Cumulative distribution networks and the derivative-sum-product algorithm
This work addresses the problem of structured ranking learning for researchers in machine learning and statistics, offering a novel graphical model with unique independence properties.
The paper introduces cumulative distribution networks (CDNs), a new graphical model that expresses joint cumulative distributions as products of local functions for ranking variables, and presents a message-passing algorithm to compute conditional cumulative distributions, demonstrating its application on a multi-player gaming dataset.
We introduce a new type of graphical model called a "cumulative distribution network" (CDN), which expresses a joint cumulative distribution as a product of local functions. Each local function can be viewed as providing evidence about possible orderings, or rankings, of variables. Interestingly, we find that the conditional independence properties of CDNs are quite different from other graphical models. We also describe a messagepassing algorithm that efficiently computes conditional cumulative distributions. Due to the unique independence properties of the CDN, these messages do not in general have a one-to-one correspondence with messages exchanged in standard algorithms, such as belief propagation. We demonstrate the application of CDNs for structured ranking learning using a previously-studied multi-player gaming dataset.