In this chapter, we define a metric distance between probability distributions of unequal dimensions. Using this metric, we then address the problem of optimally approximating a high-order distribution by another one of a lower, prespecified order. It is shown that both the problem of computing the distance and of finding the optimal reduced-order approximation can be formulated as extensible bin- packing problems, and are thus NP-hard. Polynomial-time suboptimal algorithms are provided for both problems.
Maximizing mutual information between random variables and applications to order reduction of stochastic processes, Page 1 of 2
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