sparse_hetero_example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import gpflow as gp\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "import matplotlib.pyplot as plt\n",
    "from gp_package.VSHGP import VSHGP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x121c78e5a80>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate some synthetic data\n",
    "np.random.seed(42)\n",
    "\n",
    "n = 1000 # number of samples\n",
    "\n",
    "X  = np.reshape(np.linspace(-10, 10, num = n), (-1, 1))\n",
    "SX = 0.05 + (1.0 / (1 + np.exp(-0.2 * X))) * (1 + np.sin(2 * X)) * 0.2   \n",
    "\n",
    "Y = np.sinc(X) + np.random.randn(X.shape[0], X.shape[1]) * SX\n",
    "Xs = np.reshape(np.linspace(-10, 10, num = n), (-1, 1))\n",
    "\n",
    "# normalize Y to zero mean and unit variance\n",
    "Ynorm = (Y - Y.mean()) / Y.std()\n",
    "\n",
    "# plot the training data\n",
    "plt.figure(figsize = (8, 4))\n",
    "plt.plot(Xs, Ynorm, 'k.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "╒═══════════════════════╤═══════════╤═════════════╤═════════╤═════════════╤═══════════╤═════════╤═══════════╕\n",
      "│ name                  │ class     │ transform   │ prior   │ trainable   │ shape     │ dtype   │ value     │\n",
      "╞═══════════════════════╪═══════════╪═════════════╪═════════╪═════════════╪═══════════╪═════════╪═══════════╡\n",
      "│ VSHGP.Kf.variance     │ Parameter │ Softplus    │         │ True        │ ()        │ float64 │ 1.0       │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────┤\n",
      "│ VSHGP.Kf.lengthscales │ Parameter │ Softplus    │         │ True        │ ()        │ float64 │ 1.0       │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────┤\n",
      "│ VSHGP.Kg.variance     │ Parameter │ Softplus    │         │ True        │ ()        │ float64 │ 1.0       │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────┤\n",
      "│ VSHGP.Kg.lengthscales │ Parameter │ Softplus    │         │ True        │ ()        │ float64 │ 1.0       │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────┤\n",
      "│ VSHGP.inducing_f.Z    │ Parameter │ Identity    │         │ True        │ (50, 1)   │ float64 │ [[-10.... │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────┤\n",
      "│ VSHGP.inducing_g.Z    │ Parameter │ Identity    │         │ True        │ (50, 1)   │ float64 │ [[-10.... │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────┤\n",
      "│ VSHGP.mu0             │ Parameter │ Identity    │         │ True        │ ()        │ float64 │ -9.21034  │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────┤\n",
      "│ VSHGP.diaglambda      │ Parameter │ Softplus    │         │ True        │ (1000, 1) │ float64 │ [[0.5...  │\n",
      "╘═══════════════════════╧═══════════╧═════════════╧═════════╧═════════════╧═══════════╧═════════╧═══════════╛\n"
     ]
    }
   ],
   "source": [
    "kernel_f = gp.kernels.SquaredExponential()\n",
    "kernel_g = gp.kernels.SquaredExponential()\n",
    "# how many inducing points?\n",
    "M = 50\n",
    "\n",
    "F = np.linspace(X.min(), X.max(), M)[:, None] # inducing points for the mean GP\n",
    "G = np.linspace(X.min(), X.max(), M)[:, None] # inducing points for the log-var GP\n",
    "\n",
    "inducing_f = gp.inducing_variables.InducingPoints(F)\n",
    "inducing_g = gp.inducing_variables.InducingPoints(G)\n",
    "\n",
    "model = VSHGP(data= (X, Ynorm), kernel_f=kernel_f, kernel_g =kernel_g, inducing_points_f= inducing_f, inducing_points_g= inducing_g)\n",
    "\n",
    "gp.utilities.print_summary(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [02:12<00:00,  7.53it/s, loss=439]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "╒═══════════════════════╤═══════════╤═════════════╤═════════╤═════════════╤═══════════╤═════════╤═══════════════╕\n",
      "│ name                  │ class     │ transform   │ prior   │ trainable   │ shape     │ dtype   │ value         │\n",
      "╞═══════════════════════╪═══════════╪═════════════╪═════════╪═════════════╪═══════════╪═════════╪═══════════════╡\n",
      "│ VSHGP.Kf.variance     │ Parameter │ Softplus    │         │ True        │ ()        │ float64 │ 1.00002       │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────────┤\n",
      "│ VSHGP.Kf.lengthscales │ Parameter │ Softplus    │         │ True        │ ()        │ float64 │ 0.76538       │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────────┤\n",
      "│ VSHGP.Kg.variance     │ Parameter │ Softplus    │         │ True        │ ()        │ float64 │ 1.472         │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────────┤\n",
      "│ VSHGP.Kg.lengthscales │ Parameter │ Softplus    │         │ True        │ ()        │ float64 │ 1.26271       │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────────┤\n",
      "│ VSHGP.inducing_f.Z    │ Parameter │ Identity    │         │ True        │ (50, 1)   │ float64 │ [[-9.96034... │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────────┤\n",
      "│ VSHGP.inducing_g.Z    │ Parameter │ Identity    │         │ True        │ (50, 1)   │ float64 │ [[-9.68668... │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────────┤\n",
      "│ VSHGP.mu0             │ Parameter │ Identity    │         │ True        │ ()        │ float64 │ -8.59204      │\n",
      "├───────────────────────┼───────────┼─────────────┼─────────┼─────────────┼───────────┼─────────┼───────────────┤\n",
      "│ VSHGP.diaglambda      │ Parameter │ Softplus    │         │ True        │ (1000, 1) │ float64 │ [[0.66517...  │\n",
      "╘═══════════════════════╧═══════════╧═════════════╧═════════╧═════════════╧═══════════╧═════════╧═══════════════╛\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "params = dict()\n",
    "params['no_steps'] = 1000\n",
    "params['log_interval']= 1\n",
    "params['learning_rate'] = 0.0001 # start with a small learning rate\n",
    "\n",
    "# Note: initially we set the inducing points to be non-trainable\n",
    "gp.utilities.set_trainable(model.inducing_f, True)\n",
    "gp.utilities.set_trainable(model.inducing_g, True)\n",
    "\n",
    "model.fit(params, compile=True) \n",
    "\n",
    "# look at the model summary\n",
    "gp.utilities.print_summary(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x121d0a4e8c0>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the results\n",
    "\n",
    "xtest = np.linspace(-10, 10 , 100)[:, None]\n",
    "mean, var = model.predict_f(xtest)\n",
    "\n",
    "plt.figure(figsize = (8,4))\n",
    "plt.plot(X, Ynorm, 'b.', label = 'data')\n",
    "plt.plot(xtest, mean, 'r-', label = 'mean')\n",
    "plt.plot(xtest, mean + 1.96 * np.sqrt(var), 'k-', label = '+2 std')\n",
    "plt.plot(xtest, mean - 1.96 * np.sqrt(var), 'k-', label = '-2 std')\n",
    "plt.plot(model.inducing_f.Z.numpy(), Ynorm.max() * 1.1 * np.ones_like(F), 'r*', markersize = 4, label = 'Inducing F')\n",
    "plt.plot(model.inducing_g.Z.numpy(), Ynorm.min() * 1.1 * np.ones_like(G), 'm*', markersize = 4, label = 'Inducing G')\n",
    "plt.legend(fontsize = 8, loc = 'upper left')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}