stacking.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stacking"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* * *\n",
    "![Alt text](./images/h2oEnsemble.png \"Super Learner\")\n",
    "* * *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction \n",
    "\n",
    "[Stacking](https://en.wikipedia.org/wiki/Ensemble_learning#Stacking) (sometimes called \"stacked generalization\") involves training a learning algorithm to combine the predictions of several other learning algorithms. First, all of the other algorithms are trained using the available data, then a combiner algorithm, the *metalearner*, is trained to make a final prediction using all the predictions of the other algorithms as additional inputs. If an arbitrary metalearning algorithm is used, then stacking can theoretically represent any of the ensemble techniques described in this article, although in practice, a single-layer [logistic regression](https://en.wikipedia.org/wiki/Logistic_regression) model is often used for metalearning.\n",
    "\n",
    "Stacking typically yields performance better than any single one of the trained models in the ensemble."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Background\n",
    "\n",
    "[Leo Breiman](https://en.wikipedia.org/wiki/Leo_Breiman), known for his work on classification and regression trees and the creator of the Random Forest algorithm, formalized stacking in his 1996 paper, [\"Stacked Regressions\"](http://statistics.berkeley.edu/sites/default/files/tech-reports/367.pdf). Although the idea originated with David Wolpert in 1992 under the name \"Stacked Generalization\", the modern form of stacking that uses internal k-fold cross-validation was Dr. Breiman's contribution.\n",
    "\n",
    "However, it wasn't until 2007 that the [theoretical background](http://dx.doi.org/10.2202/1544-6115.1309) for stacking was developed, which is when the algorithm took on the name, \"Super Learner\". Until this time, the mathematical reasons for why stacking worked were unknown and stacking was considered a \"black art.\" The Super Learner algorithm learns the optimal combination of the base learner fits. In an article titled, \"Super Learner\", by Mark van der Laan et al., proved that the Super Learner ensemble represents an asymptotically optimal system for learning.\n",
    "\n",
    "\n",
    "## Common Types of Ensemble Methods\n",
    "\n",
    "In statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained by any of the constituent algorithms.\n",
    "\n",
    "### Bagging\n",
    "\n",
    "- Reduces variance and increases accuracy\n",
    "- Robust against outliers or noisy data\n",
    "- Often used with Decision Trees (i.e. Random Forest)\n",
    "\n",
    "### Boosting\n",
    "\n",
    "- Also reduces variance and increases accuracy\n",
    "- Not robust against outliers or noisy data\n",
    "- Flexible - can be used with any loss function\n",
    "\n",
    "### Stacking\n",
    "\n",
    "- Used to ensemble a diverse group of strong learners\n",
    "- Involves training a second-level machine learning algorithm called a \"metalearner\" to learn the optimal combination of the base learners"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Super Learner Algorithm\n",
    "\n",
    "A common task in machine learning is to perform model selection by specifying a number of models with different parameters.  An example of this is Grid Search.  The first phase of the Super Learner algorithm is computationally equivalent to performing model selection via cross-validation.  The latter phase of the Super Learner algorithm (the metalearning step) is just training another single model (no cross-validation) on the *level one* data.  \n",
    "\n",
    "\n",
    "### 1. Set up the ensemble\n",
    "\n",
    "- Specify a list of $L$ base algorithms (with a specific set of model parameters).  These are also called *base learners*.\n",
    "- Specify a metalearning algorithm (just another algorithm).\n",
    "\n",
    "### 2. Train the ensemble\n",
    "\n",
    "#### Cross-validate Base Learners\n",
    "- Perform k-fold cross-validation on each of these learners and collect the cross-validated predicted values from each of the $L$ algorithms.\n",
    "- The $N$ cross-validated predicted values from each of the $L$ algorithms can be combined to form a new $N \\times L$ matrix. This matrix, along wtih the original response vector, is called the \"level-one\" data.\n",
    "\n",
    "![Alt text](./images/stacking_cv.png \"Stacking\")\n",
    "\n",
    "#### Metalearning\n",
    "- Train the metalearning algorithm on the level-one data.\n",
    "- Train each of the $L$ base algorithms on the full training set.\n",
    "- The \"ensemble model\" consists of the $L$ base learning models and the metalearning model, which can then be used to generate predictions on a test set.\n",
    "\n",
    "### 3. Predict on new data\n",
    "\n",
    "- To generate ensemble predictions, first generate predictions from the base learners.\n",
    "- Feed those predictions into the metalearner model to generate the ensemble prediction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stacking Software in R\n",
    "\n",
    "Stacking is a broad class of algorithms that involves training a second-level \"metalearner\" to ensemble a group of base learners.  The three packages in the R ecosystem which implement the Super Learner algorithm (stacking on cross-validated predictions) are [SuperLearner](https://github.com/ecpolley/SuperLearner), [subsemble](https://github.com/ledell/subsemble) and [h2oEnsemble](https://github.com/h2oai/h2o-3/tree/master/h2o-r/ensemble).  \n",
    "\n",
    "Among ensemble software in R, there is also [caretEnsemble](https://github.com/zachmayer/caretEnsemble), but it implements a boostrapped (rather than cross-validated) version of stacking via the `caretStack()` function.  The bootstrapped version will train faster since bootrapping (with a train/test) is a fraction of the work as k-fold cross-validation, however the the ensemble performance suffers as a result of this shortcut."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### SuperLearner\n",
    "\n",
    "Authors: Eric Polley, Erin LeDell, Mark van der Laan\n",
    "\n",
    "Backend: R with constituent algorithms written in a variety of languages\n",
    "\n",
    "The original Super Learner implemenation is the [SuperLearner](https://github.com/ecpolley/SuperLearner) R package (2010).\n",
    "\n",
    "Features:\n",
    "- Implements the Super Learner prediction method (stacking) and contains a library of prediction algorithms to be used in the Super Learner.\n",
    "- Provides a clean interface to 30+ algorithms in R and defines a consistent API for extensibility.\n",
    "- GPL-3 Licensed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### subsemble\n",
    "\n",
    "Authors: Erin LeDell, Stephanie Sapp\n",
    "\n",
    "Backend: R with constituent algorithms written in a variety of algorithms\n",
    "\n",
    "[Subsemble](https://github.com/ledell/subsemble) is a general subset ensemble prediction method, which can be used for small, moderate, or large datasets. Subsemble partitions the full dataset into subsets of observations, fits a specified underlying algorithm on each subset, and uses a unique form of k-fold cross-validation to output a prediction function that combines the subset-specific fits. An oracle result provides a theoretical performance guarantee for Subsemble. \n",
    "\n",
    "Features:\n",
    "- Implements the Subsemble Algorithm.\n",
    "- Implements the Super Learner Algorithm (stacking).\n",
    "- Uses the SuperLearner wrapper interface for defining base learners and metalearners.\n",
    "- Multicore and multi-node cluster support via the [snow](https://cran.r-project.org/web/packages/snow/index.html) R package.\n",
    "- Improved parallelization over the SuperLearner package.\n",
    "- Apache 2.0 Licensed.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### H2O Ensemble\n",
    "\n",
    "Authors: Erin LeDell\n",
    "\n",
    "Backend: Java\n",
    "\n",
    "H2O Ensemble has been implemented as a stand-alone R package called [h2oEnsemble](https://github.com/h2oai/h2o-3/tree/master/h2o-r/ensemble). The package is an extension to the [h2o](https://cran.r-project.org/web/packages/h2o/index.html) R package that allows the user to train an ensemble in the H2O cluster using any of the supervised machine learning algorithms H2O. \n",
    "\n",
    "Features:\n",
    "- Uses data-distributed and parallelized Java-based algorithms for the ensemble.\n",
    "- All training and data processing are performed in the high-performance H2O cluster rather than in R memory.\n",
    "- Supports regression and binary classification. \n",
    "- Multi-class support in development.\n",
    "- Code refactor  underway (moving from a separate R package into H2O \"proper\") so that the H2O Ensemble interface can be exposed in Python and Scala.\n",
    "- Apache 2.0 Licensed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Skipping install of 'h2oEnsemble' from a github remote, the SHA1 (612d4489) has not changed since last install.\n",
      "  Use `force = TRUE` to force installation\n"
     ]
    }
   ],
   "source": [
    "# Install from GitHub\n",
    "#install.packages(\"devtools\")\n",
    "#install.packages(\"h2o\")\n",
    "library(devtools)\n",
    "install_github(\"h2oai/h2o-3/h2o-r/ensemble/h2oEnsemble-package\")\n",
    "library(h2oEnsemble)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Higgs Demo\n",
    "\n",
    "This is an example of binary classification using the `h2o.ensemble()` function, the main stacking function in h2oEnsemble. \n",
    "\n",
    "This demo uses a subset of the [HIGGS dataset](https://archive.ics.uci.edu/ml/datasets/HIGGS), which has 28 numeric features and a binary response. The machine learning task in this example is to distinguish between a signal process which produces Higgs bosons (Y = 1) and a background process which does not (Y = 0). The dataset contains approximately the same number of positive vs negative examples. In other words, this is a balanced, rather than imbalanced, dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Start H2O Cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "H2O is not running yet, starting it now...\n",
      "\n",
      "Note:  In case of errors look at the following log files:\n",
      "    /var/folders/2j/jg4sl53d5q53tc2_nzm9fz5h0000gn/T//RtmpcfKpYn/h2o_me_started_from_r.out\n",
      "    /var/folders/2j/jg4sl53d5q53tc2_nzm9fz5h0000gn/T//RtmpcfKpYn/h2o_me_started_from_r.err\n",
      "\n",
      "\n",
      "Starting H2O JVM and connecting: . Connection successful!\n",
      "\n",
      "R is connected to the H2O cluster: \n",
      "    H2O cluster uptime:         1 seconds 306 milliseconds \n",
      "    H2O cluster version:        3.8.2.6 \n",
      "    H2O cluster name:           H2O_started_from_R_me_rdu560 \n",
      "    H2O cluster total nodes:    1 \n",
      "    H2O cluster total memory:   3.56 GB \n",
      "    H2O cluster total cores:    8 \n",
      "    H2O cluster allowed cores:  8 \n",
      "    H2O cluster healthy:        TRUE \n",
      "    H2O Connection ip:          localhost \n",
      "    H2O Connection port:        54321 \n",
      "    H2O Connection proxy:       NA \n",
      "    R Version:                  R version 3.3.0 (2016-05-03) \n",
      "\n"
     ]
    }
   ],
   "source": [
    "h2o.init(nthreads = -1)  # Start an H2O cluster with nthreads = num cores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Load Data into H2O Cluster\n",
    "\n",
    "First, import a sample binary outcome train and test set into the H2O cluster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  |======================================================================| 100%\n",
      "  |======================================================================| 100%\n"
     ]
    }
   ],
   "source": [
    "# Import a sample binary outcome train/test set into R\n",
    "train <- h2o.importFile(\"data/higgs_train_10k.csv\")\n",
    "test <- h2o.importFile(\"data/higgs_test_5k.csv\")\n",
    "\n",
    "y <- \"response\"\n",
    "x <- setdiff(names(train), y)\n",
    "family <- \"binomial\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For binary classification, the response should be encoded as factor (also known as the [enum](https://docs.oracle.com/javase/tutorial/java/javaOO/enum.html) type in Java). The user can specify column types in the `h2o.importFile()` command, or you can convert the response column as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#For binary classification, response should be a factor\n",
    "train[,y] <- as.factor(train[,y])  \n",
    "test[,y] <- as.factor(test[,y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Specify Base Learners & Metalearner"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this example, we will use the default base learner library for `h2o.ensemble`, which includes the default H2O GLM, Random Forest, GBM and Deep Neural Net (all using default model parameter values). We will also use the default metalearner, the H2O GLM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Specify the base learner library & the metalearner\n",
    "learner <- c(\"h2o.glm.wrapper\", \"h2o.randomForest.wrapper\", \n",
    "             \"h2o.gbm.wrapper\", \"h2o.deeplearning.wrapper\")\n",
    "metalearner <- \"h2o.deeplearning.wrapper\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Train an Ensemble"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Train the ensemble (using 5-fold internal CV) to generate the level-one data. Note that more CV folds will take longer to train, but should increase performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "[1] \"Metalearning\"\n",
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     ]
    },
    {
     "data": {
      "text/plain": [
       "   user  system elapsed \n",
       "  2.377   0.108  83.434 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Train the ensemble using 5-fold CV to generate level-one data\n",
    "# More CV folds will take longer to train, but should increase performance\n",
    "system.time(fit <- h2o.ensemble(x = x,\n",
    "                                y = y,\n",
    "                                training_frame = train,\n",
    "                                family = family,\n",
    "                                learner = learner,\n",
    "                                metalearner = metalearner,\n",
    "                                cvControl = list(V = 5, shuffle = TRUE)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Prediction & Model Evaluation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `predict()` method for an `h2o.ensemble()` fit will return a list of two objects. The `pred$pred` object contains the ensemble predictions, and `pred$basepred` is a matrix of predictions from each of the base learners. \n",
    "\n",
    "However, a more useful function is `h2o.ensemble_performance()` which will compute the performance metrics for the base learners and ensemble on a test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  |======================================================================| 100%\n",
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      "\n",
      "Base learner performance, sorted by specified metric:\n",
      "                   learner       AUC\n",
      "1          h2o.glm.wrapper 0.6871217\n",
      "4 h2o.deeplearning.wrapper 0.7272816\n",
      "2 h2o.randomForest.wrapper 0.7683471\n",
      "3          h2o.gbm.wrapper 0.7817065\n",
      "\n",
      "\n",
      "H2O Ensemble Performance on <newdata>:\n",
      "----------------\n",
      "Family: binomial\n",
      "\n",
      "Ensemble performance (AUC): 0.786520264970981\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Compute test set performance:\n",
    "perf <- h2o.ensemble_performance(fit, newdata = test)\n",
    "print(perf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Base learner performance, sorted by specified metric:\n",
      "                   learner       MSE\n",
      "1          h2o.glm.wrapper 0.2216865\n",
      "4 h2o.deeplearning.wrapper 0.2215248\n",
      "2 h2o.randomForest.wrapper 0.1972327\n",
      "3          h2o.gbm.wrapper 0.1900497\n",
      "\n",
      "\n",
      "H2O Ensemble Performance on <newdata>:\n",
      "----------------\n",
      "Family: binomial\n",
      "\n",
      "Ensemble performance (MSE): 0.190136448554782\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# To print the results for a particular metric, like MSE, do the following:\n",
    "print(perf, metric = \"MSE\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.786520264970981"
      ],
      "text/latex": [
       "0.786520264970981"
      ],
      "text/markdown": [
       "0.786520264970981"
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      "text/plain": [
       "[1] 0.7865203"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# To access results directly in the ensemble performance object: \n",
    "perf$ensemble@metrics$AUC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Specifying Custom Learners\n",
    "\n",
    "Here is an example of how to generate a custom learner wrappers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Here is an example of how to generate a base learner library using custom base learners:\n",
    "\n",
    "h2o.randomForest.1 <- function(..., ntrees = 1000, nbins = 100, seed = 1) {\n",
    "  h2o.randomForest.wrapper(..., ntrees = ntrees, nbins = nbins, seed = seed)\n",
    "}\n",
    "\n",
    "h2o.deeplearning.1 <- function(..., hidden = c(500,500), activation = \"Rectifier\", seed = 1) {\n",
    "  h2o.deeplearning.wrapper(..., hidden = hidden, activation = activation, seed = seed)\n",
    "}\n",
    "\n",
    "h2o.deeplearning.2 <- function(..., hidden = c(200,200,200), activation = \"Tanh\", seed = 1) {\n",
    "  h2o.deeplearning.wrapper(..., hidden = hidden, activation = activation, seed = seed)\n",
    "}\n",
    "\n",
    "learner <- c(\"h2o.randomForest.1\", \"h2o.deeplearning.1\", \"h2o.deeplearning.2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stacking with Random Grids\n",
    "\n",
    "This example uses the technique of generating a random grid of base learners for maximum diversity, along with the `h2o.stack()` function.  The `h2o.stack()` function produces the exact same output as the `h2o.ensemble()` function, however you can use `h2o.stack()` to combine (via metalearning) a set of exsiting H2O models (where cross-validation was used and the predictions were saved)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  |======================================================================| 100%\n",
      "  |======================================================================| 100%\n"
     ]
    }
   ],
   "source": [
    "#library(h2oEnsemble)\n",
    "#h2o.init(nthreads = -1)\n",
    "\n",
    "# Import a sample binary outcome train/test set into R\n",
    "train <- h2o.importFile(\"data/higgs_train_10k.csv\")\n",
    "test <- h2o.importFile(\"data/higgs_test_5k.csv\")\n",
    "\n",
    "y <- \"response\"\n",
    "x <- setdiff(names(train), y)\n",
    "family <- \"binomial\"\n",
    "\n",
    "#For binary classification, response should be a factor\n",
    "train[,y] <- as.factor(train[,y])  \n",
    "test[,y] <- as.factor(test[,y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Random Grid Search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Random Grid Search (e.g. 120 second maximum)\n",
    "# This is set to run fairly quickly, increase max_runtime_secs \n",
    "# or max_models to cover more of the hyperparameter space.\n",
    "# Also, you can expand the hyperparameter space of each of the \n",
    "# algorithms by modifying the hyper param code below.\n",
    "\n",
    "search_criteria <- list(strategy = \"RandomDiscrete\", \n",
    "                        max_runtime_secs = 120)\n",
    "nfolds <- 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### GBM Hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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     ]
    }
   ],
   "source": [
    "# GBM Hyperparamters\n",
    "learn_rate_opt <- c(0.01, 0.03) \n",
    "max_depth_opt <- c(3, 4, 5, 6, 9)\n",
    "sample_rate_opt <- c(0.7, 0.8, 0.9, 1.0)\n",
    "col_sample_rate_opt <- c(0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8)\n",
    "hyper_params <- list(learn_rate = learn_rate_opt,\n",
    "                     max_depth = max_depth_opt, \n",
    "                     sample_rate = sample_rate_opt,\n",
    "                     col_sample_rate = col_sample_rate_opt)\n",
    "\n",
    "gbm_grid <- h2o.grid(\"gbm\", x = x, y = y,\n",
    "                     training_frame = train,\n",
    "                     ntrees = 100,\n",
    "                     seed = 1,\n",
    "                     nfolds = nfolds,\n",
    "                     fold_assignment = \"Modulo\",\n",
    "                     keep_cross_validation_predictions = TRUE,\n",
    "                     hyper_params = hyper_params,\n",
    "                     search_criteria = search_criteria)\n",
    "gbm_models <- lapply(gbm_grid@model_ids, function(model_id) h2o.getModel(model_id))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### RF Hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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    }
   ],
   "source": [
    "# RF Hyperparamters\n",
    "mtries_opt <- 8:20 \n",
    "max_depth_opt <- c(5, 10, 15, 20, 25)\n",
    "sample_rate_opt <- c(0.7, 0.8, 0.9)\n",
    "col_sample_rate_per_tree_opt <- c(0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8)\n",
    "hyper_params <- list(mtries = mtries_opt,\n",
    "                     max_depth = max_depth_opt,\n",
    "                     sample_rate = sample_rate_opt,\n",
    "                     col_sample_rate_per_tree = col_sample_rate_per_tree_opt)\n",
    "\n",
    "rf_grid <- h2o.grid(\"randomForest\", x = x, y = y,\n",
    "                    training_frame = train,\n",
    "                    ntrees = 200,\n",
    "                    seed = 1,\n",
    "                    nfolds = nfolds,\n",
    "                    fold_assignment = \"Modulo\",\n",
    "                    keep_cross_validation_predictions = TRUE,                    \n",
    "                    hyper_params = hyper_params,\n",
    "                    search_criteria = search_criteria)\n",
    "rf_models <- lapply(rf_grid@model_ids, function(model_id) h2o.getModel(model_id))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Deeplearning Hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "# Deeplearning Hyperparamters\n",
    "activation_opt <- c(\"Rectifier\", \"RectifierWithDropout\", \n",
    "                    \"Maxout\", \"MaxoutWithDropout\") \n",
    "hidden_opt <- list(c(10,10), c(20,15), c(50,50,50))\n",
    "l1_opt <- c(0, 1e-3, 1e-5)\n",
    "l2_opt <- c(0, 1e-3, 1e-5)\n",
    "hyper_params <- list(activation = activation_opt,\n",
    "                     hidden = hidden_opt,\n",
    "                     l1 = l1_opt,\n",
    "                     l2 = l2_opt)\n",
    "\n",
    "dl_grid <- h2o.grid(\"deeplearning\", x = x, y = y,\n",
    "                    training_frame = train,\n",
    "                    epochs = 15,\n",
    "                    seed = 1,\n",
    "                    nfolds = nfolds,\n",
    "                    fold_assignment = \"Modulo\",\n",
    "                    keep_cross_validation_predictions = TRUE,                    \n",
    "                    hyper_params = hyper_params,\n",
    "                    search_criteria = search_criteria)\n",
    "dl_models <- lapply(dl_grid@model_ids, function(model_id) h2o.getModel(model_id))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### GLM Hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r",
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     ]
    }
   ],
   "source": [
    "# GLM Hyperparamters\n",
    "alpha_opt <- seq(0,1,0.1)\n",
    "lambda_opt <- c(0,1e-7,1e-5,1e-3,1e-1)\n",
    "hyper_params <- list(alpha = alpha_opt,\n",
    "                     lambda = lambda_opt)\n",
    "\n",
    "glm_grid <- h2o.grid(\"glm\", x = x, y = y,\n",
    "                     training_frame = train,\n",
    "                     family = \"binomial\",\n",
    "                     nfolds = nfolds,\n",
    "                     fold_assignment = \"Modulo\",\n",
    "                     keep_cross_validation_predictions = TRUE,                    \n",
    "                     hyper_params = hyper_params,\n",
    "                     search_criteria = search_criteria)\n",
    "glm_models <- lapply(glm_grid@model_ids, function(model_id) h2o.getModel(model_id))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Specify Base Learners & Metalearner"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create a list of all the base models\n",
    "models <- c(gbm_models, rf_models, dl_models, glm_models)\n",
    "\n",
    "# Specify a defalt GLM as the metalearner\n",
    "metalearner <- \"h2o.glm.wrapper\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Metalearning\"\n",
      "\r",
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      "  |======                                                                |   8%\r",
      "  |                                                                            \r",
      "  |======================================================================| 100%\n"
     ]
    }
   ],
   "source": [
    "# Let's stack!\n",
    "stack <- h2o.stack(models = models, \n",
    "                   response_frame = train[,y],\n",
    "metalearner = metalearner)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "##### Compute the Performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  |======================================================================| 100%\n",
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      "\n",
      "Base learner performance, sorted by specified metric:\n",
      "                                                                   learner\n",
      "78          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_15\n",
      "79          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_35\n",
      "80          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_53\n",
      "76          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_14\n",
      "77          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_29\n",
      "75          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_23\n",
      "74           Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_7\n",
      "23 Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_17\n",
      "20 Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_16\n",
      "73          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_48\n",
      "72           Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_5\n",
      "71           Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_9\n",
      "70          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_16\n",
      "36          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_11\n",
      "35          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_18\n",
      "34          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_41\n",
      "33          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_43\n",
      "32          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_26\n",
      "31          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_50\n",
      "30          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_45\n",
      "29          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_19\n",
      "28          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_42\n",
      "26          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_46\n",
      "27           Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_2\n",
      "42          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_31\n",
      "38          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_49\n",
      "43          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_28\n",
      "37          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_22\n",
      "50          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_47\n",
      "48           Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_6\n",
      "49          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_36\n",
      "52          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_38\n",
      "51          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_17\n",
      "39          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_32\n",
      "44          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_52\n",
      "46          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_20\n",
      "53           Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_4\n",
      "57          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_54\n",
      "58          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_27\n",
      "45          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_51\n",
      "59          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_21\n",
      "60          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_25\n",
      "61          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_39\n",
      "62           Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_3\n",
      "63          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_40\n",
      "64          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_30\n",
      "65          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_33\n",
      "66          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_34\n",
      "67          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_12\n",
      "68          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_24\n",
      "69          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_13\n",
      "54          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_37\n",
      "55           Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_1\n",
      "47          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_44\n",
      "40           Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_8\n",
      "56          Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_10\n",
      "41           Grid_GLM_RTMP_sid_a34a_24_model_R_1467014209182_10625_model_0\n",
      "19 Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_12\n",
      "18  Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_4\n",
      "14  Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_9\n",
      "16  Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_2\n",
      "25 Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_15\n",
      "12 Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_11\n",
      "13  Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_1\n",
      "11  Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_7\n",
      "15  Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_8\n",
      "24  Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_0\n",
      "17  Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_5\n",
      "22 Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_10\n",
      "21 Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_13\n",
      "9   Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_6\n",
      "3             Grid_GBM_RTMP_sid_a34a_24_model_R_1467014209182_2066_model_4\n",
      "10 Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_14\n",
      "4             Grid_GBM_RTMP_sid_a34a_24_model_R_1467014209182_2066_model_1\n",
      "8   Grid_DeepLearning_RTMP_sid_a34a_24_model_R_1467014209182_10118_model_3\n",
      "5             Grid_GBM_RTMP_sid_a34a_24_model_R_1467014209182_2066_model_3\n",
      "2             Grid_GBM_RTMP_sid_a34a_24_model_R_1467014209182_2066_model_0\n",
      "6             Grid_DRF_RTMP_sid_a34a_24_model_R_1467014209182_8155_model_1\n",
      "7             Grid_DRF_RTMP_sid_a34a_24_model_R_1467014209182_8155_model_0\n",
      "1             Grid_GBM_RTMP_sid_a34a_24_model_R_1467014209182_2066_model_2\n",
      "         AUC\n",
      "78 0.5000000\n",
      "79 0.5000000\n",
      "80 0.5000000\n",
      "76 0.5389248\n",
      "77 0.5389345\n",
      "75 0.5417750\n",
      "74 0.5822301\n",
      "23 0.5960455\n",
      "20 0.6108904\n",
      "73 0.6154459\n",
      "72 0.6354336\n",
      "71 0.6506383\n",
      "70 0.6610600\n",
      "36 0.6863669\n",
      "35 0.6863711\n",
      "34 0.6864484\n",
      "33 0.6865243\n",
      "32 0.6865479\n",
      "31 0.6866241\n",
      "30 0.6867065\n",
      "29 0.6867256\n",
      "28 0.6867815\n",
      "26 0.6868012\n",
      "27 0.6868321\n",
      "42 0.6870867\n",
      "38 0.6870935\n",
      "43 0.6870962\n",
      "37 0.6871113\n",
      "50 0.6871120\n",
      "48 0.6871134\n",
      "49 0.6871156\n",
      "52 0.6871173\n",
      "51 0.6871189\n",
      "39 0.6871217\n",
      "44 0.6871233\n",
      "46 0.6871237\n",
      "53 0.6871253\n",
      "57 0.6871295\n",
      "58 0.6871317\n",
      "45 0.6871319\n",
      "59 0.6871365\n",
      "60 0.6871365\n",
      "61 0.6871365\n",
      "62 0.6871365\n",
      "63 0.6871365\n",
      "64 0.6871365\n",
      "65 0.6871365\n",
      "66 0.6871365\n",
      "67 0.6871365\n",
      "68 0.6871365\n",
      "69 0.6871365\n",
      "54 0.6871369\n",
      "55 0.6871384\n",
      "47 0.6871406\n",
      "40 0.6871426\n",
      "56 0.6871431\n",
      "41 0.6871481\n",
      "19 0.6910824\n",
      "18 0.6950987\n",
      "14 0.6951873\n",
      "16 0.6968837\n",
      "25 0.7026618\n",
      "12 0.7055578\n",
      "13 0.7126669\n",
      "11 0.7139075\n",
      "15 0.7154103\n",
      "24 0.7230679\n",
      "17 0.7238602\n",
      "22 0.7263660\n",
      "21 0.7298324\n",
      "9  0.7394220\n",
      "3  0.7396723\n",
      "10 0.7409898\n",
      "4  0.7419225\n",
      "8  0.7481582\n",
      "5  0.7516993\n",
      "2  0.7552767\n",
      "6  0.7619598\n",
      "7  0.7633915\n",
      "1  0.7790918\n",
      "\n",
      "\n",
      "H2O Ensemble Performance on <newdata>:\n",
      "----------------\n",
      "Family: binomial\n",
      "\n",
      "Ensemble performance (AUC): 0.788529105381067\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Compute test set performance:\n",
    "perf <- h2o.ensemble_performance(stack, newdata = test)\n",
    "print(perf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Refit the Metalearner"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Metalearning\"\n",
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      "\n",
      "\n",
      "H2O Ensemble Performance on <newdata>:\n",
      "----------------\n",
      "Family: binomial\n",
      "\n",
      "Ensemble performance (AUC): 0.777667064847103\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Now let's refit the metalearner using a DL and GLM-NN\n",
    "# Note: DL is not usually the best metalearner\n",
    "\n",
    "stack2 <- h2o.metalearn(stack, metalearner = \"h2o.deeplearning.wrapper\")\n",
    "perf2 <- h2o.ensemble_performance(stack2, newdata = test, score_base_models = FALSE)\n",
    "print(perf2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Restrict to Non-Negative Weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Metalearning\"\n",
      "  |======================================================================| 100%\n",
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      "\n",
      "\n",
      "H2O Ensemble Performance on <newdata>:\n",
      "----------------\n",
      "Family: binomial\n",
      "\n",
      "Ensemble performance (AUC): 0.786483342785091\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# It's always a good idea to try a GLM restricted to non-negative weights as a metalearner\n",
    "# There have been a lot of empircal studies that show that non-negative weights can lead to better performance\n",
    "\n",
    "h2o.glm_nn <- function(..., non_negative = TRUE) h2o.glm.wrapper(..., non_negative = non_negative)\n",
    "stack3 <- h2o.metalearn(stack, metalearner = \"h2o.glm_nn\")\n",
    "perf3 <- h2o.ensemble_performance(stack3, newdata = test, score_base_models = FALSE)\n",
    "print(perf3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test set of the top base learner was 0.779, where as the best ensemble got 0.788.  The gain is more than enough to jump 100+ spots on a Kaggle competition. :-)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  }
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