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Recursive conditioning. (English) Zbl 0969.68150
Summary: We introduce an any-space algorithm for exact inference in Bayesian networks, called recursive conditioning. On one extreme, recursive conditioning takes $$O(n)$$ space and $$O(n\exp(w\log n))$$ time – where $$n$$ is the size of a Bayesian network and $$w$$ is the width of a given elimination order – therefore, establishing a new complexity result for linear-space inference in Bayesian networks. On the other extreme, recursive conditioning takes $$O(n\exp(w))$$ space and $$O(n\exp(w))$$ time, therefore, matching the complexity of state-of-the-art algorithms based on clustering and elimination. In between linear and exponential space, recursive conditioning can utilize memory at increments of $$X$$-bytes, where $$X$$ is the number of bytes needed to store a floating point number in a cache. Moreover, the algorithm is equipped with a formula for computing its average running time under any amount of space, hence, providing a valuable tool for time-space tradeoffs in demanding applications. Recursive conditioning is therefore the first algorithm for exact inference in Bayesian networks to offer a smooth tradeoff between time and space, and to explicate a smooth, quantitative relationship between these two important resources.

##### MSC:
 68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
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