Remove unused imports in GPyTorch Fully Bayesian example

examples/01_Exact_GPs/GP_Regression_Fully_Bayesian.ipynb

@@ -23,44 +23,57 @@
    "execution_count": 1,
    "metadata": {},
    "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "%load_ext autoreload\n",
+    "%autoreload 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "import math\n",
-    "import torch\n",
+    "import os\n",
+    "\n",
     "import gpytorch\n",
+    "from gpytorch.priors import UniformPrior\n",
+    "import matplotlib.pyplot as plt\n",
     "import pyro\n",
-    "from pyro.infer.mcmc import NUTS, MCMC, HMC\n",
-    "from matplotlib import pyplot as plt\n",
+    "from pyro.infer.mcmc import NUTS, MCMC\n",
+    "import torch\n",
     "\n",
-    "%matplotlib inline\n",
-    "%load_ext autoreload\n",
-    "%autoreload 2"
+    "# this is for running the notebook in our testing framework\n",
+    "smoke_test = ('CI' in os.environ)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
-    "# Training data is 11 points in [0,1] inclusive regularly spaced\n",
+    "# Training data is 4 points in [0,1] inclusive regularly spaced\n",
     "train_x = torch.linspace(0, 1, 4)\n",
     "# True function is sin(2*pi*x) with Gaussian noise\n",
     "train_y = torch.sin(train_x * (2 * math.pi)) + torch.randn(train_x.size()) * 0.2"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [],
    "source": [
     "# We will use the simplest form of GP model, exact inference\n",
     "class ExactGPModel(gpytorch.models.ExactGP):\n",
     "    def __init__(self, train_x, train_y, likelihood):\n",
-    "        super(ExactGPModel, self).__init__(train_x, train_y, likelihood)\n",
+    "        super().__init__(train_x, train_y, likelihood)\n",
     "        self.mean_module = gpytorch.means.ConstantMean()\n",
     "        self.covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.RBFKernel())\n",
-    "    \n",
+    "\n",
     "    def forward(self, x):\n",
     "        mean_x = self.mean_module(x)\n",
     "        covar_x = self.covar_module(x)\n",
@@ -78,7 +91,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -90,25 +103,17 @@
     }
    ],
    "source": [
-    "# this is for running the notebook in our testing framework\n",
-    "import os\n",
-    "smoke_test = ('CI' in os.environ)\n",
     "num_samples = 2 if smoke_test else 100\n",
     "warmup_steps = 2 if smoke_test else 100\n",
     "\n",
-    "\n",
-    "from gpytorch.priors import LogNormalPrior, NormalPrior, UniformPrior\n",
-    "# Use a positive constraint instead of usual GreaterThan(1e-4) so that LogNormal has support over full range.\n",
-    "likelihood = gpytorch.likelihoods.GaussianLikelihood(noise_constraint=gpytorch.constraints.Positive())\n",
+    "likelihood = gpytorch.likelihoods.GaussianLikelihood()\n",
     "model = ExactGPModel(train_x, train_y, likelihood)\n",
     "\n",
     "model.mean_module.register_prior(\"mean_prior\", UniformPrior(-1, 1), \"constant\")\n",
     "model.covar_module.base_kernel.register_prior(\"lengthscale_prior\", UniformPrior(0.01, 0.5), \"lengthscale\")\n",
     "model.covar_module.register_prior(\"outputscale_prior\", UniformPrior(1, 2), \"outputscale\")\n",
     "likelihood.register_prior(\"noise_prior\", UniformPrior(0.01, 0.5), \"noise\")\n",
     "\n",
-    "mll = gpytorch.mlls.ExactMarginalLogLikelihood(likelihood, model)\n",
-    "\n",
     "def pyro_model(x, y):\n",
     "    with gpytorch.settings.fast_computations(False, False, False):\n",
     "        sampled_model = model.pyro_sample_from_prior()\n",
@@ -132,7 +137,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -141,7 +146,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -158,12 +163,12 @@
    "source": [
     "## Plot Mean Functions\n",
     "\n",
-    "In the next cell, we plot the first 25 mean functions on the samep lot. This particular example has a fairly large amount of data for only 1 dimension, so the hyperparameter posterior is quite tight and there is relatively little variance."
+    "In the next cell, we plot the first 25 mean functions on the same plot. This particular example has a fairly large amount of data for only 1 dimension, so the hyperparameter posterior is quite tight and there is relatively little variance."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 62,
+   "execution_count": 8,
    "metadata": {
     "scrolled": false
    },
@@ -185,14 +190,14 @@
     "with torch.no_grad():\n",
     "    # Initialize plot\n",
     "    f, ax = plt.subplots(1, 1, figsize=(4, 3))\n",
-    "    \n",
+    "\n",
     "    # Plot training data as black stars\n",
     "    ax.plot(train_x.numpy(), train_y.numpy(), 'k*', zorder=10)\n",
-    "    \n",
+    "\n",
     "    for i in range(min(num_samples, 25)):\n",
     "        # Plot predictive means as blue line\n",
     "        ax.plot(test_x.numpy(), output.mean[i].detach().numpy(), 'b', linewidth=0.3)\n",
-    "        \n",
+    "\n",
     "    # Shade between the lower and upper confidence bounds\n",
     "    # ax.fill_between(test_x.numpy(), lower.numpy(), upper.numpy(), alpha=0.5)\n",
     "    ax.set_ylim([-3, 3])\n",
@@ -212,7 +217,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 63,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -221,7 +226,7 @@
        "<All keys matched successfully>"
       ]
      },
-     "execution_count": 63,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -235,13 +240,6 @@
     "\n",
     "model.load_state_dict(state_dict)"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {