{
"cells": [
{
"cell_type": "markdown",
"id": "0",
"metadata": {},
"source": [
"# Batch Independent GPQR"
]
},
{
"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 UnwhitenedVariationalStrategy\n",
"from gpytorch.means import Mean\n",
"from gpytorch.kernels import RBFKernel, ScaleKernel\n",
"from gpytorch.mlls import VariationalELBO\n",
"import matplotlib.pyplot as plt\n",
"\n",
"from gpytorch_qr.models import DirectQuantileGP\n",
"from gpytorch_qr.likelihoods import BatchQuantileGPLikelihood\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\", 10000))"
]
},
{
"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 = torch.linspace(0, 1, 100).reshape(-1, 1).to(device)\n",
"y = (mean(x) + torch.randn(x.shape, device=device).mul(std(x))).squeeze()\n",
"q = torch.linspace(0.1, 0.9, 9).to(device)\n",
"true_quantiles = mean(x) + std(x) * 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.cpu(), true_quantiles.cpu(), \"--\", c=\"gray\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "5",
"metadata": {},
"source": [
"## Prior mean"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6",
"metadata": {},
"outputs": [],
"source": [
"class PriorMean(Mean):\n",
" def __init__(self, batch_shape=torch.Size([])):\n",
" super().__init__()\n",
" self.batch_shape = batch_shape\n",
" self.register_parameter(\"offset\", torch.nn.Parameter(torch.zeros(*batch_shape)))\n",
"\n",
" def forward(self, x):\n",
" res = mean(x).squeeze(-1)\n",
" return res + self.offset.unsqueeze(-1)\n",
"\n",
"\n",
"prior_mean = PriorMean(batch_shape=torch.Size([len(q)])).to(device)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7",
"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_pred.cpu(), prior_mean(x_pred).detach().cpu().T)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "8",
"metadata": {},
"source": [
"## Define models and likelihoods"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9",
"metadata": {},
"outputs": [],
"source": [
"class MyGP_PriorMean(DirectQuantileGP):\n",
" def __init__(self, inducing_points, num_quantiles):\n",
" N, D = inducing_points.size()\n",
" variational_distribution = CholeskyVariationalDistribution(\n",
" N,\n",
" batch_shape=torch.Size([num_quantiles]),\n",
" )\n",
" variational_strategy = UnwhitenedVariationalStrategy(\n",
" self,\n",
" inducing_points,\n",
" variational_distribution,\n",
" learn_inducing_locations=False,\n",
" )\n",
" mean = PriorMean(batch_shape=torch.Size([num_quantiles]))\n",
" covar = ScaleKernel(\n",
" RBFKernel(ard_num_dims=D, batch_shape=torch.Size([num_quantiles])),\n",
" batch_shape=torch.Size([num_quantiles]),\n",
" )\n",
" super().__init__(variational_strategy, mean, covar, 0)\n",
"\n",
"\n",
"inducing_points = x.detach().clone()\n",
"gp_priormean = MyGP_PriorMean(inducing_points, len(q)).to(device)\n",
"likelihood_priormean = BatchQuantileGPLikelihood(q).to(device)"
]
},
{
"cell_type": "markdown",
"id": "10",
"metadata": {},
"source": [
"## Train"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "11",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jisoosong/miniconda3/envs/heavyedge/lib/python3.13/site-packages/gpytorch/distributions/multivariate_normal.py:375: NumericalWarning: Negative variance values detected. This is likely due to numerical instabilities. Rounding negative variances up to 1e-06.\n",
" warnings.warn(\n"
]
}
],
"source": [
"gp_priormean.train()\n",
"likelihood_priormean.train()\n",
"mll = VariationalELBO(likelihood_priormean, gp_priormean, num_data=y.numel())\n",
"optimizer = torch.optim.Adam(\n",
" list(gp_priormean.parameters()) + list(likelihood_priormean.parameters()),\n",
" lr=0.001,\n",
")\n",
"\n",
"for _ in range(n_epochs):\n",
" output = gp_priormean(x)\n",
" loss = -mll(output, y).sum()\n",
" loss.backward()\n",
" optimizer.step()\n",
" optimizer.zero_grad()"
]
},
{
"cell_type": "markdown",
"id": "12",
"metadata": {},
"source": [
"## Evaluate"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "13",
"metadata": {},
"outputs": [],
"source": [
"gp_priormean.eval()\n",
"with torch.no_grad():\n",
" quantiles_priormean = gp_priormean.mean_quantiles(x_pred)"
]
},
{
"cell_type": "markdown",
"id": "14",
"metadata": {},
"source": [
"## Plot result"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "15",
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"colors = plt.cm.tab10(range(len(q)))\n",
"\n",
"plt.scatter(x.cpu(), y.cpu(), c=\"gray\", marker=\".\", alpha=0.1)\n",
"plt.plot(x.cpu(), true_quantiles.cpu(), \"--\", c=\"gray\", alpha=0.5)\n",
"\n",
"for i in range(len(q)):\n",
" plt.plot(x_pred.cpu(), quantiles_priormean[i].cpu(), color=colors[i])\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "16",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "heavyedge",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.13.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}