Cumulative distribution networks and the derivative-sum-product algorithm

TL;DR

This paper introduces cumulative distribution networks (CDNs), a novel graphical model for representing joint cumulative distributions, with a new message-passing algorithm for efficient inference, demonstrated on ranking data.

Contribution

The paper proposes CDNs as a new graphical model type and develops the derivative-sum-product algorithm for efficient inference in these models.

Findings

CDNs have unique independence properties different from traditional graphical models.

The derivative-sum-product algorithm enables efficient computation of conditional cumulative distributions.

Application to ranking data shows practical effectiveness of CDNs.

Abstract

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.