History

Please fill in your query. A complete syntax description you will find on the General Help page.
On sampling from multivariate distributions. (English)
Goldberg, Leslie Ann (ed.) et al., Approximation, randomization, and combinatorial optimization. Algorithms and techniques. 14th international workshop, APPROX 2011, and 15th international workshop, RANDOM 2011, Princeton, NJ, USA, August 17‒19, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-22934-3/pbk). Lecture Notes in Computer Science 6845, 616-627 (2011).
Summary: Let \$X _{1}, X _{2}, \cdots , X _{n }\$ be a set of random variables. Suppose that in addition to the prior distributions of these random variables we are also given linear constraints relating them. We ask for necessary and sufficient conditions under which we can efficiently sample the constrained distributions, find constrained marginal distributions for each of the random variables, etc. We give a tight characterization of the conditions under which this is possible. The problem is motivated by a number of scenarios where we have separate probabilistic inferences in some domain, but domain knowledge allows us to relate these inferences. When the joint prior distribution is a product distribution, the linear constraints have to be carefully chosen and are crucial in creating the lower bound instances. No such constraints are necessary if arbitrary priors are allowed.