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AdvancedHMC.jl provides a robust, modular, and efficient implementation of advanced HMC algorithms. An illustrative example of AdvancedHMC's usage is given below. AdvancedHMC.jl is part of [Turing.jl](https://github.com/TuringLang/Turing.jl), a probabilistic programming library in Julia.
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If you are interested in using AdvancedHMC.jl through a probabilistic programming language, please check it out!
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**AdvancedHMC.jl** provides robust, modular, and efficient implementation of advanced Hamiltonian Monte Carlo (HMC) algorithms in Julia. It is a backend for probabilistic programming languages like [Turing.jl](https://github.com/TuringLang/Turing.jl), but can also be used directly for flexible MCMC sampling when fine-grained control is desired.
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## Hands on AdvancedHMC.jl
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**Key Features**
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Let's see how to sample a Hamiltonian using AdvanedHMC.jl
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- Implementation of state-of-the-art [HMC variants](https://turinglang.org/AdvancedHMC.jl/dev/api/) (e.g., NUTS).
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- The modular design allows for the customization of metrics, Hamiltonian trajectory simulation, and adaptation.
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- Integration with the [LogDensityProblems.jl](https://github.com/tpapp/LogDensityProblems.jl) interface for defining target distributions, and [LogDensityProblemsAD.jl](https://github.com/TuringLang/LogDensityProblemsAD.jl) for supporting automatic differentiation backends.
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- Built upon the [AbstractMCMC.jl](https://github.com/TuringLang/AbstractMCMC.jl) interface for MCMC sampling.
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## Installation
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AdvancedHMC.jl is a registered Julia package. You can install it using the Julia package manager:
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```julia
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using AdvancedHMC, LogDensityProblems, ForwardDiff
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# Define the target distribution using the `LogDensityProblem` interface
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using Pkg
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Pkg.add("AdvancedHMC")
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```
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## Quick Start: Sampling a Multivariate Normal
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Here's a basic example demonstrating how to sample from a target distribution (a standard multivariate normal) using the No-U-Turn Sampler (NUTS).
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```julia
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using AdvancedHMC, AbstractMCMC
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using LogDensityProblems, LogDensityProblemsAD, ADTypes # For defining the target distribution & its gradient
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using ForwardDiff # An example AD backend
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using Random # For initial parameters
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# 1. Define the target distribution using the LogDensityProblems interface
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struct LogTargetDensity
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dim::Int
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end
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# standard multivariate normal distribution
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#Log density of a standard multivariate normal distribution
# 2. Wrap the log density function and specify the AD backend.
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# This creates a callable struct that computes the log density and its gradient.
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ℓπ =LogTargetDensity(D)
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model = AdvancedHMC.LogDensityModel(LogDensityProblemsAD.ADgradient(AutoForwardDiff(), ℓπ))
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# 3. Set up the HMC sampler
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# - Use the No-U-Turn Sampler (NUTS)
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# - Specify the target acceptance probability (δ) for step size adaptation
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sampler =NUTS(0.8) # Target acceptance probability δ=0.8
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# Define the number of adaptation steps and sampling steps
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n_adapts, n_samples =2_000, 1_000
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# 4. Run the sampler!
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# We use the AbstractMCMC.jl interface.
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# Provide the model, sampler, total number of steps, and adaptation steps.
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# An initial parameter vector `initial_θ` is also required.
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initial_θ =randn(D)
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samples = AbstractMCMC.sample(
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Random.default_rng(),
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model,
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sampler,
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n_adapts + n_samples;
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n_adapts=n_adapts,
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initial_params=initial_θ,
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progress=true, # Optional: Show a progress bar
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)
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# `samples` now contains the MCMC chain. You can analyze it using packages
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# like StatsPlots.jl, ArviZ.jl, or MCMCChains.jl.
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```
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For more advanced usage, please refer to the [docs](https://turinglang.org/AdvancedHMC.jl/dev/get_started/).
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## Contributing
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Contributions are highly welcome! If you find a bug, have a suggestion, or want to contribute code, please open an issue or pull request.
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## License
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AdvancedHMC.jl is licensed under the MIT License. See the LICENSE file for details.
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## Citing AdvancedHMC.jl
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If you use AdvancedHMC.jl for your own research, please consider citing the following publication:
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}
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```
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If you using AdvancedHMC.jl directly through Turing.jl, please consider citing the following publication:
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If you are using AdvancedHMC.jl directly through Turing.jl, please consider citing the following publication:
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Hong Ge, Kai Xu, and Zoubin Ghahramani: "Turing: a language for flexible probabilistic inference.", *International Conference on Artificial Intelligence and Statistics*, 2018. ([abs](http://proceedings.mlr.press/v84/ge18b.html), [pdf](http://proceedings.mlr.press/v84/ge18b/ge18b.pdf))
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## References
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1. Neal, R. M. (2011). MCMC using Hamiltonian dynamics. Handbook of Markov chain Monte Carlo, 2(11), 2. ([arXiv](https://arxiv.org/pdf/1206.1901))
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2. Betancourt, M. (2017). A Conceptual Introduction to Hamiltonian Monte Carlo. [arXiv preprint arXiv:1701.02434](https://arxiv.org/abs/1701.02434).
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3. Girolami, M., & Calderhead, B. (2011). Riemann manifold Langevin and Hamiltonian Monte Carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73(2), 123-214. ([arXiv](https://rss.onlinelibrary.wiley.com/doi/full/10.1111/j.1467-9868.2010.00765.x))
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4. Betancourt, M. J., Byrne, S., & Girolami, M. (2014). Optimizing the integrator step size for Hamiltonian Monte Carlo. [arXiv preprint arXiv:1411.6669](https://arxiv.org/pdf/1411.6669).
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