Squashed matrix factorization for modeling incomplete dyadic data

A computer-readable medium that stores a computer program for predicting a response relationship between elements of two sets, wherein the computer program includes instructions for:

• specifying a response matrix that measures a response relationship between elements of a first set corresponding to rows of the response matrix and a second set corresponding to columns of the response matrix;
• specifying covariates that measure additional relationships between elements of the first set and the second set;
• specifying observation weights for weighing measurements for elements of the first set and the second set;
• specifying a number of row clusters for clustering elements of the first set into row clusters;
• specifying a number of column clusters for clustering elements of the second set into column clusters;
• specifying a rank for cluster factors that model average interactions between row clusters and column clusters by products of cluster factors;
• determining prediction parameters for predicting responses between elements of the first set and the second set by improving a likelihood value that relates the prediction parameters to the response matrix, the covariates, the observation weights, the row clusters and the column clusters, wherein determining the prediction parameters includes:
• updating the prediction parameters for fixed assignments of row clusters and column clusters, and
• updating assignments for row clusters and column clusters for fixed prediction parameters;
• and
• saving one or more values for the prediction parameters.

An apparatus for predicting a response relationship between elements of two sets, the apparatus comprising a computer for executing computer instructions, wherein the computer includes computer instructions for:

• specifying a response matrix that measures a response relationship between elements of a first set corresponding to rows of the response matrix and a second set corresponding to columns of the response matrix;
• specifying covariates that measure additional relationships between elements of the first set and the second set;
• specifying observation weights for weighing measurements for elements of the first set and the second set;
• specifying a number of row clusters for clustering elements of the first set into row clusters;
• specifying a number of column clusters for clustering elements of the second set into column clusters;
• specifying a rank for cluster factors that model average interactions between row clusters and column clusters by products of cluster factors;
• determining prediction parameters for predicting responses between elements of the first set and the second set by improving a likelihood value that relates the prediction parameters to the response matrix, the covariates, the observation weights, the row clusters and the column clusters, wherein determining the prediction parameters includes:
• updating the prediction parameters for fixed assignments of row clusters and column clusters, and
• updating assignments for row clusters and column clusters for fixed prediction parameters;
• and
• saving one or more values for the prediction parameters.