Computation of joint moment functions on convolutional factor graphs

Iterative algorithms on graphical models are of current research interest. In this paper, we show that for a function represented by a convolutional factor graph, its joint moment functions can be computed by a message-passing algorithm on the graph, without explicitly computing the function itself; when the function represented by the graph is a joint probability density function (pdf), these joint moment functions are effectively conditional expectations. It is also worth noting that, as an application of factor graph duality, the algorithm translates to a new message-passing algorithm on multiplicative factor graphs.