Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Expectation Propagation for approximate Bayesian inference
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
An Introduction to Copulas (Springer Series in Statistics)
An Introduction to Copulas (Springer Series in Statistics)
The Hidden Life of Latent Variables: Bayesian Learning with Mixed Graph Models
The Journal of Machine Learning Research
Cumulative distribution networks: inference, estimation and applications of graphical models for cumulative distribution functions
All of Statistics: A Concise Course in Statistical Inference
All of Statistics: A Concise Course in Statistical Inference
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
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We present a class of graphical models for directly representing the joint cumulative distribution function (CDF) of many random variables, called cumulative distribution networks (CDNs). Unlike graphs for probability density and mass functions, for CDFs the marginal probabilities for any subset of variables are obtained by computing limits of functions in the model, and conditional probabilities correspond to computing mixed derivatives. We will show that the conditional independence properties in a CDN are distinct from the conditional independence properties of directed, undirected and factor graphs, but include the conditional independence properties of bi-directed graphs. In order to perform inference in such models, we describe the `derivative-sum-product' (DSP) message-passing algorithm in which messages correspond to derivatives of the joint CDF. We will then apply CDNs to the problem of learning to rank players in multiplayer team-based games and suggest several future directions for research.