An MCMC library for probabilistic programming Rob Zinkov June 13th, - - PowerPoint PPT Presentation

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An MCMC library for probabilistic programming Rob Zinkov June 13th, - - PowerPoint PPT Presentation

Jan 19, 2024 241 likes •451 views

An MCMC library for probabilistic programming Rob Zinkov June 13th, 2014 Rob Zinkov An MCMC library for probabilistic programming June 13th, 2014 1 / 19 Special Thanks to Praveen Rob Zinkov An MCMC library for probabilistic programming

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An MCMC library for probabilistic programming

Rob Zinkov June 13th, 2014

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Special Thanks to Praveen

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Why we need it?

  • Prototyping probabilistic programming inference solutions
  • Easier exploration of mcmc algorithms
  • Easier to combine multiple mcmc strategies

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Acceptance ratios tricky to get right

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Reversible-jump: trickier still

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Split-merge proposals

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Caveats

  • We are only talking MCMC and no other inference methods
  • We will not discuss how to use this library in a probabilistic

programming system

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Core Primitives

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Providing a Density

type Density a = a -> Probability data Target a = T (Density a)

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Providing a Proposal Distribution

type Sample a = Rand -> IO a data Proposal a = P (Density a) (Sample a)

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Specifying a Step (Transition)

Steps are how we transition from one state to another type Step x = Rand -> x -> IO x

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Specifying a Kernel

type Kernel x a = Target a -> (a -> Proposal a) -> Step x

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Walking the MCMC chain

walk :: Step x -> x -> Int -> Rand -> Action x a -> IO a

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Demo

Demo!

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Features we provide

  • Blocking proposals
  • Cyclic kernels
  • Mixture kernels

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Further work

  • Langevin and Hamiltonian MC
  • Approximate MCMC (ABC, Noisy MALA)
  • Adaptive MC
  • Reversible Jump

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Conclusions

Let’s write our inference solutions in more modular ways Coming very soon to Hackage!

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Questions?

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