Fig. 1

Schematic for the asynchronous updating scheme used in CoGAPS. Updates are proposed sequentially until a conflicting proposal is generated, at which time the existing queue of proposals is evaluated in parallel. In this case, proposed change #4 is conflicting since it is in the same row as #2. When evaluating a proposal, an entire row or column of \(AP\) is used in the calculation of the conditional distribution used to perform Gibbs sampling. When a change is made in row \(n\) of \(A\), the entire nth row of \(AP\) changes. So, if another change is later proposed in row \(n\), the value of \(AP\) used will depend on the previous proposal thereby changing the conditional distribution for this new proposal. This is exactly the case here for #2 and #4. Changes #1, #2, #3 can be processed in parallel since they do not conflict with each other