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arXiv · 2501.15439

Variable Elimination as Rewriting in a Linear Lambda Calculus

Thomas Ehrhard·Claudia Faggian·Michele Pagani
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Abstract

Variable Elimination (VE) is a classical exact inference algorithm for probabilistic graphical models such as Bayesian Networks, computing the marginal distribution of a subset of the random variables in the model. Our goal is to understand Variable Elimination as an algorithm acting on programs, here expressed in an idealized probabilistic functional language -- a linear simply-typed $\lambda$-calculus suffices for our purpose. Precisely, we express VE as a term rewriting process, which transforms a global definition of a variable into a local definition, by swapping and nesting let-in expressions. We exploit in an essential way linear types.

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Thomas Ehrhard, Claudia Faggian, Michele Pagani. 2025-01-26. Variable Elimination as Rewriting in a Linear Lambda Calculus. https://arxiv.org/abs/2501.15439

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