{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Intro to AbstractGPs: one-dimensional regression\n",
"\n",
"*You are seeing the\n",
"notebook output generated by\n",
"[Literate.jl](https://github.com/fredrikekre/Literate.jl) from the\n",
"[Julia source file](https://github.com/JuliaGaussianProcesses/AbstractGPs.jl/blob/master/examples/0-intro-1d/script.jl).\n",
"The rendered HTML can be viewed [in the docs](https://juliagaussianprocesses.github.io/AbstractGPs.jl/dev/examples/0-intro-1d/).*"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Setup\n",
"\n",
"Loading the necessary packages."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Random.TaskLocalRNG()"
},
"metadata": {},
"execution_count": 1
}
],
"cell_type": "code",
"source": [
"using AbstractGPs\n",
"using Distributions\n",
"using FillArrays\n",
"using StatsFuns\n",
"\n",
"using Plots\n",
"default(; legend=:outertopright, size=(700, 400))\n",
"\n",
"using Random\n",
"Random.seed!(42) # setting the seed for reproducibility of this notebook"
],
"metadata": {},
"execution_count": 1
},
{
"cell_type": "markdown",
"source": [
"Load toy regression\n",
"[dataset](https://github.com/GPflow/GPflow/blob/7705cee6723f78066981f27954130daaede55dfc/doc/sphinx/notebooks/basics/data/regression_1D.csv)\n",
"taken from GPflow examples."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=1}",
"image/png": 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]
},
"metadata": {},
"execution_count": 2
}
],
"cell_type": "code",
"source": [
"x = [\n",
" 0.8658165855998895,\n",
" 0.6661700880180962,\n",
" 0.8049218148148531,\n",
" 0.7714303440386239,\n",
" 0.14790478354654835,\n",
" 0.8666105548197428,\n",
" 0.007044577166530286,\n",
" 0.026331737288148638,\n",
" 0.17188596617099916,\n",
" 0.8897812990554013,\n",
" 0.24323574561119998,\n",
" 0.028590102134105955,\n",
"]\n",
"y = [\n",
" 1.5255314337144372,\n",
" 3.6434202968230003,\n",
" 3.010885733911661,\n",
" 3.774442382979625,\n",
" 3.3687639483798324,\n",
" 1.5506452040608503,\n",
" 3.790447985799683,\n",
" 3.8689707574953,\n",
" 3.4933565751758713,\n",
" 1.4284538820635841,\n",
" 3.8715350915692364,\n",
" 3.7045949061144983,\n",
"]\n",
"scatter(x, y; xlabel=\"x\", ylabel=\"y\", legend=false)"
],
"metadata": {},
"execution_count": 2
},
{
"cell_type": "markdown",
"source": [
"We split the observations into train and test data."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "4-element Vector{Float64}:\n 3.4933565751758713\n 1.4284538820635841\n 3.8715350915692364\n 3.7045949061144983"
},
"metadata": {},
"execution_count": 3
}
],
"cell_type": "code",
"source": [
"x_train = x[1:8]\n",
"y_train = y[1:8]\n",
"x_test = x[9:end]\n",
"y_test = y[9:end]"
],
"metadata": {},
"execution_count": 3
},
{
"cell_type": "markdown",
"source": [
"We instantiate a Gaussian process with a Matern kernel. The kernel has\n",
"fixed variance and length scale parameters of default value 1."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "AbstractGPs.GP{AbstractGPs.ZeroMean{Float64}, KernelFunctions.Matern52Kernel{Distances.Euclidean}}(AbstractGPs.ZeroMean{Float64}(), Matern 5/2 Kernel (metric = Distances.Euclidean(0.0)))"
},
"metadata": {},
"execution_count": 4
}
],
"cell_type": "code",
"source": [
"f = GP(Matern52Kernel())"
],
"metadata": {},
"execution_count": 4
},
{
"cell_type": "markdown",
"source": [
"We create a finite dimensional projection at the inputs of the training dataset\n",
"observed under Gaussian noise with variance $noise\\_var = 0.1$, and compute the\n",
"log-likelihood of the outputs of the training dataset."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "-25.53057444906228"
},
"metadata": {},
"execution_count": 5
}
],
"cell_type": "code",
"source": [
"noise_var = 0.1\n",
"fx = f(x_train, noise_var)\n",
"logpdf(fx, y_train)"
],
"metadata": {},
"execution_count": 5
},
{
"cell_type": "markdown",
"source": [
"We compute the posterior Gaussian process given the training data, and calculate the\n",
"log-likelihood of the test dataset."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "-2.878533694097381"
},
"metadata": {},
"execution_count": 6
}
],
"cell_type": "code",
"source": [
"p_fx = posterior(fx, y_train)\n",
"logpdf(p_fx(x_test, noise_var), y_test)"
],
"metadata": {},
"execution_count": 6
},
{
"cell_type": "markdown",
"source": [
"We plot the posterior Gaussian process (its mean and a ribbon of 2 standard deviations\n",
"around it) on a grid along with the observations."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=3}",
"image/png": 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]
},
"metadata": {},
"execution_count": 7
}
],
"cell_type": "code",
"source": [
"scatter(\n",
" x_train,\n",
" y_train;\n",
" xlim=(0, 1),\n",
" xlabel=\"x\",\n",
" ylabel=\"y\",\n",
" title=\"posterior (default parameters)\",\n",
" label=\"Train Data\",\n",
")\n",
"scatter!(x_test, y_test; label=\"Test Data\")\n",
"plot!(0:0.001:1, p_fx; label=false, ribbon_scale=2)"
],
"metadata": {},
"execution_count": 7
},
{
"cell_type": "markdown",
"source": [
"## Markov Chain Monte Carlo\n",
"\n",
"Previously we computed the log likelihood of the untuned kernel parameters of the GP.\n",
"We now also perform approximate inference over said kernel parameters using different\n",
"Markov chain Monte Carlo (MCMC) methods. I.e., we approximate the posterior distribution\n",
"of the kernel parameters with samples from a Markov chain.\n",
"\n",
"We define a function which returns the log-likelihood of the data for different variance\n",
"and inverse lengthscale parameters of the Matern kernel. We ensure that these parameters are\n",
"positive with the softplus function\n",
"$$\n",
"f(x) = \\log (1 + \\exp x).\n",
"$$"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "(::Main.var\"##245\".var\"#loglikelihood#1\"{Vector{Float64}, Vector{Float64}}) (generic function with 1 method)"
},
"metadata": {},
"execution_count": 8
}
],
"cell_type": "code",
"source": [
"function gp_loglikelihood(x, y)\n",
" function loglikelihood(params)\n",
" kernel =\n",
" softplus(params[1]) * (Matern52Kernel() ∘ ScaleTransform(softplus(params[2])))\n",
" f = GP(kernel)\n",
" fx = f(x, noise_var)\n",
" return logpdf(fx, y)\n",
" end\n",
" return loglikelihood\n",
"end\n",
"\n",
"const loglik_train = gp_loglikelihood(x_train, y_train)"
],
"metadata": {},
"execution_count": 8
},
{
"cell_type": "markdown",
"source": [
"We define a Gaussian prior for the joint distribution of the two transformed kernel\n",
"parameters. We assume that both parameters are independent with mean 0 and variance 1."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "logprior (generic function with 1 method)"
},
"metadata": {},
"execution_count": 9
}
],
"cell_type": "code",
"source": [
"logprior(params) = logpdf(MvNormal(Eye(2)), params)"
],
"metadata": {},
"execution_count": 9
},
{
"cell_type": "markdown",
"source": [
"### Hamiltonian Monte Carlo\n",
"\n",
"We start with a Hamiltonian Monte Carlo (HMC) sampler. More precisely, we use the\n",
"[No-U-Turn sampler (NUTS)](http://www.jmlr.org/papers/volume15/hoffman14a/hoffman14a.pdf),\n",
"which is provided by the Julia packages\n",
"[AdvancedHMC.jl](https://github.com/TuringLang/AdvancedHMC.jl/) and\n",
"[DynamicHMC.jl](https://github.com/tpapp/DynamicHMC.jl/).\n",
"\n",
"#### AdvancedHMC\n",
"\n",
"We start with performing inference with AdvancedHMC."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using AdvancedHMC\n",
"using ForwardDiff"
],
"metadata": {},
"execution_count": 10
},
{
"cell_type": "markdown",
"source": [
"Set the number of samples to draw and warmup iterations."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "1000"
},
"metadata": {},
"execution_count": 11
}
],
"cell_type": "code",
"source": [
"n_samples = 2_000\n",
"n_adapts = 1_000"
],
"metadata": {},
"execution_count": 11
},
{
"cell_type": "markdown",
"source": [
"AdvancedHMC and DynamicHMC below require us to implement the LogDensityProblems interface for the log joint probability."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using LogDensityProblems\n",
"\n",
"struct LogJointTrain end\n",
"\n",
"# Log joint density\n",
"LogDensityProblems.logdensity(::LogJointTrain, θ) = loglik_train(θ) + logprior(θ)\n",
"\n",
"# The parameter space is two-dimensional\n",
"LogDensityProblems.dimension(::LogJointTrain) = 2\n",
"\n",
"# `LogJointTrain` does not allow to evaluate derivatives of the log density function\n",
"function LogDensityProblems.capabilities(::Type{LogJointTrain})\n",
" return LogDensityProblems.LogDensityOrder{0}()\n",
"end"
],
"metadata": {},
"execution_count": 12
},
{
"cell_type": "markdown",
"source": [
"We use [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) to compute the derivatives of the log joint density with automatic differentiation."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "ForwardDiff AD wrapper for Main.var\"##245\".LogJointTrain(), w/ chunk size 2"
},
"metadata": {},
"execution_count": 13
}
],
"cell_type": "code",
"source": [
"using LogDensityProblemsAD\n",
"\n",
"const logjoint_train = ADgradient(Val(:ForwardDiff), LogJointTrain())"
],
"metadata": {},
"execution_count": 13
},
{
"cell_type": "markdown",
"source": [
"We define an Hamiltonian system of the log joint probability."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Hamiltonian(metric=DiagEuclideanMetric([1.0, 1.0]), kinetic=AdvancedHMC.GaussianKinetic())"
},
"metadata": {},
"execution_count": 14
}
],
"cell_type": "code",
"source": [
"metric = DiagEuclideanMetric(2)\n",
"hamiltonian = Hamiltonian(metric, logjoint_train)"
],
"metadata": {},
"execution_count": 14
},
{
"cell_type": "markdown",
"source": [
"Define a leapfrog solver, with initial step size chosen heuristically."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Leapfrog(ϵ=3.2)"
},
"metadata": {},
"execution_count": 15
}
],
"cell_type": "code",
"source": [
"initial_params = rand(2)\n",
"initial_ϵ = find_good_stepsize(hamiltonian, initial_params)\n",
"integrator = Leapfrog(initial_ϵ)"
],
"metadata": {},
"execution_count": 15
},
{
"cell_type": "markdown",
"source": [
"Define an HMC sampler, with the following components:\n",
"- multinomial sampling scheme,\n",
"- generalised No-U-Turn criteria, and\n",
"- windowed adaption for step-size and diagonal mass matrix"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "StanHMCAdaptor(\n pc=WelfordVar,\n ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=3.2),\n init_buffer=75, term_buffer=50, window_size=25,\n state=window(0, 0), window_splits()\n)"
},
"metadata": {},
"execution_count": 16
}
],
"cell_type": "code",
"source": [
"proposal = HMCKernel(Trajectory{MultinomialTS}(integrator, GeneralisedNoUTurn()))\n",
"adaptor = StanHMCAdaptor(MassMatrixAdaptor(metric), StepSizeAdaptor(0.8, integrator))"
],
"metadata": {},
"execution_count": 16
},
{
"cell_type": "markdown",
"source": [
"We draw samples from the posterior distribution of kernel parameters. These samples\n",
"are in the unconstrained space $\\mathbb{R}^2$."
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"┌ Info: Finished 1000 adapation steps\n",
"│ adaptor =\n",
"│ StanHMCAdaptor(\n",
"│ pc=WelfordVar,\n",
"│ ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.7399471322394748),\n",
"│ init_buffer=75, term_buffer=50, window_size=25,\n",
"│ state=window(76, 950), window_splits(100, 150, 250, 450, 950)\n",
"│ )\n",
"│ κ.τ.integrator = Leapfrog(ϵ=0.74)\n",
"└ h.metric = DiagEuclideanMetric([0.48885885401585605, 0.555 ...])\n",
"┌ Info: Finished 2000 sampling steps for 1 chains in 0.364873445 (s)\n",
"│ h = Hamiltonian(metric=DiagEuclideanMetric([0.48885885401585605, 0.555 ...]), kinetic=AdvancedHMC.GaussianKinetic())\n",
"│ κ = AdvancedHMC.HMCKernel{AdvancedHMC.FullMomentumRefreshment, AdvancedHMC.Trajectory{AdvancedHMC.MultinomialTS, AdvancedHMC.Leapfrog{Float64}, AdvancedHMC.GeneralisedNoUTurn{Float64}}}(AdvancedHMC.FullMomentumRefreshment(), Trajectory{AdvancedHMC.MultinomialTS}(integrator=Leapfrog(ϵ=0.74), tc=AdvancedHMC.GeneralisedNoUTurn{Float64}(10, 1000.0)))\n",
"│ EBFMI_est = 1.1513282853049773\n",
"└ average_acceptance_rate = 0.8582522583685323\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "([[0.6293451231426089, 0.4503389405961936], [0.6293451231426089, 0.4503389405961936], [1.26444921901017, 0.42394743345987757], [1.3765698887739228, 2.224992727432134], [2.2656348654698686, 2.4125160303200444], [2.2656348654698686, 2.4125160303200444], [2.156313245371638, 2.2373255514265833], [2.0552356411410435, 2.2090607230802237], [1.7316243693084636, 2.3100897977252948], [2.87490212282918, 1.9926618074630333] … [2.9150064721156896, 2.413319808272841], [3.520959944758453, 3.1550686312761473], [2.9000192657297656, 3.7019308593569], [3.5372456210727026, 3.1621231544558785], [3.3645935337387556, 3.633436823763938], [2.473582736944092, 3.504171332609368], [2.9665175765621257, 2.5182513980431627], [1.5652575002771316, 1.574117151556278], [2.548420592768714, 1.4134368381080809], [2.3033219965194167, 2.649358916301893]], NamedTuple[(n_steps = 1, is_accept = true, acceptance_rate = 0.0, log_density = -27.548797865093082, hamiltonian_energy = 28.16498485690657, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 789.8321116797472, tree_depth = 1, numerical_error = false, step_size = 3.2, nom_step_size = 3.2, is_adapt = true), (n_steps = 1, is_accept = true, acceptance_rate = 0.0, log_density = -27.548797865093082, hamiltonian_energy = 28.556455551293244, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 103250.09338231276, tree_depth = 0, numerical_error = true, step_size = 7.472207330909228, nom_step_size = 7.472207330909228, is_adapt = true), (n_steps = 1, is_accept = true, acceptance_rate = 1.0, log_density = -26.12578440335325, hamiltonian_energy = 27.652259693524194, hamiltonian_energy_error = -0.4422837368165595, max_hamiltonian_energy_error = -0.4422837368165595, tree_depth = 1, numerical_error = false, step_size = 0.7367547106735891, nom_step_size = 0.7367547106735891, is_adapt = true), (n_steps = 3, is_accept = true, acceptance_rate = 0.9601998762003942, log_density = -23.35811397206731, hamiltonian_energy = 26.20662930167016, hamiltonian_energy_error = -0.6730723877713558, max_hamiltonian_energy_error = -0.6730723877713558, tree_depth = 2, numerical_error = false, step_size = 0.7673324977229767, nom_step_size = 0.7673324977229767, is_adapt = true), (n_steps = 11, is_accept = true, acceptance_rate = 0.9934452178653639, log_density = -22.719136026597965, hamiltonian_energy = 23.096685770801066, hamiltonian_energy_error = -0.470788855143514, max_hamiltonian_energy_error = -0.4798953916115636, tree_depth = 3, numerical_error = false, step_size = 0.9263064447759808, nom_step_size = 0.9263064447759808, is_adapt = true), (n_steps = 1, is_accept = true, acceptance_rate = 0.0005398633622840953, log_density = -22.719136026597965, hamiltonian_energy = 24.192019244158846, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 7.524194483231387, tree_depth = 1, numerical_error = false, step_size = 1.4135557028483081, nom_step_size = 1.4135557028483081, is_adapt = true), (n_steps = 15, is_accept = true, acceptance_rate = 0.9992763568778308, log_density = -22.61231893264123, hamiltonian_energy = 23.079002252189134, hamiltonian_energy_error = -0.0007259383727102886, max_hamiltonian_energy_error = 0.002306028819450745, tree_depth = 3, numerical_error = false, step_size = 0.11237707015439656, nom_step_size = 0.11237707015439656, is_adapt = true), (n_steps = 15, is_accept = true, acceptance_rate = 0.9988327973792602, log_density = -22.607670753976628, hamiltonian_energy = 22.75617737341463, hamiltonian_energy_error = -0.0001245974982531095, max_hamiltonian_energy_error = 0.0024837090868530254, tree_depth = 3, numerical_error = false, step_size = 0.19026062539890193, nom_step_size = 0.19026062539890193, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.9929137605283297, log_density = -22.836416387089766, hamiltonian_energy = 22.864035456294264, hamiltonian_energy_error = 0.016398202480839785, max_hamiltonian_energy_error = 0.017019538655389965, tree_depth = 3, numerical_error = false, step_size = 0.33825177397305806, nom_step_size = 0.33825177397305806, is_adapt = true), (n_steps = 3, is_accept = true, acceptance_rate = 0.890345136719615, log_density = -23.203288626045886, hamiltonian_energy = 23.616291436834565, hamiltonian_energy_error = 0.11108253115779476, max_hamiltonian_energy_error = 0.177677624099438, tree_depth = 2, numerical_error = false, step_size = 0.6084956268395584, nom_step_size = 0.6084956268395584, is_adapt = true) … (n_steps = 47, is_accept = true, acceptance_rate = 0.986951119127562, log_density = -23.36469828703376, hamiltonian_energy = 23.784632154205998, hamiltonian_energy_error = -0.001693373427286815, max_hamiltonian_energy_error = -0.12461240866978329, tree_depth = 5, numerical_error = false, step_size = 0.7399471322394748, nom_step_size = 0.7399471322394748, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8337536043583956, log_density = -25.625881801732678, hamiltonian_energy = 26.060977818202645, hamiltonian_energy_error = 0.2798697151419596, max_hamiltonian_energy_error = 0.29386300441340296, tree_depth = 2, numerical_error = false, step_size = 0.7399471322394748, nom_step_size = 0.7399471322394748, is_adapt = false), (n_steps = 39, is_accept = true, acceptance_rate = 0.9952351239385623, log_density = -25.618937811409843, hamiltonian_energy = 25.876873887728735, hamiltonian_energy_error = 0.029057644403213345, max_hamiltonian_energy_error = -0.44627545095783816, tree_depth = 5, numerical_error = false, step_size = 0.7399471322394748, nom_step_size = 0.7399471322394748, is_adapt = false), (n_steps = 19, is_accept = true, acceptance_rate = 0.9820315330703827, log_density = -25.683223174038165, hamiltonian_energy = 27.084488294013035, hamiltonian_energy_error = -0.05766099203057706, max_hamiltonian_energy_error = -0.5236555438770445, tree_depth = 4, numerical_error = false, step_size = 0.7399471322394748, nom_step_size = 0.7399471322394748, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9621653842257549, log_density = -26.386691870468862, hamiltonian_energy = 26.859122526589164, hamiltonian_energy_error = 0.12047849337885452, max_hamiltonian_energy_error = -0.3033589466740807, tree_depth = 2, numerical_error = false, step_size = 0.7399471322394748, nom_step_size = 0.7399471322394748, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9426705887710044, log_density = -24.549721001930035, hamiltonian_energy = 27.608422564944966, hamiltonian_energy_error = -0.2707970280324581, max_hamiltonian_energy_error = -0.46129591737533815, tree_depth = 2, numerical_error = false, step_size = 0.7399471322394748, nom_step_size = 0.7399471322394748, is_adapt = false), (n_steps = 23, is_accept = true, acceptance_rate = 0.9988442613309477, log_density = -23.526711807177485, hamiltonian_energy = 24.75539939818543, hamiltonian_energy_error = -0.1290482067007197, max_hamiltonian_energy_error = -0.2928197384737423, tree_depth = 4, numerical_error = false, step_size = 0.7399471322394748, nom_step_size = 0.7399471322394748, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9923891973550226, log_density = -23.196723637171107, hamiltonian_energy = 23.832528750472846, hamiltonian_energy_error = -0.0871521545611138, max_hamiltonian_energy_error = -0.13357809629013673, tree_depth = 3, numerical_error = false, step_size = 0.7399471322394748, nom_step_size = 0.7399471322394748, is_adapt = false), (n_steps = 19, is_accept = true, acceptance_rate = 0.9206539884972248, log_density = -23.32611550583593, hamiltonian_energy = 24.154858757270173, hamiltonian_energy_error = 0.08122988505995465, max_hamiltonian_energy_error = 0.20809514057667045, tree_depth = 4, numerical_error = false, step_size = 0.7399471322394748, nom_step_size = 0.7399471322394748, is_adapt = false), (n_steps = 19, is_accept = true, acceptance_rate = 0.9988807844171814, log_density = -22.933343180655985, hamiltonian_energy = 23.434560168407316, hamiltonian_energy_error = -0.06798449709959442, max_hamiltonian_energy_error = -0.12424685912450073, tree_depth = 4, numerical_error = false, step_size = 0.7399471322394748, nom_step_size = 0.7399471322394748, is_adapt = false)])"
},
"metadata": {},
"execution_count": 17
}
],
"cell_type": "code",
"source": [
"samples, _ = sample(\n",
" hamiltonian, proposal, initial_params, n_samples, adaptor, n_adapts; progress=false\n",
")"
],
"metadata": {},
"execution_count": 17
},
{
"cell_type": "markdown",
"source": [
"We transform the samples back to the constrained space and compute the mean of both\n",
"parameters:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "2-element Vector{Float64}:\n 2.3155252060914244\n 2.2891323844057307"
},
"metadata": {},
"execution_count": 18
}
],
"cell_type": "code",
"source": [
"samples_constrained = [map(softplus, p) for p in samples]\n",
"mean_samples = mean(samples_constrained)"
],
"metadata": {},
"execution_count": 18
},
{
"cell_type": "markdown",
"source": [
"We plot a histogram of the samples for the two parameters.\n",
"The vertical line in each graph indicates the mean of the samples."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=4}",
"image/png": 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},
"metadata": {},
"execution_count": 19
}
],
"cell_type": "code",
"source": [
"histogram(\n",
" reduce(hcat, samples_constrained)';\n",
" xlabel=\"sample\",\n",
" ylabel=\"counts\",\n",
" layout=2,\n",
" title=[\"variance\" \"inverse length scale\"],\n",
" legend=false,\n",
")\n",
"vline!(mean_samples'; linewidth=2)"
],
"metadata": {},
"execution_count": 19
},
{
"cell_type": "markdown",
"source": [
"We approximate the log-likelihood of the test data using the posterior Gaussian processes\n",
"for kernels with the sampled kernel parameters. We can observe that there is a significant\n",
"improvement over the log-likelihood of the test data with respect to the posterior\n",
"Gaussian process with default kernel parameters of value 1."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "-1.01607496095987"
},
"metadata": {},
"execution_count": 20
}
],
"cell_type": "code",
"source": [
"function gp_posterior(x, y, p)\n",
" kernel = softplus(p[1]) * (Matern52Kernel() ∘ ScaleTransform(softplus(p[2])))\n",
" f = GP(kernel)\n",
" return posterior(f(x, noise_var), y)\n",
"end\n",
"\n",
"mean(logpdf(gp_posterior(x_train, y_train, p)(x_test, noise_var), y_test) for p in samples)"
],
"metadata": {},
"execution_count": 20
},
{
"cell_type": "markdown",
"source": [
"We sample 5 functions from each posterior GP given by the final 100 samples of kernel\n",
"parameters."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=103}",
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]
},
"metadata": {},
"execution_count": 21
}
],
"cell_type": "code",
"source": [
"plt = plot(; xlim=(0, 1), xlabel=\"x\", ylabel=\"y\", title=\"posterior (AdvancedHMC)\")\n",
"for (i, p) in enumerate(samples[(end - 100):end])\n",
" sampleplot!(\n",
" plt,\n",
" 0:0.02:1,\n",
" gp_posterior(x_train, y_train, p);\n",
" samples=5,\n",
" seriescolor=\"red\",\n",
" label=(i == 1 ? \"samples\" : nothing),\n",
" )\n",
"end\n",
"scatter!(plt, x_train, y_train; label=\"Train Data\", markercolor=1)\n",
"scatter!(plt, x_test, y_test; label=\"Test Data\", markercolor=2)\n",
"plt"
],
"metadata": {},
"execution_count": 21
},
{
"cell_type": "markdown",
"source": [
"#### DynamicHMC\n",
"\n",
"We repeat the inference with DynamicHMC."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "2×2000 Matrix{Float64}:\n 1.79152 2.14844 2.01055 2.18536 … 2.81355 2.2351 2.16967 1.99369\n 1.35666 2.28557 2.0004 2.25738 1.54292 1.74366 2.23667 1.98292"
},
"metadata": {},
"execution_count": 22
}
],
"cell_type": "code",
"source": [
"using DynamicHMC\n",
"\n",
"samples =\n",
" mcmc_with_warmup(\n",
" Random.GLOBAL_RNG, logjoint_train, n_samples; reporter=NoProgressReport()\n",
" ).posterior_matrix"
],
"metadata": {},
"execution_count": 22
},
{
"cell_type": "markdown",
"source": [
"We transform the samples back to the constrained space and compute the mean of both\n",
"parameters:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "2-element Vector{Float64}:\n 2.3212949500446447\n 2.2919336433863458"
},
"metadata": {},
"execution_count": 23
}
],
"cell_type": "code",
"source": [
"samples_constrained = map(softplus, samples)\n",
"mean_samples = vec(mean(samples_constrained; dims=2))"
],
"metadata": {},
"execution_count": 23
},
{
"cell_type": "markdown",
"source": [
"We plot a histogram of the samples for the two parameters.\n",
"The vertical line in each graph indicates the mean of the samples."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=4}",
"image/png": 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"</svg>\n"
]
},
"metadata": {},
"execution_count": 24
}
],
"cell_type": "code",
"source": [
"histogram(\n",
" samples_constrained';\n",
" xlabel=\"sample\",\n",
" ylabel=\"counts\",\n",
" layout=2,\n",
" title=[\"variance\" \"inverse length scale\"],\n",
" legend=false,\n",
")\n",
"vline!(mean_samples'; linewidth=2)"
],
"metadata": {},
"execution_count": 24
},
{
"cell_type": "markdown",
"source": [
"Again we can observe that there is a significant improvement over the log-likelihood\n",
"of the test data with respect to the posterior Gaussian process with default kernel\n",
"parameters."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "-11.026582822135412"
},
"metadata": {},
"execution_count": 25
}
],
"cell_type": "code",
"source": [
"mean(logpdf(gp_posterior(x_train, y_train, p)(x_test), y_test) for p in eachcol(samples))"
],
"metadata": {},
"execution_count": 25
},
{
"cell_type": "markdown",
"source": [
"We sample a function from the posterior GP for the final 100 samples of kernel\n",
"parameters."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=103}",
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]
},
"metadata": {},
"execution_count": 26
}
],
"cell_type": "code",
"source": [
"plt = plot(; xlim=(0, 1), xlabel=\"x\", ylabel=\"y\", title=\"posterior (DynamicHMC)\")\n",
"scatter!(plt, x_train, y_train; label=\"Train Data\")\n",
"scatter!(plt, x_test, y_test; label=\"Test Data\")\n",
"for i in (n_samples - 100):n_samples\n",
" p = @view samples[:, i]\n",
" sampleplot!(plt, 0:0.02:1, gp_posterior(x_train, y_train, p); seriescolor=\"red\")\n",
"end\n",
"plt"
],
"metadata": {},
"execution_count": 26
},
{
"cell_type": "markdown",
"source": [
"### Elliptical slice sampling\n",
"\n",
"Instead of HMC, we use\n",
"[elliptical slice sampling](http://proceedings.mlr.press/v9/murray10a/murray10a.pdf)\n",
"which is provided by the Julia package\n",
"[EllipticalSliceSampling.jl](https://github.com/TuringLang/EllipticalSliceSampling.jl/)."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using EllipticalSliceSampling"
],
"metadata": {},
"execution_count": 27
},
{
"cell_type": "markdown",
"source": [
"We draw 2000 samples from the posterior distribution of kernel parameters."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "2000-element Vector{Vector{Float64}}:\n [0.4825349401162675, 0.7978077587032283]\n [0.16308616800412376, 2.0073621997797915]\n [0.1665376411425717, 1.7772245503556816]\n [0.3106804707472905, 0.7544449292193193]\n [0.5248583204347383, 0.6161369941599566]\n [1.4680829391935906, 0.7088288026364206]\n [1.9058743176695072, 1.4265231883971436]\n [2.0314550429278757, 1.4016090581271403]\n [1.9068832983572446, 1.4267815411804297]\n [2.0780306611959, 1.0603507979632716]\n ⋮\n [2.785001214361432, 2.1667515068076932]\n [3.140260464923709, 2.55117112502559]\n [3.1251220585083885, 2.566554526103868]\n [3.111402480032247, 2.542795968946109]\n [3.0817827270912908, 2.5443832079570914]\n [2.260205813283638, 2.272428857714431]\n [2.663459182484464, 2.0270359277901346]\n [2.664901623201619, 2.0260247147516792]\n [2.7802812843876454, 2.523759681041229]"
},
"metadata": {},
"execution_count": 28
}
],
"cell_type": "code",
"source": [
"samples = sample(ESSModel(\n",
" MvNormal(Eye(2)), # Gaussian prior\n",
" loglik_train,\n",
"), ESS(), n_samples; progress=false)"
],
"metadata": {},
"execution_count": 28
},
{
"cell_type": "markdown",
"source": [
"We transform the samples back to the constrained space and compute the mean of both\n",
"parameters:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "2-element Vector{Float64}:\n 2.311675865667157\n 2.2041974492869105"
},
"metadata": {},
"execution_count": 29
}
],
"cell_type": "code",
"source": [
"samples_constrained = [map(softplus, p) for p in samples]\n",
"mean_samples = mean(samples_constrained)"
],
"metadata": {},
"execution_count": 29
},
{
"cell_type": "markdown",
"source": [
"We plot a histogram of the samples for the two parameters.\n",
"The vertical line in each graph indicates the mean of the samples."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=4}",
"image/png": 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]
},
"metadata": {},
"execution_count": 30
}
],
"cell_type": "code",
"source": [
"histogram(\n",
" reduce(hcat, samples_constrained)';\n",
" xlabel=\"sample\",\n",
" ylabel=\"counts\",\n",
" layout=2,\n",
" title=[\"variance\" \"inverse length scale\"],\n",
")\n",
"vline!(mean_samples'; layout=2, labels=\"mean\")"
],
"metadata": {},
"execution_count": 30
},
{
"cell_type": "markdown",
"source": [
"Again we can observe that there is a significant improvement over the log-likelihood\n",
"of the test data with respect to the posterior Gaussian process with default kernel\n",
"parameters."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "-11.893223787793055"
},
"metadata": {},
"execution_count": 31
}
],
"cell_type": "code",
"source": [
"mean(logpdf(gp_posterior(x_train, y_train, p)(x_test), y_test) for p in samples)"
],
"metadata": {},
"execution_count": 31
},
{
"cell_type": "markdown",
"source": [
"We sample a function from the posterior GP for the final 100 samples of kernel\n",
"parameters."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=103}",
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]
},
"metadata": {},
"execution_count": 32
}
],
"cell_type": "code",
"source": [
"plt = plot(;\n",
" xlim=(0, 1), xlabel=\"x\", ylabel=\"y\", title=\"posterior (EllipticalSliceSampling)\"\n",
")\n",
"scatter!(plt, x_train, y_train; label=\"Train Data\")\n",
"scatter!(plt, x_test, y_test; label=\"Test Data\")\n",
"for p in samples[(end - 100):end]\n",
" sampleplot!(plt, 0:0.02:1, gp_posterior(x_train, y_train, p); seriescolor=\"red\")\n",
"end\n",
"plt"
],
"metadata": {},
"execution_count": 32
},
{
"cell_type": "markdown",
"source": [
"## Variational Inference\n",
"\n",
"Sanity check for the Evidence Lower BOund (ELBO) implemented according to\n",
"M. K. Titsias's _Variational learning of inducing variables in sparse Gaussian processes_."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "-25.695544888670685"
},
"metadata": {},
"execution_count": 33
}
],
"cell_type": "code",
"source": [
"elbo(VFE(f(rand(5))), fx, y_train)"
],
"metadata": {},
"execution_count": 33
},
{
"cell_type": "markdown",
"source": [
"We use the LBFGS algorithm to maximize the given ELBO. It is provided by the Julia\n",
"package [Optim.jl](https://github.com/JuliaNLSolvers/Optim.jl)."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using Optim"
],
"metadata": {},
"execution_count": 34
},
{
"cell_type": "markdown",
"source": [
"We define a function which returns the negative ELBO for different variance and inverse\n",
"lengthscale parameters of the Matern kernel and different pseudo-points. We ensure that\n",
"the kernel parameters are positive with the softplus function\n",
"$$\n",
"f(x) = \\log (1 + \\exp x),\n",
"$$\n",
"and that the pseudo-points are in the unit interval $[0,1]$ with the logistic function\n",
"$$\n",
"f(x) = \\frac{1}{1 + \\exp{(-x)}}.\n",
"$$"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "objective_function (generic function with 1 method)"
},
"metadata": {},
"execution_count": 35
}
],
"cell_type": "code",
"source": [
"jitter = 1e-6 # \"observing\" the latent process with some (small) amount of jitter improves numerical stability\n",
"\n",
"function objective_function(x, y)\n",
" function negative_elbo(params)\n",
" kernel =\n",
" softplus(params[1]) * (Matern52Kernel() ∘ ScaleTransform(softplus(params[2])))\n",
" f = GP(kernel)\n",
" fx = f(x, noise_var)\n",
" z = logistic.(params[3:end])\n",
" approx = VFE(f(z, jitter))\n",
" return -elbo(approx, fx, y)\n",
" end\n",
" return negative_elbo\n",
"end"
],
"metadata": {},
"execution_count": 35
},
{
"cell_type": "markdown",
"source": [
"We randomly initialize the kernel parameters and 5 pseudo points, and minimize the\n",
"negative ELBO with the LBFGS algorithm and obtain the following optimal parameters:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": " * Status: success\n\n * Candidate solution\n Final objective value: 1.086925e+01\n\n * Found with\n Algorithm: L-BFGS\n\n * Convergence measures\n |x - x'| = 0.00e+00 ≤ 0.0e+00\n |x - x'|/|x'| = 0.00e+00 ≤ 0.0e+00\n |f(x) - f(x')| = 0.00e+00 ≤ 0.0e+00\n |f(x) - f(x')|/|f(x')| = 0.00e+00 ≤ 0.0e+00\n |g(x)| = 2.57e-08 ≰ 1.0e-08\n\n * Work counters\n Seconds run: 0 (vs limit Inf)\n Iterations: 28\n f(x) calls: 73\n ∇f(x) calls: 73\n"
},
"metadata": {},
"execution_count": 36
}
],
"cell_type": "code",
"source": [
"x0 = rand(7)\n",
"opt = optimize(objective_function(x_train, y_train), x0, LBFGS())"
],
"metadata": {},
"execution_count": 36
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "7-element Vector{Float64}:\n 8.379380148385884\n 3.9327375478736575\n -1.7583267674423126\n -4.133679980107152\n 1.2763097365197713\n 0.6917102805170131\n 1.8479571192093442"
},
"metadata": {},
"execution_count": 37
}
],
"cell_type": "code",
"source": [
"opt.minimizer"
],
"metadata": {},
"execution_count": 37
},
{
"cell_type": "markdown",
"source": [
"The optimized value of the variance is"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "8.379609674232473"
},
"metadata": {},
"execution_count": 38
}
],
"cell_type": "code",
"source": [
"softplus(opt.minimizer[1])"
],
"metadata": {},
"execution_count": 38
},
{
"cell_type": "markdown",
"source": [
"and of the inverse lengthscale is"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "3.9521381047409525"
},
"metadata": {},
"execution_count": 39
}
],
"cell_type": "code",
"source": [
"softplus(opt.minimizer[2])"
],
"metadata": {},
"execution_count": 39
},
{
"cell_type": "markdown",
"source": [
"We compute the log-likelihood of the test data for the resulting approximate\n",
"posterior. We can observe that there is a significant improvement over the\n",
"log-likelihood with the default kernel parameters of value 1."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "-2.068599768743355"
},
"metadata": {},
"execution_count": 40
}
],
"cell_type": "code",
"source": [
"opt_kernel =\n",
" softplus(opt.minimizer[1]) *\n",
" (Matern52Kernel() ∘ ScaleTransform(softplus(opt.minimizer[2])))\n",
"opt_f = GP(opt_kernel)\n",
"opt_fx = opt_f(x_train, noise_var)\n",
"ap = posterior(VFE(opt_f(logistic.(opt.minimizer[3:end]), jitter)), opt_fx, y_train)\n",
"logpdf(ap(x_test, noise_var), y_test)"
],
"metadata": {},
"execution_count": 40
},
{
"cell_type": "markdown",
"source": [
"We visualize the approximate posterior with optimized parameters."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=4}",
"image/png": 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]
},
"metadata": {},
"execution_count": 41
}
],
"cell_type": "code",
"source": [
"scatter(\n",
" x_train,\n",
" y_train;\n",
" xlim=(0, 1),\n",
" xlabel=\"x\",\n",
" ylabel=\"y\",\n",
" title=\"posterior (VI with sparse grid)\",\n",
" label=\"Train Data\",\n",
")\n",
"scatter!(x_test, y_test; label=\"Test Data\")\n",
"plot!(0:0.001:1, ap; label=false, ribbon_scale=2)\n",
"vline!(logistic.(opt.minimizer[3:end]); label=\"Pseudo-points\")"
],
"metadata": {},
"execution_count": 41
},
{
"cell_type": "markdown",
"source": [
"## Exact Gaussian Process Inference\n",
"\n",
"Here we use Type-II MLE to train the hyperparameters of the Gaussian process.\n",
"This means that our loss function is the negative log marginal likelihood."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"We re-calculate the log-likelihood of the test dataset with the\n",
"default kernel parameters of value 1 for the sake of comparison."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "-232.51565975779937"
},
"metadata": {},
"execution_count": 42
}
],
"cell_type": "code",
"source": [
"logpdf(p_fx(x_test), y_test)"
],
"metadata": {},
"execution_count": 42
},
{
"cell_type": "markdown",
"source": [
"We define a function which returns the negative log marginal\n",
"likelihood for different variance and inverse lengthscale parameters\n",
"of the Matern kernel and different pseudo-points. We ensure that the\n",
"kernel parameters are positive with the softplus function\n",
"$f(x) = \\log (1 + \\exp x)$."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "loss_function (generic function with 1 method)"
},
"metadata": {},
"execution_count": 43
}
],
"cell_type": "code",
"source": [
"function loss_function(x, y)\n",
" function negativelogmarginallikelihood(params)\n",
" kernel =\n",
" softplus(params[1]) * (Matern52Kernel() ∘ ScaleTransform(softplus(params[2])))\n",
" f = GP(kernel)\n",
" fx = f(x, noise_var)\n",
" return -logpdf(fx, y)\n",
" end\n",
" return negativelogmarginallikelihood\n",
"end"
],
"metadata": {},
"execution_count": 43
},
{
"cell_type": "markdown",
"source": [
"We randomly initialize the kernel parameters, and minimize the\n",
"negative log marginal likelihood with the LBFGS algorithm\n",
"and obtain the following optimal parameters:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": " * Status: success\n\n * Candidate solution\n Final objective value: 1.085252e+01\n\n * Found with\n Algorithm: L-BFGS\n\n * Convergence measures\n |x - x'| = 9.94e-05 ≰ 0.0e+00\n |x - x'|/|x'| = 1.19e-05 ≰ 0.0e+00\n |f(x) - f(x')| = 9.14e-10 ≰ 0.0e+00\n |f(x) - f(x')|/|f(x')| = 8.43e-11 ≰ 0.0e+00\n |g(x)| = 8.35e-09 ≤ 1.0e-08\n\n * Work counters\n Seconds run: 0 (vs limit Inf)\n Iterations: 15\n f(x) calls: 50\n ∇f(x) calls: 50\n"
},
"metadata": {},
"execution_count": 44
}
],
"cell_type": "code",
"source": [
"θ0 = randn(2)\n",
"opt = Optim.optimize(loss_function(x_train, y_train), θ0, LBFGS())"
],
"metadata": {},
"execution_count": 44
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "2-element Vector{Float64}:\n 8.385520807797775\n 3.968794157371341"
},
"metadata": {},
"execution_count": 45
}
],
"cell_type": "code",
"source": [
"opt.minimizer"
],
"metadata": {},
"execution_count": 45
},
{
"cell_type": "markdown",
"source": [
"The optimized value of the variance is"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "8.38574892868317"
},
"metadata": {},
"execution_count": 46
}
],
"cell_type": "code",
"source": [
"softplus(opt.minimizer[1])"
],
"metadata": {},
"execution_count": 46
},
{
"cell_type": "markdown",
"source": [
"and of the inverse lengthscale is"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "3.9875140470052703"
},
"metadata": {},
"execution_count": 47
}
],
"cell_type": "code",
"source": [
"softplus(opt.minimizer[2])"
],
"metadata": {},
"execution_count": 47
},
{
"cell_type": "markdown",
"source": [
"We compute the log-likelihood of the test data for the resulting optimized\n",
"posterior. We can observe that there is a significant improvement over the\n",
"log-likelihood with the default kernel parameters of value 1."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "-2.092647844311541"
},
"metadata": {},
"execution_count": 48
}
],
"cell_type": "code",
"source": [
"opt_kernel =\n",
" softplus(opt.minimizer[1]) *\n",
" (Matern52Kernel() ∘ ScaleTransform(softplus(opt.minimizer[2])))\n",
"\n",
"opt_f = GP(opt_kernel)\n",
"opt_fx = opt_f(x_train, noise_var)\n",
"opt_p_fx = posterior(opt_fx, y_train)\n",
"logpdf(opt_p_fx(x_test, noise_var), y_test)"
],
"metadata": {},
"execution_count": 48
},
{
"cell_type": "markdown",
"source": [
"We visualize the posterior with optimized parameters."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=3}",
"image/png": 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]
},
"metadata": {},
"execution_count": 49
}
],
"cell_type": "code",
"source": [
"scatter(\n",
" x_train,\n",
" y_train;\n",
" xlim=(0, 1),\n",
" xlabel=\"x\",\n",
" ylabel=\"y\",\n",
" title=\"posterior (optimized parameters)\",\n",
" label=\"Train Data\",\n",
")\n",
"scatter!(x_test, y_test; label=\"Test Data\")\n",
"plot!(0:0.001:1, opt_p_fx; label=false, ribbon_scale=2)"
],
"metadata": {},
"execution_count": 49
},
{
"cell_type": "markdown",
"source": [
"<hr />\n",
"<h6>Package and system information</h6>\n",
"<details>\n",
"<summary>Package information (click to expand)</summary>\n",
"<pre>\n",
"Status `~/work/AbstractGPs.jl/AbstractGPs.jl/examples/0-intro-1d/Project.toml`\n",
" [99985d1d] AbstractGPs v0.5.23 `/home/runner/work/AbstractGPs.jl/AbstractGPs.jl#28319c5`\n",
"⌅ [0bf59076] AdvancedHMC v0.6.4\n",
" [31c24e10] Distributions v0.25.118\n",
" [bbc10e6e] DynamicHMC v3.5.0\n",
" [cad2338a] EllipticalSliceSampling v2.0.0\n",
" [1a297f60] FillArrays v1.13.0\n",
" [f6369f11] ForwardDiff v0.10.38\n",
" [98b081ad] Literate v2.20.1\n",
" [6fdf6af0] LogDensityProblems v2.1.2\n",
" [996a588d] LogDensityProblemsAD v1.13.0\n",
" [429524aa] Optim v1.11.0\n",
" [91a5bcdd] Plots v1.40.10\n",
" [4c63d2b9] StatsFuns v1.3.2\n",
" [9a3f8284] Random v1.11.0\n",
"Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`\n",
"</pre>\n",
"To reproduce this notebook's package environment, you can\n",
"<a href=\"./Manifest.toml\">\n",
"download the full Manifest.toml</a>.\n",
"</details>\n",
"<details>\n",
"<summary>System information (click to expand)</summary>\n",
"<pre>\n",
"Julia Version 1.11.4\n",
"Commit 8561cc3d68d (2025-03-10 11:36 UTC)\n",
"Build Info:\n",
" Official https://julialang.org/ release\n",
"Platform Info:\n",
" OS: Linux (x86_64-linux-gnu)\n",
" CPU: 4 × AMD EPYC 7763 64-Core Processor\n",
" WORD_SIZE: 64\n",
" LLVM: libLLVM-16.0.6 (ORCJIT, znver3)\n",
"Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)\n",
"Environment:\n",
" JULIA_DEBUG = Documenter\n",
" JULIA_LOAD_PATH = :/home/runner/.julia/packages/JuliaGPsDocs/7M86H/src\n",
"</pre>\n",
"</details>"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"---\n",
"\n",
"*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
],
"metadata": {}
}
],
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"file_extension": ".jl",
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