hmc_perf_experiments.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "848e6e38",
   "metadata": {},
   "source": [
    "# Hamiltonian Monte Carlo Performance Experiments\n",
    "This notebook is used to generate evaluation data by running experiments on the Hamiltonian Monte Carlo implementation.\n",
    "This notebook contains a modified version of the neural network code from the ProbabilisticLayers notebook, in order to make it work for the sampling code.\n",
    "The cells in this notebook simply runs HMC sampling for all the experiments shown in the final report. The output is unfortunately printed out by the AdvancedHMC.jl library, and there is no programmatic way of accessing it. The last few cells collected data from the prints, and creates figures.\n",
    "\n",
    "! NOTE ! If running this notebook, ensure that there is a subfolder called images in the same location as this notebook. Otherwise there will be failures.\n",
    "\n",
    "! NOTE ! The plots are generated with static data from the print statements of AdvancedHMC.jl, rerunning the notebook may have different results.\n",
    "\n",
    "! NOTE ! This notebook usually takes ~3 minutes to run using Zygote AD back-end. It can take a very long time > 30 minutes using ForwardDiff."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "65327231",
   "metadata": {},
   "outputs": [],
   "source": [
    "begin\n",
    "    using Random\n",
    "    using Plots\n",
    "    using Zygote\n",
    "    include(\"./BayesHMC.jl\")\n",
    "    using .BayesHMC\n",
    "    include(\"./Datasets.jl\")\n",
    "    using .Datasets\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c9fb6d01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "log_posterior (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "begin\n",
    "    # Automatic Differentiation back-end used for HMC. Tested with ForwardDiff, and Zygote. This variable controls the AD back-end for all experiments in this notebook.\n",
    "    # Change the backend to ForwardDiff to see results for that AD back-end. It can take a very long time for the notebook to execute.\n",
    "    diff_backend = Zygote\n",
    "    # Set random seed for reproducibility.\n",
    "    Random.seed!(0)\n",
    "    # Build dataset\n",
    "    inputs, targets = build_dataset_1()\n",
    "    # Define the neural network once\n",
    "    num_weights, predictions, logprob = make_neural_network_functions([1, 20, 20, 1], 0.1, 0.01, rbf)\n",
    "    log_posterior(weights) = logprob(weights, inputs, targets)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdf19adf",
   "metadata": {},
   "source": [
    "# Experiment 1 - Increasing Sample Size\n",
    "This experiment runs sample sizes 10, 20, 30, 40, and 50 with adapts fixed to 5.\n",
    "The total running time for sampling and average acceptance rate is taken from the output printed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "21c6a2c3",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Finished 5 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.004871404697348373),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -45), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.00487)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 10 sampling steps for 1 chains in 2.776346 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.00487), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 2.290938041506467\n",
      "│   average_acceptance_rate = 0.0009104221417880395\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 5 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.008271086331971522),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -45), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.00827)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 20 sampling steps for 1 chains in 0.5912041 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.00827), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 2.0170415663612857\n",
      "│   average_acceptance_rate = 3.049747548179221e-18\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 5 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.006121874163812646),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -45), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.00612)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 30 sampling steps for 1 chains in 4.121955 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.00612), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 0.948832791906184\n",
      "│   average_acceptance_rate = 0.2612024179284616\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 5 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.007987729104709556),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -45), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.00799)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 40 sampling steps for 1 chains in 0.1603669 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.00799), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 0.12162958860585572\n",
      "│   average_acceptance_rate = 0.1296670944298947\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 5 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.0037672415104968156),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -45), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.00377)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 50 sampling steps for 1 chains in 11.94586 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.00377), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 0.22504332767586066\n",
      "│   average_acceptance_rate = 0.5082654664826602\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n"
     ]
    }
   ],
   "source": [
    "begin\n",
    "    sample_sizes = collect(10:10:50)\n",
    "    for sample_size in sample_sizes\n",
    "        run_hmc_sampler(sample_size, 5, num_weights, log_posterior)\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "781e9099",
   "metadata": {},
   "source": [
    "# Experiment 2 - Increasing Adapts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "927d5d95",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Finished 50 sampling steps for 1 chains in 0.1764878 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.0125), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 0.05700425149426635\n",
      "│   average_acceptance_rate = 0.12601430740842745\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 1 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.1070157552959158),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -49), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.107)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 50 sampling steps for 1 chains in 0.0355883 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.107), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 1.5018888503449284\n",
      "│   average_acceptance_rate = 0.0\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 2 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.05612617449551968),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -48), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.0561)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 50 sampling steps for 1 chains in 0.0604932 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.0561), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 2.069413690174231\n",
      "│   average_acceptance_rate = 0.0\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 3 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.01599933920962987),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -47), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.016)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 50 sampling steps for 1 chains in 0.1450017 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.016), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 0.1701863794071542\n",
      "│   average_acceptance_rate = 0.06504182457980931\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 4 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.013145816787181127),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -46), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.0131)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 50 sampling steps for 1 chains in 0.3097722 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.0131), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 0.10757742842358067\n",
      "│   average_acceptance_rate = 0.11281429513260761\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 5 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.005934441776078742),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -45), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.00593)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 50 sampling steps for 1 chains in 8.3709309 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.00593), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 0.44946401398080393\n",
      "│   average_acceptance_rate = 0.28524826878850507\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 6 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.008982570707476906),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -44), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.00898)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 50 sampling steps for 1 chains in 0.5093567 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.00898), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 0.976412138617139\n",
      "│   average_acceptance_rate = 0.0919716313211075\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 7 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.00734427792841159),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -43), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.00734)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 50 sampling steps for 1 chains in 0.5316288 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.00734), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 1.4904933946117416\n",
      "│   average_acceptance_rate = 0.023943926674920426\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 8 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.0022048623862575816),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -42), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.0022)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 50 sampling steps for 1 chains in 13.8800874 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.0022), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 0.5009452841144915\n",
      "│   average_acceptance_rate = 0.9156731858248602\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 9 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.002796649600030001),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -41), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.0028)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Finished 50 sampling steps for 1 chains in 13.0493474 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.0028), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 0.6829964306952903\n",
      "│   average_acceptance_rate = 0.6612339650485619\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n",
      "┌ Info: Finished 10 adapation steps\n",
      "│   adaptor = StanHMCAdaptor(\n",
      "    pc=WelfordVar,\n",
      "    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.003219500902206755),\n",
      "    init_buffer=75, term_buffer=50, window_size=25,\n",
      "    state=window(76, -40), window_splits()\n",
      ")\n",
      "│   κ.τ.integrator = Leapfrog(ϵ=0.00322)\n",
      "│   h.metric = DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...])\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:189\n",
      "┌ Info: Finished 50 sampling steps for 1 chains in 11.223811 (s)\n",
      "│   h = Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0, 1.0, 1.0, 1.0, 1 ...]))\n",
      "│   κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.00322), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
      "│   EBFMI_est = 0.30185686060057143\n",
      "│   average_acceptance_rate = 0.5091349546377566\n",
      "└ @ AdvancedHMC C:\\Users\\andre\\.julia\\packages\\AdvancedHMC\\51xgc\\src\\sampler.jl:214\n"
     ]
    }
   ],
   "source": [
    "begin\n",
    "    adapts = collect(0:10)\n",
    "    for adapt in adapts\n",
    "        run_hmc_sampler(50, adapt, num_weights, log_posterior)\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cfea932",
   "metadata": {},
   "source": [
    "# ForwardDiff Plotting Experiment Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "67e26ae5",
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "begin\n",
    "    times = [304.234, 139.801, 666.909]\n",
    "    ylabels = [\"Dataset 1\", \"Dataset 2\", \"Dataset 3\"]\n",
    "    fd_sampling = bar(ylabels, times, label=\"\", title=\"ForwardDiff - Sampling Time\", ylabel=\"Time (s)\", titlefontsize=11)\n",
    "    savefig(fd_sampling, \"images/forward_sampling_time.png\")\n",
    "    current()\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "12cdfca5",
   "metadata": {},
   "outputs": [
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   "source": [
    "begin\n",
    "    times = [0.9357, 0.4699, 0.7166]\n",
    "    ylabels = [\"Dataset 1\", \"Dataset 2\", \"Dataset 3\"]\n",
    "    fd_avg_acceptance = bar(ylabels, times, label=\"\", title=\"ForwardDiff - Average Acceptance Rate (%)\", ylabel=\"Average Acceptance Rate(%)\", titlefontsize=11)\n",
    "    savefig(fd_avg_acceptance, \"images/forward_average_acceptance.png\")\n",
    "    current()\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "42b30e59",
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "begin\n",
    "    times_exp_1 = [122.8130329, 222.0697514, 368.6357424, 511.9018468, 670.6136887]\n",
    "    fd_1 = bar([string(i) for i in 10:10:50], times_exp_1, label=\"\", title=\"ForwardDiff - Increasing Number of Samples\", xlabel=\"Num of Samples\", ylabel=\"Sampling Time (s)\", titlefontsize=11)\n",
    "    savefig(fd_1, \"images/forward_time_vs_samples.png\")\n",
    "    current()\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "adcbf44f",
   "metadata": {},
   "outputs": [
    {
     "data": {
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   "source": [
    "begin\n",
    "    accepts = [0.0011, 0.0236, 0.0161, 0.0340, 0.0584]\n",
    "    fd_2 = bar([string(i) for i in 10:10:50], accepts, label=\"\", title=\"ForwardDiff - Average Acceptance vs Increasing Sample Size\", xlabel=\"Num of Samples\", ylabel=\"Average Acceptance Rate\", titlefontsize=11)\n",
    "    savefig(fd_2, \"images/forward_acceptance_vs_samples.png\")\n",
    "    current()\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8cdda4f7",
   "metadata": {},
   "outputs": [
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   "source": [
    "begin\n",
    "    times_exp_2 = [22.7190668, 4.422797, 4.4115758, 15.9278964, 14.2161519, 642.8452905, 666.7616154, 836.140891, 879.0121533, 1017.5494517, 1027.9404283]\n",
    "    x_plot = [string(i) for i in 0:10]\n",
    "    fd_3 = bar(x_plot, times_exp_2, label=\"\", title=\"ForwardDiff - Increasing Adapts\", xlabel=\"Num of Adapts\", ylabel=\"Sampling Time (s)\", titlefontsize=11)\n",
    "    savefig(fd_3, \"images/forward_time_vs_adapts.png\")\n",
    "    current()\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "86ca98d8",
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "begin\n",
    "    accepts_exp_1 = [0.138, 0.0, 0.0, 0.154, 0.007, 0.058, 0.496, 0.721, 0.699, 0.857, 0.885]\n",
    "    fd_4 = bar([string(i) for i in 0:10], accepts_exp_1, label=\"\", title=\"ForwardDiff - Average Acceptance vs Increasing Adapts\", xlabel=\"Num of Adapts\", ylabel=\"Average Acceptance Rate\", titlefontsize=11)\n",
    "    savefig(fd_4, \"images/forward_acceptance_vs_adapts.png\")\n",
    "    current()\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13f2dac4",
   "metadata": {},
   "source": [
    "# Zygote Plotting Experiment Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "82843d32",
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 11,
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     "output_type": "execute_result"
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   "source": [
    "begin\n",
    "    times = [6.671, 4.02, 6.753]\n",
    "    ylabels = [\"Dataset 1\", \"Dataset 2\", \"Dataset 3\"]\n",
    "    zy_sampling = bar(ylabels, times, label=\"\", title=\"Zygote - Sampling Time\", ylabel=\"Time(s)\", titlefontsize=11)\n",
    "    savefig(zy_sampling, \"images/zygote_sampling_time.png\")\n",
    "    current()\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8fe6d6b6",
   "metadata": {},
   "outputs": [
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     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "begin\n",
    "    times = [0.6849, 0.5782, 0.7735]\n",
    "    ylabels = [\"Dataset 1\", \"Dataset 2\", \"Dataset 3\"]\n",
    "    zy_avg_acceptance = bar(ylabels, times, label=\"\", title=\"Zygote - Average Acceptance Rate(%)\", ylabel=\"Average Acceptance Rate(%)\", titlefontsize=11)\n",
    "    savefig(zy_avg_acceptance, \"images/zygote_average_acceptance.png\")\n",
    "    current()\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f1c9bb88",
   "metadata": {},
   "outputs": [
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   "source": [
    "begin\n",
    "    times_exp_1 = [3.185, 5.258, 7.014, 8.825, 10.72]\n",
    "    zy_1 = bar([string(i) for i in 10:10:50], times_exp_1, label=\"\", title=\"Zygote - Increasing Number of Samples\", xlabel=\"Num of Samples\", ylabel=\"Sampling Time (s)\", titlefontsize=11)\n",
    "    savefig(zy_1, \"images/zygote_time_vs_samples.png\")\n",
    "    current()\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d6111350",
   "metadata": {},
   "outputs": [
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   "source": [
    "begin\n",
    "    accepts = [0.0009, 0.2323, 0.2774, 0.318, 0.3012]\n",
    "    zy_2 = bar([string(i) for i in 10:10:50], accepts, label=\"\", title=\"Zygote - Average Acceptance vs Increasing Sample Size\", xlabel=\"Num of Samples\", ylabel=\"Average Acceptance Rate\", titlefontsize=11)\n",
    "    savefig(zy_2, \"images/zygote_acceptance_vs_samples.png\")\n",
    "    current()\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3f53f4b6",
   "metadata": {},
   "outputs": [
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   "source": [
    "begin\n",
    "    times_exp_2 = [0.389, 0.082, 0.082, 0.275, 0.244, 10.65, 12.126, 14.619, 14.407, 14.447, 14.353]\n",
    "    x_plot = [string(i) for i in 0:10]\n",
    "    zy_3 = bar(x_plot, times_exp_2, label=\"\", title=\"Zygote - Increasing Adapts\", xlabel=\"Num of Adapts\", ylabel=\"Sampling Time (s)\", titlefontsize=11)\n",
    "    savefig(zy_3, \"images/zygote_time_vs_adapts.png\")\n",
    "    current()\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "900816ed",
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       "</svg>\n"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "begin\n",
    "    accepts_exp_1 = [0.1385, 0.0, 0.0, 0.1546, 0.0072, 0.3012, 0.6132, 0.6209, 0.6673, 0.6383, 0.708]\n",
    "    zy_4 = bar([string(i) for i in 0:10], accepts_exp_1, label=\"\", title=\"Zygote - Average Acceptance vs Increasing Adapts\", xlabel=\"Num of Adapts\", ylabel=\"Average Acceptance Rate\", titlefontsize=11)\n",
    "    savefig(zy_4, \"images/zygote_acceptance_vs_adapts.png\")\n",
    "    current()\n",
    "end"
   ]
  }
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