{
"cells": [
{
"cell_type": "markdown",
"id": "0",
"metadata": {},
"source": [
"(mtgpqr_cg_example)=\n",
"# Multitask Correlated GPQR (Center-Gap)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1",
"metadata": {},
"outputs": [],
"source": [
"import os\n",
"\n",
"import torch\n",
"from torch.distributions import Normal\n",
"from gpytorch.variational import CholeskyVariationalDistribution\n",
"from gpytorch.variational import VariationalStrategy\n",
"from gpytorch.means import ConstantMean\n",
"from gpytorch.kernels import RBFKernel, ScaleKernel\n",
"from gpytorch.mlls import VariationalELBO\n",
"import matplotlib.pyplot as plt\n",
"\n",
"from gpytorch_qr.means import CenterGapMean\n",
"from gpytorch_qr.models import CenterGapQuantileGP\n",
"from gpytorch_qr.variational import CGLmcVariationalStrategy\n",
"from gpytorch_qr.likelihoods import MultitaskCenterGapQuantileGPLikelihood\n",
"\n",
"try:\n",
" import sys\n",
"\n",
" sys.path.insert(0, os.path.abspath(\"..\"))\n",
"\n",
" import config_notebook\n",
"except ImportError:\n",
" print(\"Output will not be deterministic SVG.\")\n",
"\n",
"torch.manual_seed(42)\n",
"device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
"\n",
"n_epochs = int(os.getenv(\"GPYTORCHQR_N_EPOCHS\", 5000))"
]
},
{
"cell_type": "markdown",
"id": "2",
"metadata": {},
"source": [
"## Data preparation"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3",
"metadata": {},
"outputs": [],
"source": [
"def mean(x):\n",
" return torch.cos(x * 2 * 3.14)\n",
"\n",
"\n",
"def std(x):\n",
" return x + 0.1\n",
"\n",
"\n",
"x_range = torch.linspace(0, 1, 100).reshape(-1, 1).to(device)\n",
"x = x_range.repeat(5, 1)\n",
"y = (mean(x) + torch.randn(x.shape, device=device).mul(std(x))).squeeze()\n",
"q = torch.tensor([0.1, 0.25, 0.5, 0.75, 0.9]).to(device)\n",
"true_quantiles = mean(x_range) + std(x_range) * Normal(0, 1).icdf(q)\n",
"x_pred = torch.linspace(0, 1.5, 100).reshape(-1, 1).to(device)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4",
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.scatter(x.cpu(), y.cpu(), c=\"k\", marker=\".\")\n",
"plt.plot(x_range.cpu(), true_quantiles.cpu(), \"--\", c=\"gray\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "5",
"metadata": {},
"source": [
"## Define model and likelihood\n",
"\n",
"To model the correlation between quantiles, the number of latent GP should be smaller than the number of tasks (= number of quantiles)."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6",
"metadata": {},
"outputs": [],
"source": [
"class MyGP(CenterGapQuantileGP):\n",
" def __init__(\n",
" self,\n",
" inducing_points,\n",
" num_quantiles,\n",
" num_lower_quantiles,\n",
" num_latents,\n",
" ):\n",
" N, D = inducing_points.size()\n",
" variational_distribution = CholeskyVariationalDistribution(\n",
" N,\n",
" batch_shape=torch.Size([num_latents]),\n",
" )\n",
" variational_strategy = CGLmcVariationalStrategy(\n",
" VariationalStrategy(\n",
" self,\n",
" inducing_points,\n",
" variational_distribution,\n",
" learn_inducing_locations=True,\n",
" ),\n",
" num_quantiles=num_quantiles,\n",
" num_latents=num_latents,\n",
" )\n",
"\n",
" mean = CenterGapMean(\n",
" ConstantMean(batch_shape=torch.Size([1])),\n",
" ConstantMean(batch_shape=torch.Size([num_latents - 1])),\n",
" latent_dim=-1,\n",
" )\n",
" covar = ScaleKernel(\n",
" RBFKernel(ard_num_dims=D, batch_shape=torch.Size([num_latents])),\n",
" batch_shape=torch.Size([num_latents]),\n",
" )\n",
" super().__init__(variational_strategy, mean, covar, -1, num_lower_quantiles)\n",
"\n",
"\n",
"inducing_points = torch.linspace(0, 1, 10).reshape(-1, 1).to(device)\n",
"central_q_index = (q - 0.5).abs().argmin().item()\n",
"num_latents = len(q) - 2\n",
"gp = MyGP(inducing_points, len(q), central_q_index, num_latents).to(device)\n",
"likelihood = MultitaskCenterGapQuantileGPLikelihood(q, central_q_index).to(device)"
]
},
{
"cell_type": "markdown",
"id": "7",
"metadata": {},
"source": [
"## Train"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8",
"metadata": {},
"outputs": [],
"source": [
"gp.train()\n",
"likelihood.train()\n",
"mll = VariationalELBO(likelihood, gp, num_data=y.numel())\n",
"optimizer = torch.optim.Adam(\n",
" list(gp.parameters()) + list(likelihood.parameters()),\n",
" lr=0.001,\n",
")\n",
"\n",
"for _ in range(n_epochs):\n",
" output = gp(x)\n",
" loss = -mll(output, y)\n",
" loss.backward()\n",
" optimizer.step()\n",
" optimizer.zero_grad()"
]
},
{
"cell_type": "markdown",
"id": "9",
"metadata": {},
"source": [
"## Plot result"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "10",
"metadata": {},
"outputs": [],
"source": [
"gp.eval()\n",
"with torch.no_grad():\n",
" mean_q = gp.mean_quantiles_mc(x_pred)\n",
" lower_q, upper_q = gp.quantile_quantiles_mc(\n",
" x_pred, torch.tensor([0.025, 0.975]).to(device)\n",
" )"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "11",
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"colors = plt.cm.tab10.colors\n",
"\n",
"plt.scatter(x.cpu(), y.cpu(), c=\"gray\", marker=\".\", alpha=0.1)\n",
"plt.plot(x_range.cpu(), true_quantiles.cpu(), \"--\", c=\"k\")\n",
"\n",
"for i in range(len(q)):\n",
" plt.plot(x_pred.cpu(), mean_q[:, i].cpu(), color=colors[i])\n",
" plt.fill_between(\n",
" x_pred.cpu().squeeze(),\n",
" lower_q[:, i].cpu(),\n",
" upper_q[:, i].cpu(),\n",
" color=colors[i],\n",
" alpha=0.3,\n",
" )\n",
"plt.show()"
]
}
],
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"display_name": "heavyedge",
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