Variable Elimination as Rewriting in a Linear Lambda Calculus
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913666695168000 |
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| author | Ehrhard, Thomas Faggian, Claudia Pagani, Michele |
| author_facet | Ehrhard, Thomas Faggian, Claudia Pagani, Michele |
| contents | 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 $λ$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variable Elimination as Rewriting in a Linear Lambda Calculus Ehrhard, Thomas Faggian, Claudia Pagani, Michele Logic in Computer Science 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 $λ$-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. |
| title | Variable Elimination as Rewriting in a Linear Lambda Calculus |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2501.15439 |