procedure scales linearly with the number of topics, the average number of authors on documents, and the number of iterations. The memory requirements scale linearly with the number of topics, documents, and authors.

A good setting for the number of iterations will depend on the number of topics and the complexity of problem. For most problems, 500 to 2000 iterations will suffice.

Appropriate values for ALPHA and BETA depend on the number of topics and the number of words in vocabulary. For most applications, good results can be obtained by setting ALPHA = 50 / T and BETA = 200 / W

The sampler uses its own random number generator and setting the seed for this function will not influence the random number seed for Matlab functions

Equivalence of LDA and AT model

As shown in Rosen-Zvi et al. (2004), the AT model is identical to the LDA model if each document has a single unique author. Therefore, if the AD matrix is diagonal, the output of the AT model and the LDA model are identical

References