Py_XGBoost_.ipynb

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      "name": "Py_XGBoost .ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyM06GLqHfEkywkvFRpRAShI",
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
    }
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/yuvalofek/py_xgboost/blob/main/Py_XGBoost_.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wc6LJvBBRjb8"
      },
      "source": [
        "# Implementing XGBoost in Python\n",
        "XGBoost has been and is to this day one of the most popular and useful machine learning algorithms. In order to learn more about it, I decided to implement it!\n",
        "\n",
        "Check out the official XGBoost paper here: https://arxiv.org/pdf/1603.02754.pdf\n",
        "\n",
        "\n",
        "Other resources:\n",
        "* [An End-to-End Guide to Understand the Math behind XGBoost](https://www.analyticsvidhya.com/blog/2018/09/an-end-to-end-guide-to-understand-the-math-behind-xgboost/?utm_source=blog&utm_medium=4-boosting-algorithms-machine-learning)\n",
        "* [XGBoost Documentation](https://xgboost.readthedocs.io/en/latest/index.html)\n",
        "* [StatQuest XGBoost](https://www.youtube.com/watch?v=OtD8wVaFm6E&list=PLblh5JKOoLULU0irPgs1SnKO6wqVjKUsQ&ab_channel=StatQuestwithJoshStarmer)\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IkvwgYlSRNM7"
      },
      "source": [
        "import numpy as np\n",
        "from collections import defaultdict\n",
        "import xgboost as xgb\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8V38Jn-IUVsz"
      },
      "source": [
        "## Notes\n",
        "* Scalable\n",
        "* End-to-end\n",
        "* weighted quantile for efficient proposal calculation\n",
        "* sparcity aware algorithm\n",
        "* cache aware block structure\n",
        "* CART - space of regression trees \n",
        "* Uses Taylor expansion of the costum loss up to second order\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rHjqkAYTpvHj"
      },
      "source": [
        "For convenience, we opt to use MSE as a loss since it is common and to not worry about taking a Taylor expansion. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-PiPiiWiJ8z4"
      },
      "source": [
        "class Node:\n",
        "  def __init__(self, value, depth):\n",
        "    self.value = value\n",
        "    self.depth = depth\n",
        "    self.gain = None\n",
        "    self.feature = -1\n",
        "    self.left = None\n",
        "    self.right = None"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wt5v0BdNWnCd"
      },
      "source": [
        "class XGBoostTree:\n",
        "  def __init__(self, max_depth=6, gamma = 0, lambd=0, el = 50, approx:int=20,\n",
        "               g=lambda y, y_h: y_h-y, h= lambda y, y_h: 1):\n",
        "    self.max_depth = max_depth\n",
        "    self.root = None\n",
        "    self.gamma = gamma\n",
        "    self.lambd = lambd\n",
        "    self.el = el\n",
        "    self.approx = approx\n",
        "\n",
        "    # Equations to get the gradient and hermetian (1st and 2nd derivatives)\n",
        "    # This is for generalizing to any loss function (default is MSE)\n",
        "    self.g = g\n",
        "    self.h = h\n",
        "\n",
        "  def __fit(self, node, max_depth):\n",
        "    \"\"\"\n",
        "    Recursively fit data \n",
        "    node - node object to fit to data, node.value contains data to fit\n",
        "    max_depth - maximum depth allowed\n",
        "    \"\"\"    \n",
        "    X, Y, Y_HAT = zip(*node.value)\n",
        "\n",
        "    if node.depth > max_depth:\n",
        "      # Exceded depth allowed\n",
        "      node.value = list(Y)\n",
        "      return \n",
        "\n",
        "    feature = -1\n",
        "    try:\n",
        "      # If multiple features, choose a single feature\n",
        "      n_dim = len(X[0])\n",
        "      feature = npr.randint(0, n_dim)\n",
        "      X_feature = [x[feature] for x in X]\n",
        "    except TypeError:\n",
        "      X_feature = X\n",
        "      \n",
        "    # Split\n",
        "    if len(X)>self.approx:\n",
        "      split, gain = self.__get_split_approx(X_feature,Y, Y_HAT)\n",
        "    else:\n",
        "      split, gain = self.__get_split_greedy(X_feature,Y,Y_HAT)\n",
        "    \n",
        "    if split is None:\n",
        "      # If there is no split --> one element, set prediction = label of element\n",
        "      node.right = None\n",
        "      node.left = None\n",
        "      node.value = [Y[0]]\n",
        "      return \n",
        "    \n",
        "    \n",
        "    # update node values\n",
        "    node.value = split\n",
        "    node.feature = feature\n",
        "    node.gain = gain\n",
        "\n",
        "    # Build the rest of the tree\n",
        "    right = [(x, y, y_hat) for x, y, y_hat, x_f in zip(X, Y, Y_HAT, X_feature) if x_f>=node.value]\n",
        "    node.right = Node(right, node.depth+1)\n",
        "    self.__fit(node.right,  max_depth)\n",
        "    \n",
        "    left = [(x, y, y_hat) for x, y, y_hat, x_f in zip(X, Y, Y_HAT, X_feature) if x_f<node.value]\n",
        "    node.left = Node(left, node.depth+1)\n",
        "    self.__fit(node.left, max_depth)\n",
        "\n",
        "  def fit(self, X, Y, Y_HAT=None):\n",
        "    \"\"\"\n",
        "    Fit tree model to input data and labels, optional Y_HAT parameter for boosting\n",
        "    if Y_HAT not provided, it is replaced by the average Y value. \n",
        "    \"\"\"\n",
        "    if Y_HAT is None:\n",
        "      # If we have no prior, use average of labels\n",
        "      avg = sum(Y)/len(Y)\n",
        "      Y_HAT = [avg for _ in range(len(Y))]\n",
        "    self.root = Node(zip(X,Y,Y_HAT), 1)\n",
        "    self.__fit(self.root, self.max_depth)\n",
        "    if self.gamma is not None:\n",
        "      self.prune()\n",
        "\n",
        "  @staticmethod\n",
        "  def __join_on_x(X, Y, Y_HAT):\n",
        "    \"\"\"\n",
        "    Join the Y & Y_HAT values for identical X by averaging\n",
        "    \"\"\"\n",
        "    # Load data to a dictionary, which has unique keys\n",
        "    unique_x = defaultdict(list)\n",
        "    for x,y,  y_h in zip(X, Y, Y_HAT):\n",
        "      unique_x[x].append((y, y_h))\n",
        "    \n",
        "    # Read of the keys and average all of the labels and predictions for each key\n",
        "    Y = []\n",
        "    Y_HAT = []\n",
        "    for x, ys in unique_x.items():\n",
        "      y, y_h = zip(*ys)\n",
        "      Y.append(sum(y)/len(y))\n",
        "      Y_HAT.append(sum(y_h)/len(y_h))\n",
        "    return list(unique_x.keys()), Y, Y_HAT\n",
        "\n",
        "\n",
        "  def __get_split_greedy(self, X, Y, Y_HAT):\n",
        "    \"\"\"\n",
        "    Greedy split search for X data, Y labels, and Y_HAT prior prediction\n",
        "    \"\"\"\n",
        "    if len(X) <= 1:\n",
        "      # If we get one element, no split\n",
        "      return None, None\n",
        "    \n",
        "    # join features with same x value (average) \n",
        "    X, Y, Y_HAT = self.__join_on_x(X, Y, Y_HAT)\n",
        "\n",
        "    # Compute G^2 / (H + lambda)\n",
        "    g_j = [self.g(y, y_h) for y, y_h in zip(Y, Y_HAT)]\n",
        "    h_j = [self.h(y, y_h) for y, y_h in zip(Y, Y_HAT)]\n",
        "    G = sum(g_j)\n",
        "    H = sum(h_j)\n",
        "    sim_root = G**2/(H+self.lambd)\n",
        "\n",
        "    # sort residuals by x\n",
        "    X, g_j, h_j = zip(*sorted(zip(X,g_j, h_j)))\n",
        "\n",
        "    # Find split that results in least gain\n",
        "    max_gain = -float('infinity')\n",
        "    best_split = None\n",
        "    for r in range(len(X)-1):\n",
        "      split = sum(X[r:r+2])/2\n",
        "\n",
        "      # Compute G_L^2 / (H_L + lambda)\n",
        "      G_L = sum(g_j[:r+1])\n",
        "      H_L = sum(h_j[:r+1])\n",
        "      sim_left = G_L**2/(H_L+self.lambd)\n",
        "\n",
        "      # Compute G_R^2 / (H_R + lambda)\n",
        "      G_R = sum(g_j[r+1:])\n",
        "      H_R = sum(h_j[r+1:])\n",
        "      sim_right = G_R**2/(H_R+self.lambd)\n",
        "\n",
        "      # Get the score\n",
        "      g = sim_right + sim_left - sim_root\n",
        "\n",
        "      # Find min \n",
        "      if g > max_gain:\n",
        "        max_gain = g\n",
        "        best_split = split\n",
        "\n",
        "    return best_split, max_gain\n",
        "\n",
        "  def __get_split_approx(self, X, Y, Y_HAT):\n",
        "    \"\"\"\n",
        "    Aproximate greedy search using np.percentile for X data, Y labels, and Y_HAT\n",
        "    prior predictions. \n",
        "    \"\"\"\n",
        "    if len(X) <= 1:\n",
        "      # If we get one element, no split\n",
        "      return None, None\n",
        "\n",
        "    # join features with same x value (average) \n",
        "    X, Y, Y_HAT = self.__join_on_x(X, Y, Y_HAT)\n",
        "\n",
        "\n",
        "    # Using np.percentile to determine feature percentiles for splits\n",
        "    splits = np.percentile(X, [val*100/(self.el+1) for val in range(1, self.el+1)])\n",
        "    if len(splits) <= 1:\n",
        "      return None, None\n",
        "\n",
        "    # Compute G^2 / (H + lambda)\n",
        "    g_j = [self.g(y, y_h) for y, y_h in zip(Y, Y_HAT)]\n",
        "    h_j = [self.h(y, y_h) for y, y_h in zip(Y, Y_HAT)]\n",
        "    G = sum(g_j)\n",
        "    H = sum(h_j)\n",
        "    sim_root = G**2/(H+self.lambd)\n",
        "\n",
        "    # Find split that results in least gain\n",
        "    max_gain = -float('infinity')\n",
        "    best_split = None\n",
        "    for split in splits:\n",
        "      # Compute G_L^2 / (H_L + lambda)\n",
        "      left = [(g_, h_) for g_, h_, x in zip(g_j, h_j, X) if x<split]\n",
        "      if len(left) <=0:\n",
        "        continue\n",
        "        \n",
        "      g_l, h_l = zip(*left)\n",
        "      G_L = sum(g_l)\n",
        "      H_L = sum(h_l)\n",
        "      sim_left = G_L**2/(H_L+self.lambd)\n",
        "\n",
        "      # Compute G_R^2 / (H_R + lambda)\n",
        "      right = [(g_, h_) for g_, h_, x in zip(g_j, h_j, X) if x>=split]\n",
        "      if len(right) <=0:\n",
        "        continue\n",
        "      g_r, h_r = zip(*right)\n",
        "      G_R = sum(g_r)\n",
        "      H_R = sum(h_r)\n",
        "      sim_right = G_R**2/(H_R+self.lambd)\n",
        "      \n",
        "\n",
        "      # Get the score\n",
        "      g = sim_right + sim_left - sim_root\n",
        "\n",
        "      # Find min \n",
        "      if g > max_gain:\n",
        "        max_gain = g\n",
        "        best_split = split\n",
        "    return best_split, max_gain\n",
        "\n",
        "  def __prune(self, node):\n",
        "    \"\"\"\n",
        "    Recursive pruning using a gamma parameter\n",
        "    \"\"\"\n",
        "    if node.left is None:\n",
        "      # If leaf, return that it is pruned\n",
        "      return True\n",
        "    \n",
        "    # prune children\n",
        "    prune_left = self.__prune(node.left)\n",
        "    prune_right = self.__prune(node.right)\n",
        "\n",
        "    if (prune_left and prune_right):\n",
        "      # if we pruned both children, check for pruning\n",
        "      if node.gain < self.gamma:\n",
        "        # If need to prune, take the values of the children and store them, clean out node\n",
        "        node.value = node.left.value + node.right.value\n",
        "        node.left = None\n",
        "        node.right = None\n",
        "        node.gain = None\n",
        "        return True\n",
        "    return False\n",
        "\n",
        "  def prune(self):\n",
        "    \"\"\"\n",
        "    Prune the trained tree using hyperparameter gamma\n",
        "    \"\"\"\n",
        "    self.__prune(self.root)\n",
        "\n",
        "  def __print_tree(self, node):\n",
        "    \"\"\"\n",
        "    Recursively print tree\n",
        "    \"\"\"\n",
        "    if node.value is None:\n",
        "      return\n",
        "    print('    '*node.depth + str(node.value), f'|f_idx:{node.feature}|', f'({node.gain})')\n",
        "    if node.left is not None:\n",
        "      self.__print_tree(node.left)\n",
        "      self.__print_tree(node.right)\n",
        "\n",
        "  def print_tree(self):\n",
        "    \"\"\" \n",
        "    call the recursive print using the tree root\n",
        "    \"\"\"\n",
        "    self.__print_tree(self.root)\n",
        "\n",
        "  def __get_output(self, Y):\n",
        "    \"\"\" \n",
        "    XGBoost weighted output value \n",
        "    \"\"\"\n",
        "    return sum(Y)/(len(Y)+self.lambd)\n",
        "\n",
        "  def __predict(self, x, node):\n",
        "    \"\"\"\n",
        "    Recursively predict label for input value x, follow the splits to get to the \n",
        "    final leaf and then return the output\n",
        "    \"\"\"\n",
        "    if node.left is None:\n",
        "      return self.__get_output(node.value)\n",
        "    \n",
        "    x_ = x\n",
        "    if node.feature != -1:\n",
        "      x_ = x[node.feature]\n",
        "    if x_ > node.value:\n",
        "      return self.__predict(x, node.right)\n",
        "    else:\n",
        "      return self.__predict(x, node.left)\n",
        "\n",
        "  def predict(self, X):\n",
        "    \"\"\"\n",
        "    Predict labels for iterable X\n",
        "    \"\"\"\n",
        "    y = []\n",
        "    for x in X:\n",
        "      y.append(self.__predict(x, self.root))\n",
        "    return y\n",
        "\n"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "runi7tw-G2uH"
      },
      "source": [
        "class XGBoost:\n",
        "  def __init__(self, n_trees , max_depth=6, gamma = 0, lambd=0, eta=0.3):\n",
        "    self.trees = [XGBoostTree(max_depth=max_depth, gamma = gamma, lambd=lambd) for _ in range(n_trees)]\n",
        "    self.eta = eta\n",
        "    self.baseline = None\n",
        "\n",
        "  def fit(self, X,Y):\n",
        "    if len(X) != len(Y):\n",
        "      raise ValueError('Input lengths do not match')\n",
        "      return \n",
        "    # Get the average for a baseline\n",
        "    self.baseline = sum(Y)/len(Y)\n",
        "\n",
        "    Y_ = Y\n",
        "    # Loop over the trees, building them one at a time, and update the prediction each run\n",
        "    for i in range(len(self.trees)):\n",
        "      y_hat = self.predict(X, i)\n",
        "      # How much y is left to learn:\n",
        "      Y_ = [y-p for y,p in zip(Y,y_hat)]\n",
        "      self.trees[i].fit(X,Y_,y_hat)\n",
        "      \n",
        "\n",
        "  def predict(self, X, n_trees=None):\n",
        "    if self.baseline is None:\n",
        "      raise ValueError('Model not trained!')\n",
        "      return\n",
        "    \n",
        "    # initialize prediction \n",
        "    y_pred = [self.baseline]*len(X)\n",
        "\n",
        "    # parallelization potential!!\n",
        "    trees = self.trees\n",
        "    if n_trees is not None:\n",
        "      trees = self.trees[:n_trees]\n",
        "    for i in range(len(trees)):\n",
        "      y_pred = [y_delta*self.eta+y_h for y_delta,y_h in zip(self.trees[i].predict(X), y_pred)]\n",
        "    return y_pred\n",
        "\n",
        "  def print_trees(self):\n",
        "    print(f'Baseline: {self.baseline}')\n",
        "    for i, tree in enumerate(self.trees):\n",
        "      print(f'Tree {i}:')\n",
        "      tree.print_tree()\n",
        "\n"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2vuHmiaGNleE"
      },
      "source": [
        ""
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 700
        },
        "id": "2ydGtpYMERbz",
        "outputId": "8bcb008b-6e54-4712-f198-6c0c40ca97d5"
      },
      "source": [
        "X = [10, 20, 21, 15,  25, 33, 35]\n",
        "Y = [-10, 7, 7.5, 0, 8, -7, -8]\n",
        "\n",
        "n_trees = 20\n",
        "xg = XGBoost(n_trees, max_depth=4)\n",
        "xg.fit(X,Y)\n",
        "\n",
        "\n",
        "X_ = range(1, 40)\n",
        "plt.figure(figsize=(12,12))\n",
        "plt.scatter(X,Y, label='Input')\n",
        "\n",
        "plt.plot(X_, xg.predict(X_), label=f'Prediction')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x864 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UHl103y5TU4E"
      },
      "source": [
        "## Checking with Other funcitons"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xZbgHeMJPHrf"
      },
      "source": [
        "import math\n",
        "import numpy.random as npr"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 716
        },
        "id": "0qaCkt0RTneP",
        "outputId": "dbe8dedd-c01f-4ace-8dcb-9096c682fc7e"
      },
      "source": [
        "N = 1000\n",
        "X_clean = [val/N*math.pi*2 for val in range(0, N)]\n",
        "Y_clean = [math.sin(x) for x in X_clean]\n",
        "noise_y = list(npr.normal(size=N)*.2)\n",
        "noise_x = list(npr.normal(size=N)*.1)\n",
        "\n",
        "X = [x+n for x,n in zip(X_clean, noise_x)]\n",
        "Y = [y+n for y,n in zip(Y_clean, noise_y)]\n",
        "n_trees = 10\n",
        "tr = XGBoost(n_trees=n_trees, max_depth=2, lambd=1)\n",
        "tr.fit(X,Y)\n",
        "\n",
        "\n",
        "plt.figure(figsize=(12,12))\n",
        "#plt.plot(X_clean, tr.predict(X_clean), 'red')\n",
        "for i in range(n_trees+1):\n",
        "  plt.plot(X_clean, tr.predict(X_clean, i), label=f'Sum of {i} trees')\n",
        "plt.scatter(X, Y)\n",
        "plt.legend()\n",
        "plt.title('Regression of Noisy Sinusoidal using PyXGBoost')\n",
        "plt.savefig('./predicting_sin.png')\n",
        "plt.show()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x864 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QAGBsK0wlZKa"
      },
      "source": [
        "## Multi-Dimensional"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UWdk74GmlciF"
      },
      "source": [
        "import plotly.graph_objects as go\n",
        "from plotly.subplots import make_subplots "
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "1f55zvdHuUy3",
        "outputId": "dd45faf8-e378-4cbb-ae04-fcd0b1be9f19"
      },
      "source": [
        "size = 20\n",
        "sigma_x = 1\n",
        "sigma_y = 1\n",
        "\n",
        "min_max = 3\n",
        "x = np.linspace(-min_max, min_max, size)\n",
        "y = np.linspace(-min_max, min_max, size)\n",
        "\n",
        "x, y = np.meshgrid(x, y)\n",
        "z = (1/(2*np.pi*sigma_x*sigma_y) * np.exp(-(x**2/(2*sigma_x**2)\n",
        "     + y**2/(2*sigma_y**2))))\n",
        "\n",
        "x = x + npr.random(size=x.shape)\n",
        "y = y + npr.random(size=x.shape)\n",
        "X = [[x,y] for x,y in zip(x.flatten().tolist(),y.flatten().tolist())]\n",
        "\n",
        "Z = (z+npr.random(size=z.shape)*0.05).flatten()\n",
        "\n",
        "\n",
        "n_trees = 10\n",
        "tr = XGBoost(n_trees=n_trees, max_depth=5, lambd=1)\n",
        "tr.fit(X, Z.tolist())\n",
        "\n",
        "size = 40\n",
        "min_max = 3\n",
        "x_ = np.linspace(-min_max, min_max, size)\n",
        "y_ = np.linspace(-min_max, min_max, size)\n",
        "x_, y_ = np.meshgrid(x_, y_)\n",
        "\n",
        "X_ = [[x_i,y_i] for x_i,y_i in zip(x_.flatten().tolist(),y_.flatten().tolist())]\n",
        "\n",
        "pred = tr.predict(X_)\n",
        "\n",
        "trace_1 = go.Scatter3d(x=x.flatten(),\n",
        "                      y=y.flatten(),\n",
        "                      z=Z,\n",
        "                      mode='markers',\n",
        "                      marker={'size': 3},\n",
        "                      opacity=0.8)\n",
        "\n",
        "\n",
        "trace_2 = go.Mesh3d(x=x_.flatten(),\n",
        "                      y=y_.flatten(),\n",
        "                      z=pred,\n",
        "                      opacity=0.3)\n",
        "\n",
        "\n",
        "fig = make_subplots()\n",
        "fig.add_trace(trace_1)\n",
        "fig.add_trace(trace_2)\n",
        "fig.update_layout(width=1200, height=1200, margin=dict(l=0, r=0, t=0, b=0))\n",
        "fig.show()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<html>\n",
              "<head><meta charset=\"utf-8\" /></head>\n",
              "<body>\n",
              "    <div>\n",
              "            <script src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_SVG\"></script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script>\n",
              "                <script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script>\n",
              "        <script src=\"https://cdn.plot.ly/plotly-latest.min.js\"></script>    \n",
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              "            <script type=\"text/javascript\">\n",
              "                \n",
              "                    window.PLOTLYENV=window.PLOTLYENV || {};\n",
              "                    \n",
              "                if (document.getElementById(\"8715ee71-3126-4555-8bc4-048e07788a78\")) {\n",
              "                    Plotly.newPlot(\n",
              "                        '8715ee71-3126-4555-8bc4-048e07788a78',\n",
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