demo5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Decision tree regression learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "\n",
    "from sklearn.tree import DecisionTreeRegressor, export_graphviz\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from IPython.display import display, SVG, Image\n",
    "from graphviz import Source\n",
    "\n",
    "import ipywidgets as widgets\n",
    "\n",
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "xmin = 0.01\n",
    "xmax = 1\n",
    "xres = 100\n",
    "plot_res = 10000\n",
    "\n",
    "x = np.linspace(xmin, xmax, xres)\n",
    "x_plot = np.linspace(xmin, xmax, plot_res)\n",
    "y = np.polynomial.polynomial.polyval(x, [0, 2, 5]) + np.sin(10*x) + 0.2 * np.random.normal(size=xres)\n",
    "\n",
    "depth_max = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def classify(depth):\n",
    "    return DecisionTreeRegressor(max_depth=depth, random_state=1).fit(x.reshape(-1, 1), y)\n",
    "\n",
    "# from https://scikit-learn.org/stable/auto_examples/tree/plot_unveil_tree_structure.html\n",
    "def parse_tree(dtree):\n",
    "    n_nodes = dtree.tree_.node_count\n",
    "    children_left = dtree.tree_.children_left\n",
    "    children_right = dtree.tree_.children_right\n",
    "    feature = dtree.tree_.feature\n",
    "    threshold = dtree.tree_.threshold\n",
    "\n",
    "    # The tree structure can be traversed to compute various properties such\n",
    "    # as the depth of each node and whether or not it is a leaf.\n",
    "    node_depth = np.zeros(shape=n_nodes, dtype=np.int64)\n",
    "    is_leaves = np.zeros(shape=n_nodes, dtype=bool)\n",
    "    stack = [(0, -1)]  # seed is the root node id and its parent depth\n",
    "    while len(stack) > 0:\n",
    "        node_id, parent_depth = stack.pop()\n",
    "        node_depth[node_id] = parent_depth + 1\n",
    "\n",
    "        # If we have a test node\n",
    "        if (children_left[node_id] != children_right[node_id]):\n",
    "            stack.append((children_left[node_id], parent_depth + 1))\n",
    "            stack.append((children_right[node_id], parent_depth + 1))\n",
    "        else:\n",
    "            is_leaves[node_id] = True\n",
    "    return (n_nodes, node_depth, is_leaves, children_left, children_right, feature, threshold)\n",
    "\n",
    "def get_splits(dtree):\n",
    "    n_nodes, node_depth, is_leaves, children_left, children_right, feature, threshold = parse_tree(dtree)\n",
    "    result = []\n",
    "    for i in range(n_nodes):\n",
    "        if not is_leaves[i]:\n",
    "            result.append([node_depth[i], threshold[i]])\n",
    "    return(np.array(result))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_predicted_saves = np.zeros((depth_max, plot_res))\n",
    "tree_saves = [None] * depth_max\n",
    "split_saves = [None] * depth_max\n",
    "image_saves = [None] * depth_max\n",
    "loss_computed_saves = np.zeros(depth_max)\n",
    "\n",
    "for save_step in range(0, depth_max):\n",
    "    model = classify(save_step+1)\n",
    "    tree_saves[save_step] = model\n",
    "    y_predicted_saves[save_step] = model.predict(x_plot.reshape(-1, 1))\n",
    "    loss_computed_saves[save_step] = mean_squared_error(y, model.predict(x.reshape(-1, 1)))\n",
    "    split_saves[save_step] = get_splits(model)\n",
    "    #image_saves[save_step] = Source(export_graphviz(model, out_file=None, filled = True, rounded=True))\n",
    "    image_saves[save_step] = Image(Source(export_graphviz(model, out_file=None, filled = True, rounded=True)).pipe(format='png'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(image_saves[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10,7))\n",
    "plt.plot(x, y, '+', x_plot, y_predicted_saves[2], 'r')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10,7))\n",
    "plt.plot(np.arange(0, depth_max), loss_computed_saves)\n",
    "plt.xlabel('step')\n",
    "plt.ylabel('loss')\n",
    "plt.xlim((0, depth_max))\n",
    "plt.ylim((0, np.max(loss_computed_saves)))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlMAAAGbCAYAAADgEhWsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvDW2N/gAADFxJREFUeJzt3bFuHFUfxuF3bUMSOWg7KiKh1BTfJVDjJmmRXJGSCESVUE1FoCOOu6TjBtJYtFwENSClo7MiK7GDs18xWwc576DV2M9Tzx79q9VPZ2fPWaxWqwAA8H62Nj0AAMCciSkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAi6NTx8c/fzpg6OfNz0HcLXsbHoAgAn9b9MDAFePnSkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgIKYAgAoiCkAgMLOpgcAqA3L60n2vtu5+8luXm9n+PLbJC+SHGU4fr3h6YBLbrFarTY9A8D7GZa3k9xPci/J27PV9s2dnG9tLXKa5DTj7vvTJIcZjv/Y4KTAJSamgPkZloskj5J8kzGYPnzH02dJzpMcJHmY4diXHjApMQXMyxhSvyS5k2T3Ap88SfI8yb6gAqbkBXRgbh7l4iGV9fN3kvww+UTAlWZnCpiP8R2p35PcKFZ5leQz71ABU7EzBczJ/STb5RrbSb6eYBaAJHamgLkYljeS/J3k5gSrvUzysWMTgCnYmQLm4oskbydaa5Vkb6K1gCtOTAFzcSvJtYnWurZeD6AmpoC5+CjvPk/qIj5YrwdQE1PAXLzMeADnFN6s1wOoiSlgLl5kvCJmCqfr9QBqYgqYi6NM9521WK8HUBNTwDyMxxg8S/9T31mSZ45FAKYipoA5eZLx0uLGeZLDCWYBSCKmgDkZr4A5yHhp8fs4SfLYVTLAlMQUMDcPkzzPxYPqZP257yefCLjSxBQwL8PxKsl+xp/qXuXf36E6Wz/3JMn++vMAk3E3HzBfw/J2xkuL7yVZna22b+7kfGtrkdOMxx8skjxNcpjh+M8NTgpcYmIKmL9heT3J3sE/d3/azevtr3Z+fZzxHKkj/9oD/mtiCrg0Pn1w9FuS/PXj3uebnQS4SrwzBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQEFMAAAUxBQBQ2Nn0AAC1YXk9yd53O3c/2c3r7QxffpvkRZKjDMevNzwdcMktVqvVpmcAeD/D8naS+0nuJXl7ttq+uZPzra1FTpOcZtx9f5rkMMPxHxucFLjExBQwP8NykeRRkm8yBtOH73j6LMl5koMkDzMc+9IDJiWmgHkZQ+qXJHeS7F7gkydJnifZF1TAlLyADszNo1w8pLJ+/k6SHyafCLjS7EwB8zG+I/V7khvFKq+SfOYdKmAqdqaAObmfZLtcYzvJ1xPMApDEzhQwF8PyRpK/k9ycYLWXST52bAIwBTtTwFx8keTtRGutkuxNtBZwxYkpYC5uJbk20VrX1usB1MQUMBcf5d3nSV3EB+v1AGpiCpiLlxkP4JzCm/V6ADUxBczFi4xXxEzhdL0eQE1MAXNxlOm+sxbr9QBqYgqYh/EYg2fpf+o7S/LMsQjAVMQUMCdPMl5a3DhPcjjBLABJxBQwJ+MVMAcZLy1+HydJHrtKBpiSmALm5mGS57l4UJ2sP/f95BMBV5qYAuZlOF4l2c/4U92r/Ps7VGfr554k2V9/HmAy7uYD5mtY3s54afG9JKuz1fbNnZxvbS1ymvH4g0WSp0kOMxz/ucFJgUtMTAHzNyyvJ9k7+OfuT7t5vf3Vzq+PM54jdeRfe8B/TUwBl8anD45+S5K/ftz7fLOTAFeJd6YAAApiCgCgIKYAAApiCgCgIKYAAApiCgCgIKYAAApiCgCgIKYAAApiCgCgIKYAAApiCgCgIKYAAAo7mx4AoDYsryfZ+27n7ie7eb2d4ctvk7xIcpTh+PWGpwMuucVqtdr0DADvZ1jeTnI/yb0kb89W2zd3cr61tchpktOMu+9PkxxmOP5jg5MCl5iYAuZnWC6SPEryTcZg+vAdT58lOU9ykORhhmNfesCkxBQwL2NI/ZLkTpLdC3zyJMnzJPuCCpiSF9CBuXmUi4dU1s/fSfLD5BMBV5qdKWA+xnekfk9yo1jlVZLPvEMFTMXOFDAn95Nsl2tsJ/l6glkAktiZAuZiWN5I8neSmxOs9jLJx45NAKZgZwqYiy+SvJ1orVWSvYnWAq44MQXMxa0k1yZa69p6PYCamALm4qO8+zypi/hgvR5ATUwBc/Ey4wGcU3izXg+gJqaAuXiR8YqYKZyu1wOoiSlgLo4y3XfWYr0eQE1MAfMwHmPwLP1PfWdJnjkWAZiKmALm5EnGS4sb50kOJ5gFIImYAuZkvALmIOOlxe/jJMljV8kAUxJTwNw8TPI8Fw+qk/Xnvp98IuBKE1PAvAzHqyT7GX+qe5V/f4fqbP3ckyT7688DTMbdfMB8DcvbGS8tvpfxiphrGQ/kfJPx+INFkqdJDjMc/7mpMYHLTUwB8zcsr2e8a+9WxpPNX2Y8R+rIv/aA/5qYAgAoeGcKAKAgpgAACmIKAKAgpgAACmIKAKAgpgAACmIKAKAgpgAACmIKAKAgpgAACmIKAKAgpgAACmIKAKAgpgAACmIKAKAgpgAACmIKAKAgpgAACmIKAKAgpgAACmIKAKAgpgAACmIKAKAgpgAACmIKAKAgpgAACmIKAKAgpgAACmIKAKDwfxmBoPc2kKm0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10,7))\n",
    "ax = plt.axes()\n",
    "ax.axis('off')\n",
    "\n",
    "plt.plot([0, 0], [1, 0])\n",
    "plt.plot([0, 0, 0], [0,.1,.3], 'o', markersize=19)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Play widget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "171c10921f404b00baa08c6ae7b1780d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(Output(), HBox(children=(FloatProgress(value=0.5644928576435941, bar_style='info', description=…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ymin, ymax = np.min(y_predicted_saves), np.max(y_predicted_saves)\n",
    " \n",
    "plot_output = widgets.Output()\n",
    "tree_output = widgets.Output()\n",
    "\n",
    "rmse_output = widgets.HTML()\n",
    "rmse_progress = widgets.FloatProgress(\n",
    "    min=0,\n",
    "    max=1.0,\n",
    "    step=0.01,\n",
    "    description='Cost :',\n",
    "    bar_style='info',\n",
    "    orientation='horizontal'\n",
    ")\n",
    "rmse_ui = widgets.HBox([rmse_progress, rmse_output], layout={'margin':'10px 10px 10px 10px'})\n",
    "\n",
    "depth_slider = widgets.IntSlider(\n",
    "    value=1,\n",
    "    min=1,\n",
    "    max=depth_max,\n",
    "    description='Tree depth :')\n",
    "depth_ui = widgets.HBox([depth_slider], layout={'margin':'10px 10px 10px 10px'})\n",
    "\n",
    "ui = widgets.VBox([plot_output, rmse_ui, tree_output, depth_ui], layout={'border':'1px solid black'})\n",
    "\n",
    "def update_plot(ev):\n",
    "    plot_output.clear_output(wait=True)\n",
    "    with plot_output:\n",
    "        fig = plt.figure(figsize=(10,7))\n",
    "        plt.plot(x, y, '+', x_plot, y_predicted_saves[depth_slider.value - 1], 'r')\n",
    "        plt.xlabel('x')\n",
    "        plt.ylabel('f(x)')\n",
    "        plt.ylim((ymin, ymax))\n",
    "        plt.show()\n",
    "        \n",
    "        rmse_output.value = str(loss_computed_saves[depth_slider.value - 1])\n",
    "        rmse_progress.value = loss_computed_saves[depth_slider.value - 1]\n",
    "        \n",
    "    tree_output.clear_output(wait=True)\n",
    "    with tree_output:\n",
    "        display(image_saves[depth_slider.value - 1])\n",
    "\n",
    "        \n",
    "depth_slider.observe(update_plot, names='value')\n",
    "# initialize widget\n",
    "update_plot(None) \n",
    "\n",
    "display(ui)"
   ]
  },
  {
   "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": "3.6.7"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "0ceeca0ad4e7462bad263330fd3005b7": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_9d91542d604f44d38fd10137cd9f04cd",
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": "<IPython.core.display.Image object>"
         },
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         "output_type": "display_data"
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      "model_module_version": "1.4.0",
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       ],
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     "4fa6d073f8fd476581945971ea94cc1d": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.4.0",
      "model_name": "HBoxModel",
      "state": {
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        "IPY_MODEL_f869989c03c54f08b0202d79f30d5b6e",
        "IPY_MODEL_fb51f92d09504e3fb1418ae226dfe166"
       ],
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      }
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     "65e63889227b424ea0c2e4c13599b7d5": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.1.0",
      "model_name": "LayoutModel",
      "state": {
       "margin": "10px 10px 10px 10px"
      }
     },
     "6ed237b36248445299426c8a4bc40e91": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.1.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "7410a7b62bb6408f87f884668ffbaedf": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_95e65411440d4d908f9d8033cb7caf11",
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": "<Figure size 720x504 with 1 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "8263f27f7f8f462f9cfe05ecfe0596d7": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.4.0",
      "model_name": "SliderStyleModel",
      "state": {
       "description_width": ""
      }
     },
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