MicroCanonicalHMC.jl

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MicroCanonicalHMC.jl

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Implementation of Arxiv:2212.08549 in Julia

MicroCanonicalHMC.jl 최신버젼 다운로드

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# MicroCanonicalHMC.jl

[![Build Status](https://github.com/JaimeRZP/MCHMC.jl/workflows/CI/badge.svg)](https://github.com/JaimeRZP/MicroCanonicalHMC.jl/actions?query=workflow%3AMCHMC-CI+branch%3Amaster)
[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://jaimerzp.github.io/MicroCanonicalHMC.jl/dev/)
![size](https://img.shields.io/github/repo-size/jaimerzp/MicroCanonicalHMC.jl)

A Julia implementation of [Micro-Canonical HMC](https://arxiv.org/pdf/2212.08549.pdf). You can checkout the JAX version [here](https://github.com/JakobRobnik/MicroCanonicalHMC).

## Features

- GPU support through CUDA.jl
- Integrated within Turing.jl ecosystem.

## How to use it

### Define the Model
Start by drawing a Neal's funnel model in Turing.jl:

```julia
# The statistical inference frame-work we will use
using Turing
using Random
using PyPlot
using LinearAlgebra
using MicroCanonicalHMC

d = 21
@model function funnel()
    θ ~ Normal(0, 3)
    z ~ MvNormal(zeros(d-1), exp(θ)*I)
    x ~ MvNormal(z, I)
end

(; x) = rand(funnel() | (θ=0,))
funel_model = funnel() | (; x);
```

### Define the Sampler

```julia
nadapt = 10_000
TEV = 0.001
spl = MCHMC(nadapt, TEV)
```
The first two entries mean that the step size and the trajectory length will be self-tuned. In the ensemble sampler, the third number represents the number of workers.
`VaE_wanted` sets the hamiltonian error per dimension that will be targeted. Fixing `sigma=ones(d)` avoids tunin the preconditioner.

### Start Sampling

```julia
samples_mchmc = sample(funel_model, externalsampler(spl), 100_000)
```

### Compare to NUTS

```julia
samples_hmc = sample(funnel_model, NUTS(5_000, 0.95), 50_000)
```

![](https://raw.githubusercontent.com/JaimeRZP/MicroCanonicalHMC.jl/master/docs/src/assets/mchmc_comp.png)

- NUTS effective samples per second --> ~630
- MCHMC effective samples per second --> ~1340
- Ensemble MCHMC effective samples per second per worker --> ~957

## Using your own likelihood function

### Define a Target
Start by defining your likelihood function and its gradient
```julia
d=2
function ℓπ(x; a=a, b=b)
    x1 = x[1:Int(d / 2)]
    x2 = x[Int(d / 2)+1:end]
    m = @.((a - x1)^2 + b * (x2 - x1^2)^2)
    return -0.5 * sum(m)
end
function ∂lπ∂θ(x)
    return ℓπ(x), ForwardDiff.gradient(ℓπ, x)
end
θ_start = rand(MvNormal(zeros(d), ones(d)))
```
Wrap it into a `CustomTarget`
```julia
target = CustomTarget(ℓπ, ∂lπ∂θ, θ_start)
```
### Start Sampling
```julia
samples_mchmc = Sample(spl, target, 500_000; dialog=true);
```
![](https://raw.githubusercontent.com/JaimeRZP/MicroCanonicalHMC.jl/master/docs/src/assets/mchmc_comp_2.png)

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