SubsurfaceDataAnalytics_Gradient_Boosting_Simple.ipynb

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    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "## Machine Learning with Tree-based Gradient Boosting Regressor Methods\n",
    "\n",
    "### Tree-based Gradient Boosting for Subsurface Modeling in Python \n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, The University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1) | [GeostatsPy](https://github.com/GeostatsGuy/GeostatsPy)\n",
    "\n",
    "### Simple Demonstration of Tree-based Gradient Boosting Regressors for Subsurface Modeling in Python \n",
    "\n",
    "Here's a simple workflow, demonstration of tree-based gradient boosting for subsurface modeling workflows. This should help you get started with building subsurface models that data analytics and machine learning. Here's some basic details about tree-based gradient boosting.  \n",
    "\n",
    "#### Boosting Methods\n",
    "\n",
    "Boosting applies mulitple, additive week learners to build a stronger learner\n",
    "\n",
    "* a weak learner is one that offers predictions just marginally better than random selection\n",
    "\n",
    "I'll explain the method with words and then with equations.\n",
    "\n",
    "* build a simple model with a high error rate, the model can be be quite inaccurate, but moves in the correct direction\n",
    "\n",
    "* calculate the error from the model\n",
    "\n",
    "* fit another model to the error\n",
    "\n",
    "* calculate the error from this addition of the first and second model\n",
    "\n",
    "* repeat until the desired accuracy is obtained or some other stopping criteria\n",
    "\n",
    "The general workflow for predicting $Y$ from $X_1,\\ldots,X_m$ is:\n",
    "\n",
    "* build a week learner to predict $Y$ from $X_1,\\ldots,X_m$, $\\hat{F}_k(X)$ from the training data $x_{i,j}$.\n",
    "\n",
    "* loop over number of desired estimators, $k = 1,\\ldots,K$\n",
    "\n",
    "    1. calculate the residuals at the the training data, $h_k(x_{i}) = y_i - \\hat{F}_k(x_{i})$\n",
    "\n",
    "    2. fit another week learner to predict $h_k$ from $X_1,\\ldots,X_m$, $\\hat{F}_k(X)$ from the training data $x_{i,j}$.\n",
    "\n",
    "We have a hiearchy of simple $K$ models. \n",
    "\n",
    "* each model builds on the previous to improve the accuracy\n",
    "\n",
    "Our regression estimator is the summation over the $K$ simple models.\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{Y} =\\sum_{k=1}^{K} F_k(X_1,\\ldots,X_m)\n",
    "\\end{equation}\n",
    "\n",
    "#### Gradient Boosting Methods\n",
    "\n",
    "The previous method, it becomes clear that it could be mapped to a gradient descent problem\n",
    "\n",
    "At each step, $k$, a model is being fit, then the error is calculated, $h_k(X_1,\\ldots,X_m).\n",
    "\n",
    "We can assign a loss function\n",
    "\n",
    "\\begin{equation}\n",
    "L\\left(y,F(X)\\right) = \\frac{\\left(y - F(X)\\right)^2}{2}\n",
    "\\end{equation}\n",
    "\n",
    "So we want to minimize the $\\ell2$ loos function:\n",
    "\n",
    "\\begin{equation}\n",
    "J = \\sum_{i=1}^{n} L\\left(y_i, F_k(X) \\right)\n",
    "\\end{equation}\n",
    "\n",
    "by adjusting our model result over our training data $F(x_1), F(x_2),\\ldots,F(x_n)$.\n",
    "\n",
    "We can take the partial derivative of the error vs. our model. \n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\partial J}{\\partial F(x_i)} = F(x_i) - y_i\n",
    "\\end{equation}\n",
    "\n",
    "We can interpret the residuals as negative gradients.\n",
    "\n",
    "\\begin{equation}\n",
    "y_i - F(x_i) = -1 \\frac{\\partial J}{\\partial F(x_i)} \n",
    "\\end{equation}\n",
    "\n",
    "So now we have  a gradient descent problem:\n",
    "\n",
    "\\begin{equation}\n",
    "F_{k+1}(X_i) = F_k(X_i) + h(X_i)\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "F_{k+1}(X_i) = F_k(X_i) + y_i - F_k(X_i)\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "F_{k+1}(X_i) = F_k(X_i) - 1 \\frac{\\partial J}{\\partial F_k(X_i)}\n",
    "\\end{equation}\n",
    "\n",
    "Of the general form:\n",
    "\n",
    "\\begin{equation}\n",
    "\\phi_{k+1} = \\phi_k - \\rho \\frac{\\partial J}{\\partial \\phi_k}\n",
    "\\end{equation}\n",
    "\n",
    "where $phi_k$ is the current state, $\\rho$ is the learning rate, $J$ is the loss function, and $\\phi_{k+1}$ is the next state of our estimator.\n",
    "\n",
    "If we consider our residual at training data to be a gradient then we are performing gradient descent.  \n",
    "\n",
    "* fitting a series of models to negative gradients\n",
    "\n",
    "By approaching the problem as a gradient decent problem we are able to apply a variety of loss functions\n",
    "\n",
    "* $\\ell2$: $\\frac{\\left(y - F(X)\\right)^2}{2}$ is practical, but is not robust with outliers\n",
    "\n",
    "\\begin{equation}\n",
    "- 1 \\frac{\\partial J}{\\partial F_k(X_i)} = y_i - F_k(X_i)\n",
    "\\end{equation}\n",
    "\n",
    "* $\\ell1$: $|y - F(X)|$ is more robust with outliers\n",
    "\n",
    "\\begin{equation}\n",
    "- 1 \\frac{\\partial J}{\\partial F_k(X_i)} = sign(y_i - F_k(X_i))\n",
    "\\end{equation}\n",
    "\n",
    "* there are other alternatives like Huber Loss\n",
    "\n",
    "#### Classification\n",
    "\n",
    "The response is a finite set of possible catergories.  \n",
    "\n",
    "* For each training data the truth is 100% probability in the observed category and 0% otherwise\n",
    "\n",
    "* Estimate the probability of each category with the a decision tree\n",
    "\n",
    "* Use a measure of difference between the true and estimated distributions as the loss function to minimize\n",
    "\n",
    "#### Tree-based Boosting Methods\n",
    "\n",
    "Machine learning method for supervised learning for classification and regression analysis. Here are some key aspects of random forest.\n",
    "\n",
    "**Prediction**\n",
    "\n",
    "* estimate a function $\\hat{f}$ such that we predict a response feature $Y$ from a set of predictor features $X_1,\\ldots,X_m$. \n",
    "\n",
    "* the prediction is of the form $\\hat{Y} = \\hat{f}(X_1,\\ldots,X_m)$ \n",
    "\n",
    "**Supervised Learning**\n",
    "\n",
    "* the response feature label, $Y$, is available over the training and testing data\n",
    "    \n",
    "**Hiearchical, Binary Segmentation of the Feature Space**\n",
    "\n",
    "The fundamental idea is to divide the predictor space, $𝑋_1,\\ldots,X_m$, into $J$ mutually exclusive, exhaustive regions\n",
    "\n",
    "* **mutually exclusive** – any combination of predictors only belongs to a single region, $R_j$\n",
    "\n",
    "* **exhaustive** – all combinations of predictors belong a region, $R_j$, regions cover entire feature space (range of the variables being considered)\n",
    "\n",
    "For every observation in a region, $R_j$, we use the same prediction, $\\hat{Y}(R_j)$    \n",
    "\n",
    "For example predict production, $\\hat{Y}$, from porosity, ${X_1}$\n",
    "\n",
    "* given the data within a mD feature space, $X_1,\\ldots,X_m$, find that boundary maximizes the gap between the two categories\n",
    "\n",
    "* new cases are classified based on where they fall relative to this boundary \n",
    " \n",
    "**Proceedure for Tree Construction**\n",
    "\n",
    "The tree is constructed from the top down.  We begin with a sigle region that covers the entire feature space and then proceed with a sequence of splits.\n",
    "\n",
    "* **Scan All Possible Splits** over all regions and over all features.\n",
    "\n",
    "* **Greedy Optimization**  The method proceeds by finding the first segmentation (split) in any feature that minimizes the residual sum of squares of errors over all the training data $y_i$ over all of the regions $j = 1,\\ldots,J$.\n",
    "\n",
    "\\begin{equation}\n",
    "RSS = \\sum^{J}_{j=1} \\sum_{i \\in R_j} (y_i - \\hat{y}_{R_j})^2\n",
    "\\end{equation}\n",
    "\n",
    "* **Stopping Criteria** is typically based on minimum number of training data in each region for a robust estimation and / or minimum reduction in RSS for the next split \n",
    "\n",
    "**Interpretability**\n",
    "\n",
    "Compared to decision trees, the ensemble methods have reduced interpretability.  One tool to improve model interpretability is feature importance.\n",
    "\n",
    "We calculate variable importance through calculating the average of:\n",
    "\n",
    "* residual sum of square reduction for all splits involving each predictor feature for regression\n",
    "\n",
    "* the decrease in the Gini index for all splits involving each predictor feature for classification\n",
    "\n",
    "Both are standardized to sum to 1.0 over the features.\n",
    "\n",
    "##### Applications to Subsurface Modeling\n",
    "\n",
    "We will predict unconventional well production from a single petrophysical and geomechanical predictor feature\n",
    "\n",
    "##### Why Cover Ensemble Methods with Tree-based Gradient Boosting?\n",
    "\n",
    "Here's some thoughts:\n",
    "\n",
    "* build on from easy to understand decision trees\n",
    "* demonstrate reduction in model variance through an ensemble approach\n",
    "* random forest is quite powerful and is a top performing machine learning method in various types of problems \n",
    "\n",
    "#### Workflow Goals\n",
    "\n",
    "Learn the basics of ensemble tree methods in python to segment facies given petrophysical properties. This includes:\n",
    "\n",
    "* Loading and visualizing sample data\n",
    "* Trying out bagging tree and random forest \n",
    "* Test and observe the model behavoir and prove concepts\n",
    "\n",
    "#### Objective \n",
    "\n",
    "The objective is to remove the hurdles of learning machine learning workflow construction by providing a very simple demonstration in a well-documented, Python workflow with [scikit-learn](https://scikit-learn.org/stable/) one of the most popular machine learning Python packages.     \n",
    "\n",
    "#### Getting Started\n",
    "\n",
    "Here's the steps to get setup in Python with the GeostatsPy package:\n",
    "\n",
    "1. Install Anaconda 3 on your machine (https://www.anaconda.com/download/). \n",
    "2. From Anaconda Navigator (within Anaconda3 group), go to the environment tab, click on base (root) green arrow and open a terminal. \n",
    "3. In the terminal type: pip install geostatspy. \n",
    "4. Open Jupyter and in the top block get started by copy and pasting the code block below from this Jupyter Notebook to start using the geostatspy functionality. \n",
    "\n",
    "YOu can either load the data from my GitHub account or work with a local copy of the data file in your working directory. The data file:\n",
    "\n",
    "* Tabular data - 12_sample_data.csv found [here](https://github.com/GeostatsGuy/GeoDataSets/blob/master/12_sample_data.csv).\n",
    "\n",
    "#### Import Required Packages\n",
    "\n",
    "We will also need some standard packages. These should have been installed with Anaconda 3.\n",
    "\n",
    "* The following code loads the required libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os                                                   # to set current working directory \n",
    "import math                                                 # basic calculations like square root\n",
    "from sklearn import tree                                    # tree program from scikit learn (package for machine learning)\n",
    "from sklearn.tree import _tree                              # for accessing tree information\n",
    "from sklearn import metrics                                 # measures to check our models\n",
    "from sklearn.tree import export_graphviz                    # graphical visualization of trees\n",
    "from sklearn.preprocessing import StandardScaler            # standardize variables to mean of 0.0 and variance of 1.0\n",
    "\n",
    "from sklearn.model_selection import cross_val_score         # cross validation methods\n",
    "from sklearn.tree import DecisionTreeRegressor              # decision tree method\n",
    "from sklearn import model_selection\n",
    "from sklearn.ensemble import GradientBoostingRegressor      # tree-based gradient boosting\n",
    "\n",
    "import pandas as pd                                         # DataFrames and plotting\n",
    "import pandas.plotting as pd_plot\n",
    "import numpy as np                                          # arrays and matrix math\n",
    "import matplotlib.pyplot as plt                             # plotting\n",
    "from subprocess import check_call\n",
    "import geostatspy.GSLIB as GSLIB                            # geostatistics and spatial methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you get a package import error, you may have to first install some of these packages. This can usually be accomplished by opening up a command window on Windows and then typing 'python -m pip install [package-name]'. More assistance is available with the respective package docs.  \n",
    "\n",
    "#### Declare functions\n",
    "\n",
    "Let's define a couple of functions to streamline plotting correlation matrices and visualization and test our regression models. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set the working directory\n",
    "\n",
    "I always like to do this so I don't lose files and to simplify subsequent read and writes (avoid including the full address each time).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#os.chdir(\"c:/PGE383\")                                       # set the working directory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Generate a Data Set\n",
    "\n",
    "Let's make a simple synthetic dataset with a single predictor feature and response feature.\n",
    "\n",
    "* we will build an additive model with a random component and a cyclic component"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "nsample = 20                                                # number of data values\n",
    "np.random.seed(63079)                                       # random number seed for a consistent model      \n",
    "wt_random = 0.3                                             # weights for the random and cyclic components (sum to 1.0)\n",
    "wt_cycle = 0.7\n",
    "x = np.linspace(0,100,20)                                   # make a set of values to evaluate our models\n",
    "Y = (wt_random*np.random.rand(nsample) + wt_cycle*np.sin(x/10)+1.0)*0.5\n",
    "\n",
    "indices = np.random.permutation(x.shape[0])                 # get the indicies for randomize the order of the values\n",
    "training_idx, test_idx = indices[:int(nsample*4/5)], indices[int(nsample*4/5):] # extract 80% training and 20% testing\n",
    "x_train, x_test = x[training_idx], x[test_idx]             \n",
    "Y_train, Y_test = Y[training_idx], Y[test_idx]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize our synthetic dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(121)                                            # plot jackknife results for all cases\n",
    "plt.scatter(x_train,Y_train,s=None, c='red', marker=None, cmap=None, norm=None, vmin=None, vmax=None, alpha=1.0, linewidths=0.3, edgecolors=\"black\", label = \"Training\")\n",
    "plt.scatter(x_test,Y_test,s=None, c='blue', marker=None, cmap=None, norm=None, vmin=None, vmax=None, alpha=1.0, linewidths=0.3, edgecolors=\"black\", label = \"Testing\")\n",
    "\n",
    "plt.title('Simple Dataset'); plt.xlabel('Predictor Feature'); plt.ylabel('Response Feature')\n",
    "plt.xlim(0,100); plt.ylim(0,1.0); plt.legend(loc='lower right')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=4.5, top=0.8, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Build a Tree-based Boosting Model Sequentially\n",
    "\n",
    "Let's build a tree based boosting model sequentially.\n",
    "\n",
    "* Visualize the model fitting to the training data in original feature space \n",
    "\n",
    "* Visualize the model fitting to the training data in the feature residual space\n",
    "\n",
    "#### Tree-based Boosting Model in Original Feature Space\n",
    "\n",
    "We will start in original feature space for $1,\\dots,12$ trees.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Complete of 12:  1,  2,  3,  4,  5,  6,  7,  8,  9,  10,  11,  12,  "
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')                           # suppress warnings\n",
    "\n",
    "ntrees = 12                                                 # number of estimators / trees for our boosting model\n",
    "\n",
    "params = {\n",
    "    'loss': 'ls',                                           # L2 Norm - least squares\n",
    "    'max_depth': 1,                       \n",
    "    'learning_rate': 1,\n",
    "    'criterion': 'mse'                                      # tree construction criteria is mean square error over training\n",
    "}\n",
    "\n",
    "num_trees = np.linspace(1,12,ntrees)                        # build a list of numbers of trees \n",
    "boosting_models = []; score = []; pred = []                 # arrays for storage of models and model summaries\n",
    "x_pred = np.linspace(0,100,100)\n",
    "\n",
    "cmap = plt.get_cmap('gnuplot')\n",
    "colors = [cmap(i) for i in np.linspace(0, 1, ntrees)]\n",
    "\n",
    "index = 1\n",
    "print('Complete of ' + str(len(num_trees)) + ': ', end =\" \")\n",
    "for num_tree in num_trees:                                  # loop over number of trees\n",
    "    boosting_models.append(GradientBoostingRegressor(n_estimators=int(num_tree),**params))\n",
    "    boosting_models[index-1].fit(X = x_train.reshape(-1, 1), y = Y_train)\n",
    "    score.append(boosting_models[index-1].score(X = x_test.reshape(-1, 1), y = Y_test))\n",
    "    Y_pred = boosting_models[index-1].predict(x_pred.reshape(-1, 1))\n",
    "    plt.subplot(4,3,index)\n",
    "    plt.scatter(x_train,Y_train,s=None, c='black', marker=None, cmap=None, norm=None, vmin=None, vmax=None, alpha=0.2, linewidths=0.3, edgecolors=\"black\", label = \"Training\")\n",
    "    plt.plot(x_pred,Y_pred, c=colors[index-1], alpha=0.7, label = \"Testing\") \n",
    "    plt.title('Boosting with ' + str(int(num_trees[index-1])) + ' Trees' ); plt.xlabel('Predictor Feature'); plt.ylabel('Response Feature')\n",
    "    plt.xlim(0,100); plt.ylim(0,1.0); \n",
    "    print(str(index)+ ', ', end =\" \") \n",
    "    index = index + 1\n",
    "    \n",
    "#plt.legend(loc='lower right')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.8, top=2.5, wspace=0.3, hspace=0.4)\n",
    "plt.show()    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe the additive nature of the boosting model.\n",
    "\n",
    "* this is due to the fitting of residuals from the previous model\n",
    "\n",
    "* we are fitting the model error from the previous models\n",
    "\n",
    "We can actually visualize the model fits with the training data and model residuals.\n",
    "\n",
    "\n",
    "#### Tree-based Boosting Model in Feature Residual Space\n",
    "\n",
    "We will start in feature residual space for $1,\\dots,12$ trees.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Complete of 12:  1,  2,  3,  4,  5,  6,  7,  8,  9,  10,  11,  12,  "
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')                           # suppress warnings\n",
    "\n",
    "ntrees = 12\n",
    "\n",
    "params = {\n",
    "    'loss': 'ls',                                           # L2 Norm - least squares\n",
    "    'max_depth': 1,                       \n",
    "    'learning_rate': 1,\n",
    "    'criterion': 'mse'                                      # tree construction criteria is mean square error over training\n",
    "}\n",
    "\n",
    "num_trees = np.linspace(1,12,ntrees)                              # build a list of numbers of trees \n",
    "boosting_models = []; score = []; pred = []                 # arrays for storage of models and model summaries\n",
    "x_pred = np.linspace(0,100,100)\n",
    "\n",
    "cmap = plt.get_cmap('gnuplot')\n",
    "colors = [cmap(i) for i in np.linspace(0, 1, ntrees)]\n",
    "Y_zero = np.zeros(100)\n",
    "\n",
    "index = 1\n",
    "print('Complete of ' + str(len(num_trees)) + ': ', end =\" \")\n",
    "for num_tree in num_trees:                                  # loop over number of trees\n",
    "    boosting_models.append(GradientBoostingRegressor(n_estimators=int(num_tree),**params))\n",
    "    boosting_models[index-1].fit(X = x_train.reshape(-1, 1), y = Y_train)\n",
    "    Y_pred = boosting_models[index-1].predict(x_pred.reshape(-1, 1))\n",
    "    if index == 1:\n",
    "        Y_pred_prev = np.zeros(100)\n",
    "    else:\n",
    "        Y_pred_prev = boosting_models[index-2].predict(x_pred.reshape(-1, 1))\n",
    "    Y_train_pred = boosting_models[index-1].predict(x_train.reshape(-1, 1))\n",
    "    if index == 1:\n",
    "        Y_train_pred_prev = np.zeros(x_train.shape[0])\n",
    "    else:\n",
    "        Y_train_pred_prev = boosting_models[index-2].predict(x_train.reshape(-1, 1))\n",
    "    plt.subplot(4,3,index)\n",
    "    plt.scatter(x_train,Y_train-Y_train_pred_prev,s=None, c='black', marker=None, cmap=None, norm=None, vmin=None, vmax=None, alpha=0.2, linewidths=0.3, edgecolors=\"black\", label = \"Training\")\n",
    "    plt.plot(x_pred,Y_pred-Y_pred_prev, c=colors[index-1], alpha=0.7, label = \"Testing\") \n",
    "    plt.title('Boosting with ' + str(int(num_trees[index-1])) + ' Trees' ); plt.xlabel('Predictor Feature'); plt.ylabel('Response Feature')\n",
    "    if index == 1:\n",
    "        plt.xlim(0,100); plt.ylim(0,1.0); \n",
    "    else:\n",
    "        plt.xlim(0,100); plt.ylim(-0.5,0.5); \n",
    "        plt.plot(x_pred,Y_zero, c='black', alpha=0.7, linestyle='dashed', label = \"Testing\") \n",
    "    print(str(index)+ ', ', end =\" \") \n",
    "    index = index + 1    \n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.8, top=3.5, wspace=0.3, hspace=0.4)\n",
    "plt.show()   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observations:\n",
    "\n",
    "* See the initial model and then working with residuals.\n",
    "\n",
    "* See the residual from $k$ fit by the $k+1$ model\n",
    "\n",
    "* See the reduction in residual magnitude as the number boosting trees increases\n",
    "\n",
    "#### Comments\n",
    "\n",
    "This was a simple demonstration of tree-based boosting. \n",
    "\n",
    "I have other demonstrations on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, trend modeling and many other workflows available at https://github.com/GeostatsGuy/PythonNumericalDemos and https://github.com/GeostatsGuy/GeostatsPy. \n",
    "  \n",
    "I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "#### The Author:\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
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