Nonparametric Involutive Markov Chain Monte Carlo: a MCMC algorithm for universal probabilistic programming
<p>Probabilistic programming, the idea to write probabilistic models as computer programs, has proven to be a powerful tool for statistical analysis thanks to the computation power of built-in inference algorithms. Developing suitable inference algorithms that work for arbitrary programs in a...
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| Format: | Thesis |
| Language: | English |
| Published: |
2022
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| Summary: | <p>Probabilistic programming, the idea to write probabilistic models as computer programs, has proven to be a powerful tool for statistical analysis thanks to the computation power of built-in inference algorithms. Developing suitable inference algorithms that work for arbitrary programs in a Turing-complete probabilistic programming language (PPL) has become increasingly important. This thesis presents the Nonparametric Involutive Markov chain Monte Carlo (NP-iMCMC) framework for the construction of MCMC inference machines for nonparametric models that can be expressed in Turing-complete PPLs. Relying on the tree representable structure of probabilistic programs, the NP-iMCMC algorithm automates the trans-dimensional movement in the sampling process and only requires the specification of proposal distributions and mappings on fixed dimensional spaces which are provided by inferences like the popular Hamiltonian Monte Carlo (HMC). We gave a theoretical justification for the NP-iMCMC algorithm and put NP-iMCMC into action by introducing the Nonparametric HMC (NP-HMC) algorithm, a nonparametric variant of the HMC sampler. This NP-HMC sampler works out-of-the-box and can be applied to virtually all useful probabilistic models. We further improved NP-HMC by applying the techniques specified for NP-iMCMC to construct irreversible extensions that have shown significant performance improvements against other existing inference methods.</p> |
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