20th June 2005 — Sam Roweis, modelling data matrices

Sam says:

I’ll talk about a new model that Zoubin and I cooked up for factorizing matrices using a simple additive model based on binary latent variables. In particular, think of a “dyadic” data matrix, e.g. word-document counts, user-movie ratings, experiment-probe genetic arrays, etc. In such matrices there are “row objects” and “column objects”. Our model assumes that there are some latent binary “row attributes” and some latent binary “column attributes” and that each row/column can have zero or more of these latent attributes turned on. The response (data) at row i, col j is a function only of the attributes row i has activated and the attributes col j has activated. This model is like a two-way Indian Buffet Process in that, given the row attributes it models the data as a column-wise IBP and given the column attributes it models the data as a row-wise IBP.

I’ll talk about how to do calculations with this model, how to extend it to infinite number of row/column attributes and show almost no results.