Toward General Analysis of Recursive Probability Models

There is increasing interest within the research community in the design and use of recursive probability models. There remains concern about computational complexity costs and the fact that computing exact solutions can be intractable for many nonrecursive models. Although inference is undecidable in the general case for recursive problems, several research groups are actively developing computational techniques for recursive stochastic languages. We have developed an extension to the traditional λcalculus as a framework for families of Turing complete stochastic languages. We have also developed a class of exact inference algorithms based on the traditional reductions of the λcalculus. We further propose that using the deBruijn notation (a λ-calculus notation with nameless dummies) supports effective caching in such systems, as the reuse of partial solutions is an essential component of efficient computation. Finally, our extension to the λ-calculus offers a foundation and general theory for the construction of recursive stochastic modeling languages as well as promise for effective caching and efficient approximation algorithms for inference.