examples/10_GP_Regression_Derivative_Information/Simple_GP_Regression_Derivative_Information_2d.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GPyTorch regression with derivative information in 2d\n",
    "\n",
    "## Introduction\n",
    "In this notebook, we show how to train a GP regression model in GPyTorch of a 2-dimensional function given function values and derivative observations. We consider modeling the Franke function where the values and derivatives are contaminated with independent $\\mathcal{N}(0, 0.5)$ distributed noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/gpleiss/miniconda3/envs/gpytorch/lib/python3.7/site-packages/matplotlib/__init__.py:1003: UserWarning: Duplicate key in file \"/home/gpleiss/.config/matplotlib/matplotlibrc\", line #57\n",
      "  (fname, cnt))\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import gpytorch\n",
    "import math\n",
    "from matplotlib import cm\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Franke function\n",
    "The following is a vectorized implementation of the 2-dimensional Franke function (https://www.sfu.ca/~ssurjano/franke2d.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def franke(X, Y):\n",
    "    term1 = .75*torch.exp(-((9*X - 2).pow(2) + (9*Y - 2).pow(2))/4)\n",
    "    term2 = .75*torch.exp(-((9*X + 1).pow(2))/49 - (9*Y + 1)/10)\n",
    "    term3 = .5*torch.exp(-((9*X - 7).pow(2) + (9*Y - 3).pow(2))/4)\n",
    "    term4 = .2*torch.exp(-(9*X - 4).pow(2) - (9*Y - 7).pow(2))\n",
    "    \n",
    "    f = term1 + term2 + term3 - term4\n",
    "    dfx = -2*(9*X - 2)*9/4 * term1 - 2*(9*X + 1)*9/49 * term2 + \\\n",
    "          -2*(9*X - 7)*9/4 * term3 + 2*(9*X - 4)*9 * term4\n",
    "    dfy = -2*(9*Y - 2)*9/4 * term1 - 9/10 * term2 + \\\n",
    "          -2*(9*Y - 3)*9/4 * term3 + 2*(9*Y - 7)*9 * term4\n",
    "    \n",
    "    return f, dfx, dfy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up the training data\n",
    "We use a grid with 100 points in $[0,1] \\times [0,1]$ with 10 uniformly distributed points per dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "xv, yv = torch.meshgrid([torch.linspace(0, 1, 10), torch.linspace(0, 1, 10)])\n",
    "train_x = torch.cat((\n",
    "    xv.contiguous().view(xv.numel(), 1), \n",
    "    yv.contiguous().view(yv.numel(), 1)),\n",
    "    dim=1\n",
    ")\n",
    "\n",
    "f, dfx, dfy = franke(train_x[:, 0], train_x[:, 1])\n",
    "train_y = torch.stack([f, dfx, dfy], -1).squeeze(1)\n",
    "train_y += 0.05 * torch.randn(train_y.size())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up the model\n",
    "A GP prior on the function values implies a multi-output GP prior on the function values and the partial derivatives, see 9.4 in http://www.gaussianprocess.org/gpml/chapters/RW9.pdf for more details. This allows using a `MultitaskMultivariateNormal` and `MultitaskGaussianLikelihood` to train a GP model from both function values and gradients. The resulting RBF kernel that models the covariance between the values and partial derivatives has been implemented in `RBFKernelGrad` and the extension of a constant mean is implemented in `ConstantMeanGrad`.\n",
    "\n",
    "The `RBFKernelGrad` is generally worse conditioned than the `RBFKernel`, so we place a lower bound on the noise parameter to keep the smallest eigenvalues of the kernel matrix away from zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "class GPModelWithDerivatives(gpytorch.models.ExactGP):\n",
    "    def __init__(self, train_x, train_y, likelihood):\n",
    "        super(GPModelWithDerivatives, self).__init__(train_x, train_y, likelihood)\n",
    "        self.mean_module = gpytorch.means.ConstantMeanGrad()\n",
    "        self.base_kernel = gpytorch.kernels.RBFKernelGrad()\n",
    "        self.covar_module = gpytorch.kernels.ScaleKernel(self.base_kernel)\n",
    "        \n",
    "    def forward(self, x):\n",
    "        mean_x = self.mean_module(x)\n",
    "        covar_x = self.covar_module(x)\n",
    "        return gpytorch.distributions.MultitaskMultivariateNormal(mean_x, covar_x)\n",
    "\n",
    "likelihood = gpytorch.likelihoods.MultitaskGaussianLikelihood(num_tasks=3)  # Value + x-derivative + y-derivative\n",
    "likelihood.initialize(noise=0.01*train_y.std())  # Require 1% noise (approximately)\n",
    "likelihood.raw_noise.requires_grad = False\n",
    "model = GPModelWithDerivatives(train_x, train_y, likelihood)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training the model\n",
    "The model training is similar to training a standard GP regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/gpleiss/workspace/gpytorch/gpytorch/utils/pivoted_cholesky.py:101: UserWarning: torch.potrs is deprecated in favour of torch.cholesky_solve and will be removed in the next release. Please use torch.cholesky instead and note that the :attr:`upper` argument in torch.cholesky_solve defaults to ``False``.\n",
      "  R = torch.potrs(low_rank_mat, torch.cholesky(shifted_mat, upper=True))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iter 1/50 - Loss: 110.599   lengthscale: 0.693   noise: 0.009\n",
      "Iter 2/50 - Loss: 108.303   lengthscale: 0.644   noise: 0.009\n",
      "Iter 3/50 - Loss: 103.957   lengthscale: 0.598   noise: 0.009\n",
      "Iter 4/50 - Loss: 99.515   lengthscale: 0.554   noise: 0.009\n",
      "Iter 5/50 - Loss: 95.034   lengthscale: 0.513   noise: 0.009\n",
      "Iter 6/50 - Loss: 92.725   lengthscale: 0.473   noise: 0.009\n",
      "Iter 7/50 - Loss: 89.589   lengthscale: 0.436   noise: 0.009\n",
      "Iter 8/50 - Loss: 82.739   lengthscale: 0.402   noise: 0.009\n",
      "Iter 9/50 - Loss: 76.709   lengthscale: 0.370   noise: 0.009\n",
      "Iter 10/50 - Loss: 74.856   lengthscale: 0.340   noise: 0.009\n",
      "Iter 11/50 - Loss: 69.440   lengthscale: 0.313   noise: 0.009\n",
      "Iter 12/50 - Loss: 69.494   lengthscale: 0.291   noise: 0.009\n",
      "Iter 13/50 - Loss: 70.631   lengthscale: 0.277   noise: 0.009\n",
      "Iter 14/50 - Loss: 65.169   lengthscale: 0.272   noise: 0.009\n",
      "Iter 15/50 - Loss: 61.315   lengthscale: 0.273   noise: 0.009\n",
      "Iter 16/50 - Loss: 54.774   lengthscale: 0.279   noise: 0.009\n",
      "Iter 17/50 - Loss: 50.667   lengthscale: 0.287   noise: 0.009\n",
      "Iter 18/50 - Loss: 45.541   lengthscale: 0.297   noise: 0.009\n",
      "Iter 19/50 - Loss: 42.602   lengthscale: 0.306   noise: 0.009\n",
      "Iter 20/50 - Loss: 42.981   lengthscale: 0.313   noise: 0.009\n",
      "Iter 21/50 - Loss: 36.291   lengthscale: 0.316   noise: 0.009\n",
      "Iter 22/50 - Loss: 35.341   lengthscale: 0.315   noise: 0.009\n",
      "Iter 23/50 - Loss: 30.169   lengthscale: 0.309   noise: 0.009\n",
      "Iter 24/50 - Loss: 26.163   lengthscale: 0.301   noise: 0.009\n",
      "Iter 25/50 - Loss: 21.606   lengthscale: 0.290   noise: 0.009\n",
      "Iter 26/50 - Loss: 20.486   lengthscale: 0.279   noise: 0.009\n",
      "Iter 27/50 - Loss: 17.299   lengthscale: 0.270   noise: 0.009\n",
      "Iter 28/50 - Loss: 14.477   lengthscale: 0.265   noise: 0.009\n",
      "Iter 29/50 - Loss: 12.003   lengthscale: 0.265   noise: 0.009\n",
      "Iter 30/50 - Loss: 5.255   lengthscale: 0.268   noise: 0.009\n",
      "Iter 31/50 - Loss: 3.595   lengthscale: 0.270   noise: 0.009\n",
      "Iter 32/50 - Loss: 0.765   lengthscale: 0.270   noise: 0.009\n",
      "Iter 33/50 - Loss: -5.474   lengthscale: 0.270   noise: 0.009\n",
      "Iter 34/50 - Loss: -8.094   lengthscale: 0.268   noise: 0.009\n",
      "Iter 35/50 - Loss: -8.584   lengthscale: 0.264   noise: 0.009\n",
      "Iter 36/50 - Loss: -16.166   lengthscale: 0.258   noise: 0.009\n",
      "Iter 37/50 - Loss: -16.839   lengthscale: 0.251   noise: 0.009\n",
      "Iter 38/50 - Loss: -16.507   lengthscale: 0.245   noise: 0.009\n",
      "Iter 39/50 - Loss: -19.224   lengthscale: 0.242   noise: 0.009\n",
      "Iter 40/50 - Loss: -21.473   lengthscale: 0.240   noise: 0.009\n",
      "Iter 41/50 - Loss: -22.681   lengthscale: 0.238   noise: 0.009\n",
      "Iter 42/50 - Loss: -27.049   lengthscale: 0.234   noise: 0.009\n",
      "Iter 43/50 - Loss: -25.780   lengthscale: 0.233   noise: 0.009\n",
      "Iter 44/50 - Loss: -26.668   lengthscale: 0.233   noise: 0.009\n",
      "Iter 45/50 - Loss: -30.996   lengthscale: 0.234   noise: 0.009\n",
      "Iter 46/50 - Loss: -34.794   lengthscale: 0.233   noise: 0.009\n",
      "Iter 47/50 - Loss: -34.021   lengthscale: 0.228   noise: 0.009\n",
      "Iter 48/50 - Loss: -34.319   lengthscale: 0.222   noise: 0.009\n",
      "Iter 49/50 - Loss: -34.365   lengthscale: 0.215   noise: 0.009\n",
      "Iter 50/50 - Loss: -31.525   lengthscale: 0.209   noise: 0.009\n"
     ]
    }
   ],
   "source": [
    "# Find optimal model hyperparameters\n",
    "model.train()\n",
    "likelihood.train()\n",
    "\n",
    "# Use the adam optimizer\n",
    "optimizer = torch.optim.Adam([\n",
    "    {'params': model.parameters()},  # Includes GaussianLikelihood parameters\n",
    "], lr=0.1)\n",
    "\n",
    "# \"Loss\" for GPs - the marginal log likelihood\n",
    "mll = gpytorch.mlls.ExactMarginalLogLikelihood(likelihood, model)\n",
    "\n",
    "n_iter = 50\n",
    "for i in range(n_iter):\n",
    "    optimizer.zero_grad()\n",
    "    output = model(train_x)\n",
    "    loss = -mll(output, train_y)\n",
    "    loss.backward()\n",
    "    print('Iter %d/%d - Loss: %.3f   lengthscale: %.3f   noise: %.3f' % (\n",
    "        i + 1, n_iter, loss.item(),\n",
    "        model.covar_module.base_kernel.lengthscale.item(),\n",
    "        model.likelihood.noise.item()\n",
    "    ))\n",
    "    optimizer.step()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Making predictions with the model\n",
    "Model predictions are also similar to GP regression with only function values, but we need more CG iterations to get accurate estimates of the predictive variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x720 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set into eval mode\n",
    "model.eval()\n",
    "likelihood.eval()\n",
    "\n",
    "# Initialize plots\n",
    "fig, ax = plt.subplots(2, 3, figsize=(14, 10))\n",
    "\n",
    "# Test points\n",
    "n1, n2 = 50, 50\n",
    "xv, yv = torch.meshgrid([torch.linspace(0, 1, n1), torch.linspace(0, 1, n2)])\n",
    "f, dfx, dfy = franke(xv, yv)\n",
    "\n",
    "# Make predictions\n",
    "with torch.no_grad(), gpytorch.settings.max_cg_iterations(50):\n",
    "    test_x = torch.stack([xv.reshape(n1*n2, 1), yv.reshape(n1*n2, 1)], -1).squeeze(1)\n",
    "    predictions = likelihood(model(test_x))\n",
    "    mean = predictions.mean\n",
    "\n",
    "extent = (xv.min(), xv.max(), yv.max(), yv.min())\n",
    "ax[0, 0].imshow(f, extent=extent, cmap=cm.jet)\n",
    "ax[0, 0].set_title('True values')\n",
    "ax[0, 1].imshow(dfx, extent=extent, cmap=cm.jet)\n",
    "ax[0, 1].set_title('True x-derivatives')\n",
    "ax[0, 2].imshow(dfy, extent=extent, cmap=cm.jet)\n",
    "ax[0, 2].set_title('True y-derivatives')\n",
    "\n",
    "ax[1, 0].imshow(mean[:, 0].detach().numpy().reshape(n1, n2), extent=extent, cmap=cm.jet)\n",
    "ax[1, 0].set_title('Predicted values')\n",
    "ax[1, 1].imshow(mean[:, 1].detach().numpy().reshape(n1, n2), extent=extent, cmap=cm.jet)\n",
    "ax[1, 1].set_title('Predicted x-derivatives')\n",
    "ax[1, 2].imshow(mean[:, 2].detach().numpy().reshape(n1, n2), extent=extent, cmap=cm.jet)\n",
    "ax[1, 2].set_title('Predicted y-derivatives')\n",
    "\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}