{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## The Highly Adaptive LASSO and the `hal9001` R package\n", "\n", "## Lab 10 for PH 290: Targeted Learning in Biomedical Big Data\n", "\n", "### Author: [Nima Hejazi](https://nimahejazi.org)\n", "\n", "### Date: 21 March 2018" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# I. The Highly Adaptive LASSO (HAL)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Recommended Reading\n", "\n", "* Benkeser, D, and van der Laan, MJ (2016). \"The Highly Adaptive Lasso Estimator.\" IEEE International Conference on Data Science and Advanced Analytics. (http://ieeexplore.ieee.org/abstract/document/7796956/)\n", "* R package: Coyle, JR, and Hejazi, NS (2018). \"hal9001: A fast and scalable Highly Adaptive LASSO.\" (https://github.com/jeremyrcoyle/hal9001)\n", "\n", "### What's HAL All About?\n", "\n", "\"Estimation of a regression function is a common goal of statistical learning. We propose a novel _nonparametric regression estimator_ that, in contrast to many existing methods, does not rely on _local smoothness assumptions_ nor is it constructed using _local smoothing techniques_. Instead, our estimator respects global smoothness constraints by virtue of falling in a class of right-hand continuous functions with left-hand limits that have variation norm bounded by a constant. Using empirical process theory, we establish a fast minimal rate of convergence of our proposed estimator and illustrate how such an estimator can be constructed using standard software.\" -excerpted from Benkeser & vdL (2016).\n", "\n", "### Why Care About Prediction?\n", "\n", "* Consider observed data $O = (X, Y)$, where $X$ is a set of covariates and $Y$ a vector outcome of interest.\n", "* Let us further write $O \\sim P_0 \\in \\mathcal{M}^{NP}$, where $P_0$ is the true distribution of the observed data $O$, contained in the nonparametric (infinite-dimensional) statistical model $\\mathcal{M}^{NP}$.\n", "* Let the _target parameter_ be the prediction function $\\psi_0$ s.t. we have $\\psi_0 \\in \\Psi$, a class of prediction functions that minimize the average of a scientifically relevant loss function (e.g., negative log-likelihood for binary outcomes).\n", "* Thus, our goal is to estimate $\\Psi(P_0)(X) = \\text{argmin}_{\\psi \\in \\Psi} E_{P_0}{L(\\psi)(X, Y)}$ for an arbitrary loss function $L(\\psi)$.\n", "\n", "### How Can Prediction Go Wrong?\n", "\n", "* \"Parametric and semiparametric methods for estimating the conditional mean assume its form is known up to a finite number of parameters.\"\n", "* Consider GLMs, which express the conditional mean as a transformation of a linear function of the conditioning variables - e.g., $E(Y \\mid X) = \\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\ldots$\n", "* Parametric methods suffer from a large bias when the assumed functional form is different from the true conditional mean (e.g., $E(Y \\mid X) = \\beta_0 + \\beta_i X_1 X_2 + \\beta_j X_1^2 + \\beta_k X_2^3 + \\ldots$).\n", "* Even nonparametrics is plagued by assumptions: \"For example, many methods assume $\\psi_0$ has nearly constant, linear, or low-order polynomial behavior for all points sufficiently close to each other in a given metric.\"\n", "\n", "### Theory and Properties of HAL\n", "\n", "* \"We assume that the true conditional mean function is right-hand continuous with left-hand limits (cadlag) and has variation norm smaller than a constant $M$. These are exceedingly mild assumptions that are expected to hold in almost every practical application.\"\n", "* We make two key smoothness assumptions about $\\psi_0$: (1) $\\psi_0$ is an element of the Banach space of d-variate cadlag functions; (2) $\\psi_0$ has finite variation norm, where the variation norm is defined $\\mid\\mid \\psi \\mid\\mid_{v} = \\int_{[0, \\tau]} \\mid \\psi(dx) \\mid$. The definition of HAL follows directly from an alternate formulation of the variation norm...\n", "* For any function $\\psi \\in D[0, \\tau]$, we define the s-th section of $\\psi$ as $\\psi_s(x) = \\psi(x_1 I(1 \\in s), \\ldots, x_d I(d \\in s))$, which is _the function that varies along the variables in $x_s$ according to $\\psi$, but sets the variables in $x_{s,c}$ equal to zero_. \n", "* Under the conditions above, $\\psi$ admits the following representation: $$\\psi(x) = \\psi(0) + \\sum_{s \\subset \\{1, \\ldots, d\\}} \\int_{0_s}^{x_s} \\psi_s(du) = \\psi(0) + \\sum_{s \\subset \\{1, \\ldots, d\\}} \\int_{0_s}^{\\tau_s} I(u \\leq x_s) \\psi_s(du).$$\n", "* By approximating $\\psi$ above with a discrete measure $\\psi_m$ over $m$ support points, one may write $$\\psi_m(x) = \\psi(0) + \\sum_{s \\subset \\{1, \\ldots, d\\}} \\sum_{j} I(u_{s,j} \\leq x_s) d\\psi_{m,s,j},$$ where this approximation consists of a linear combination of basis functions with\n", "corresponding coefficients $d\\psi_{m,s,j}$ summed over $s$ and $j$.\n", "* The following nice property follows directly from the definition of the HAL estimator: the sum of the absolute values of these coefficients gives the variation norm of $\\psi_m$ - i.e., $$\\mid\\mid\\psi_m \\mid\\mid_v = \\psi(0) + \\sum_{s \\subset \\{1, \\ldots, d\\}} \\sum_{j} \\mid d\\psi_{m,s,j} \\mid.$$\n", " \n", "\n", "\n", "### How Does HAL Help Us?\n", "\n", "* Since HAL has been shown to consistently estimate the true functional relation at a rate faster than $n^{−\\frac{1}{4}}$ as a function of sample size $n$, whenever the true target function has finite variation norm, we are able to obtain very good convergence rates when using it as an estimator.\n", "* The assumption of finite variation norm may be easily included in our statistical model without any concern for misspecification, since it is unlikely that the true functional relations have infinite variation as a function of the different covariates." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# II. Nonparametric Estimation / Prediction with `hal9001`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's load the packages we'll be using and some core project management tools." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "options(repr.plot.width = 5, repr.plot.height = 5) ## resizing plots\n", "options(scipen = 999) ## has scientific notation ever annoyed you?" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "here() starts at /Users/nimahejazi/Dropbox/UC_Berkeley-grad/teaching/2018_Spring/tlbbd-labs/lab_10\n", "── Attaching packages ─────────────────────────────────────── tidyverse 1.2.1 ──\n", "✔ ggplot2 2.2.1 ✔ purrr 0.2.4\n", "✔ tibble 1.4.2 ✔ dplyr 0.7.4\n", "✔ tidyr 0.8.0 ✔ stringr 1.3.0\n", "✔ readr 1.1.1 ✔ forcats 0.3.0\n", "── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──\n", "✖ dplyr::filter() masks stats::filter()\n", "✖ dplyr::lag() masks stats::lag()\n", "\n", "Attaching package: ‘data.table’\n", "\n", "The following objects are masked from ‘package:dplyr’:\n", "\n", " between, first, last\n", "\n", "The following object is masked from ‘package:purrr’:\n", "\n", " transpose\n", "\n" ] } ], "source": [ "library(here)\n", "library(usethis)\n", "library(tidyverse)\n", "library(data.table, quietly = TRUE)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Loading required package: plotmo\n", "Loading required package: plotrix\n", "Loading required package: TeachingDemos\n", "Loading required package: Matrix\n", "\n", "Attaching package: ‘Matrix’\n", "\n", "The following object is masked from ‘package:tidyr’:\n", "\n", " expand\n", "\n", "Loading required package: foreach\n", "\n", "Attaching package: ‘foreach’\n", "\n", "The following objects are masked from ‘package:purrr’:\n", "\n", " accumulate, when\n", "\n", "Loaded glmnet 2.0-13\n", "\n", "randomForest 4.6-12\n", "Type rfNews() to see new features/changes/bug fixes.\n", "\n", "Attaching package: ‘randomForest’\n", "\n", "The following object is masked from ‘package:dplyr’:\n", "\n", " combine\n", "\n", "The following object is masked from ‘package:ggplot2’:\n", "\n", " margin\n", "\n", "hal9001 v0.1.1: A fast and scalable Highly Adaptive LASSO\n" ] } ], "source": [ "library(earth)\n", "library(glmnet)\n", "library(randomForest)\n", "library(hal9001)\n", "library(sl3)\n", "set.seed(385971)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We begin by simulating a simple data set and illustrating a simple execution of how to use `hal9001` for prediction." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
X1X2X3X4Y
0.2086134 -0.16809762 0.3635787 0 0.4550150
-0.9477350 -0.68371703-1.2229561 0 0.1571233
0.9254026 -1.42357891 0.1638252 1 0.1943260
0.5603774 -0.09578228 1.4152984 1 1.6964338
0.6430260 1.01289165-1.1249601 0 0.5796670
-0.9730101 0.18683905 0.3577011 0 -0.7109583
\n" ], "text/latex": [ "\\begin{tabular}{r|lllll}\n", " X1 & X2 & X3 & X4 & Y\\\\\n", "\\hline\n", "\t 0.2086134 & -0.16809762 & 0.3635787 & 0 & 0.4550150 \\\\\n", "\t -0.9477350 & -0.68371703 & -1.2229561 & 0 & 0.1571233 \\\\\n", "\t 0.9254026 & -1.42357891 & 0.1638252 & 1 & 0.1943260 \\\\\n", "\t 0.5603774 & -0.09578228 & 1.4152984 & 1 & 1.6964338 \\\\\n", "\t 0.6430260 & 1.01289165 & -1.1249601 & 0 & 0.5796670 \\\\\n", "\t -0.9730101 & 0.18683905 & 0.3577011 & 0 & -0.7109583 \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "X1 | X2 | X3 | X4 | Y | \n", "|---|---|---|---|---|---|\n", "| 0.2086134 | -0.16809762 | 0.3635787 | 0 | 0.4550150 | \n", "| -0.9477350 | -0.68371703 | -1.2229561 | 0 | 0.1571233 | \n", "| 0.9254026 | -1.42357891 | 0.1638252 | 1 | 0.1943260 | \n", "| 0.5603774 | -0.09578228 | 1.4152984 | 1 | 1.6964338 | \n", "| 0.6430260 | 1.01289165 | -1.1249601 | 0 | 0.5796670 | \n", "| -0.9730101 | 0.18683905 | 0.3577011 | 0 | -0.7109583 | \n", "\n", "\n" ], "text/plain": [ " X1 X2 X3 X4 Y \n", "1 0.2086134 -0.16809762 0.3635787 0 0.4550150\n", "2 -0.9477350 -0.68371703 -1.2229561 0 0.1571233\n", "3 0.9254026 -1.42357891 0.1638252 1 0.1943260\n", "4 0.5603774 -0.09578228 1.4152984 1 1.6964338\n", "5 0.6430260 1.01289165 -1.1249601 0 0.5796670\n", "6 -0.9730101 0.18683905 0.3577011 0 -0.7109583" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 1000\n", "p = 3\n", "x <- cbind(matrix(rnorm(n * p), n, p), rbinom(n, 1, 0.61))\n", "y <- sin(x[, 1]) * sin(x[, 2]) + x[, 1]^2 * (x[, 1] > x[, 2]) + x[, 3] * x[,4] +\n", " rnorm(n, mean = 0, sd = 0.3)\n", "data <- as.data.table(cbind(x, y))\n", "setnames(data, c(paste0(\"X\", seq_len(p + 1)), \"Y\"))\n", "head(data)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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SNGmCSnf/g67d+/v+EAUDxmf/vb306F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\nr+8nVH+/ncX+rkT7ZQGeVDe+Nf7yaGdS2XzDwvQkxc0ynPdSmN0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onguTxhjGAoZFE5sUZGHId8c3n+X5fVKXRrhmzmBho4JROB2BcSkD\nbBpiVYheF1uXWiFRD+Kptt4IPzNMAKxSBgwYULdG0zBTYkTu9wGHWsNE8pEzyEMMBAzO7AIL\n2ZNIHrxneFJHsuQyWPyGyUHqBDFwUQbvMbtIhWCAmCjk6CQmJ+Ix4ME0uWVzhiX1EykoK0Mk\nX5wZKW1jIGNliITETSvl1fLVVf9wL31Bnd0+EuYEJihNH6VNS5/DEKGywAkoTG45xISFjRyq\nKN4TaR+TD9I63o8kCWc55VcrLTv02BjD95RVX7FogFGVd5q+x1kr17i+ivruyA+mzd/lWS3M\naqFc1KmMW8X2W48WNyQ+oQ7+7W9/a79b15P7e++9Z+158QWHtF0I7QJjGN+qUlsE/qtl8h3Q\n9nFpT9iNgCEvnDGTCpM7qip/5e/nzmCLkR0fYjFboEUtwYDOBMeKSKQFbhkyQEaF8fEjGhfx\nKGnRTwMNL86JJ57YKkzyJh15syMtZJhMuxlIosKYjJlYZdUg+XJF9EudosLQgUv73XTcgz8f\nCswuu25gFsQgVFZ+4pcmlDYqDAYYjKgX92mJARHsmZSYnLIitubDmCPOZiUmgzJnErK7T947\n/MRgl0M/tPta3E3fMSBhA8UAAS68h9gT7bjjjoWdZ9SZwQtbMNLTHzBXSDfJn0GKd4D+IAyj\ndnAnP3AiP3bfYDsikwKLj9kt0i7KRzXD4MW3Qx7HH3+8xYhVIe90vUlJeHfAn3pTf7ePwJKV\n8S233GJXw0l9lDYtfUGfoLLlm6C/3T8YYel3991DzQEjxffhSljoB94JXAcwDsBcs2JHQkZf\nwWjDxPEtVIPRYsygnUhhhXFx21XKPSpp/nh/+Z6y6iskwtgrih85+gomjt+8J24/cS995X93\njIfUa9KkSbbNnVt2SqMuzKr99CXfHN+0MJfF4Ei9mYdELV5M2lLjMreAL/Mmi4FS+s0vm3eA\nEwv4XsQMgzi8a5x+wFgGRoxt9BeuSxBAuJJ4P8+sfjN2UC5jPXOnSyEJnhue9T3jA+9fErWu\nZVLsmHAmFXZL4SGZAYuO4rgRjOLcY0fcLIjDxMJflhOvW0ap90g3oGqcX1Rqnf10rEDAlonB\nlb748er1Nx89R+JMmDDB2t7QDgZu7G9EBcgzmE0+QJ8hZWCAKWLQx6s7TCN2Bvvttx/JLPEM\nNQbvMXEg3lVW+5TjSmgxdmdyZqcNgx1EOKs+11UAkiy8UTM4IRGBQcOWgYlIFgo2cQP8c/to\nxIgRFjt8UaXpo7RpxWXCohbDdv58ojyRNPphUb+RAENIxmA6IPoGw3nyYsNCoxHvKobMOCnO\nqq8Yd9xvRDasIInizyfpK/+749vj2+K7Q13vf8t+Ps30m0WajIPF9lsxODFejm85XkrmRs7m\nxPk2dlpKYQSWa5lglhpPhMNTP2US5wiQm266qZCGZ6xWsQMKEat71CX9+/e3Z4YxQUV5kg2l\nF+dmcNSsmJEIhKQvSBNoZlQYLyhSFjHIpCwGUVbFSC742N0wqQvpyBt1D8yiT0wQrNKiwhiw\nmfhDEi64dOoUFQYHj0PKEPHis6KCmNgxFMfTLiszwsAiyjgbrjwqjFU7qyZW/sWoYcCQVTei\nbAbJPIg2YjPAak52GKYtB+kabQKbuPrRBiZb4tAWkYz65bAaJj/6KG5FyztFPDB31Wo8h0Hj\nna43p4q8O/QF9falb6y2Wfnx3RRLcWlZ3BHO7lK+qSyJvqRN1BvXAPJ+wNTRT8VI3LOqF2MG\n3z6q7VKwDNWDRQhtYsziG4rDO5TefeamzQInvjvGdsZEvrk82i/fnLTfbU+ae6RyzEOiKUiT\nptw4MJlIlRg/RALrYl9u/qH0zB0wxsy9SOTBq1KE9Jg5MfSdV9qTvCyKk9qemQQLwP2JjU5H\n7AqTIAOTWyEMmPEvxUTEoaxRxCB3ySWXtApm+7UYoDL4QQyuvuiQ5/JMrjwTkokNEbSIm9l6\nzwqVutEGypcwScdVJlhWaCFGiPKEuXPTcS91cVd3bhzwigsjbtTgioRFwmBYL774YjNz5kzT\nq1cv2w98JBLulsk95UaFEV7qBEnaPInJPIoxTCqXdwB1VBLRlwxmDPZxBEYwa0nEOyUDY1Lc\nRggvZzAuJ2052NGXad6NcsqoxbTl4F1O2hAWfHf8KSUjkDX2fonMLSzUVYLoIxP+nRmDxYrK\nn5iR/MB4MCGFOj6tA0AYHNlGKs1gUsRJo0tMWCFGSOLEhbkrXxxAQvi/oRxhwiQf/8rKJYqE\nkYoKjxs44sLILy5cwji4dfDgwVaSiBgZ4iORcPvA+xcXxoQTF+5lpT8VAUVAEVAEFIGmRCAz\nBgsmxFeFyW/x1VEqwuQtTI/kgSQB6RgE4wQzB1eNqNsnYZ5CYTBHMAwY0KH+Ql2EmhMuHXsc\njOrkuZ8v6UiPWBYm0CfqhFoyKox6oyJCouSTqDyjwmB0SBsimFnqBCEFQ9rHzk7sfZD6kaeE\n++kpl+24IUJEDz4irg/F0WeKgCKgCCgCioAi0KKpygoEJt9FnoEpTAuTfZzkKE35SFxCtg5i\ngyVSIhgZGACfUOXBVESFER9mkHCMWtHzYoSLugwJXFS+ohYkrTCTbtmUGRcm5Uo+obRRYcQN\ntUfycMMw1IfBgnFkV2QUFqG08kyuSWklnl4VAUVAEVAEFIFmRiAzi2MMLjHMdRkNPFP7dlm1\nDja7xaB63j3oY4yLACRZU6ZMadU/fjz9rQgoAoqAIqAIKALZIJAZg7XbbrvZGuGnBKkLOw3Y\n/n700UcXaorPIiREtUrsvGPrPLsUxNFkrda1mHqhosUbPSpVdm4qKQKKgCKgCCgCikC+CGTG\nYKEGvPDCC62PDPz59OvXz/qMcf3/zJo1K9JlQ77NTJc7B+2iDsRvUaMRR+dAY8eObbSmaXsU\nAUVAEVAEFIGaQyAzGyxaxrES+MLCTwlG6L5rBg6FjCJ/l2BUvLyeI3UbNWqUdZ/gHhGQV3mV\nzhe/TUjl8NKLCwrfR1Ee9WFTAQbxYg+GhBB7ujxIymBTAe9fXoS/HAhpIBsN8iBRs4NfOW3B\nVUQS3uIVPKt2kB9EvwtWWeUdlQ8bUSDxPRYVL8vn9BH2iOX0D/VJ4wkeLN0NOrJFns0o0vZy\n2ybvHPmV2ya3Llnh5OYp7WejTt7tZw5jLksi3gU2Q2WJXVKZlAflPeb59XC/camDHyeP39LX\n/ndero13HnWVPDNlsCTTNIOGxK2VK8f6MJDhZTvOOWSt1LeUevTs2dOccsoplpE8++yzS8mi\nqDRMCq4z1EoMPgw2/OVNpfrcKqZePn7FpCUuE0MSg8Vk5fZRsWVExY/aiRoVP4vnsqs4i7zS\n5lEudmnGSrAM4Rm1Ezht3UPxyn3nQnnyrFycQvmGMAnFK+aZ3342UKVhsFigw2zk0c6k+sPw\nCNOTFDfLcOZL/ipN/nfuu4eqdH3iysuFwYorsFbDxAP90KFDa7WKZdera9eu5qKLLrJHGnG+\nYt4vJm4s2rWcacWgw8CFh2hfqll2o77OAGkJu0pxjZHWv1opZSOFg4FbbbXVCs5iS8knLg3S\nOM6+A780g3tUXknMFemQZIobk6h8innOgMvET72pfyUIZpcJhg01ST7rsqoP3uqZUHm/8yYk\nka7EWRgunpfrAkfqntU7J/nJlfcYKVaWJxJUsv1pxyvisVu9kk5phRlkHK+kUADvAOy0x3NA\nlDNs6f8srzBWLAhxzixOvsmfb5461SIpg9XSK7jZn91y+G6nTp0K3uFrsbPKrROi1N/85jdm\n4MCB9oxCmKw8iRcff2Ii7eE+7YBVbL1EakUbKScvEqkBjJz7kWdZnqjWBL8BHobZAABAAElE\nQVQs8/bzAq8sRewwHWDExJ9nP7jtgKmDwWKwz5JZdMvw71k0wMBWoo342nOdGTOxQjCwWS2S\nJE/e6SzbBE4wWFnmKXXNsv3yzZXaft4FpF1ZttN/5/zfYqKQ95jnlyvmGJX8xqmDMFGMvZX6\nzv22F/s7MyP3YguupfhIdaC8GY5aaDMMFoP1mDFjWtl11ELdtA6KgCKgCCgCikCjIFDXEiwR\ni4pUBI46xNnC6WOEGArj3EEOo950003t7kFfrcKqhFVNSN0hDk5ZtZC/T7KiiQojviv6d9NT\n57gw4kr73XTcg0dUGG054YQTzLBhw2y7TzrppFbJKTcqLRFpU1x4q8z0hyKgCCgCioAi0KQI\n1DWDJQZ2IiJFdCw7Ddz+hPGCyfHDMEzkfD7Czj///III0k2L2gG1B38+EUbe6IVlF44bB8YL\n1UVUGMwMYs8QA4YH/LgwGB1pv1sm99ggRYWhN+/fv7+59tpr7QHaBx10UCs9elxabD5oC3lz\nr6QIKAKKgCKgCCgCYQTqWkWIzyr+hEGBYZJn7pXnoTDcMsyZM8fsv//+pkuXLsG05B1K65br\nluXek9b97d4n1ZnuiipXutLNz70n3P3t3lMuzNFxxx1nt7VffvnlreLG1dktV+71qggoAoqA\nIqAIKAJtEahrBqttc9I/efzxx83gwYOtugtGq9mob9++ZuWVV7a2WBxppKQIKAKKgCKgCCgC\n2SHQlAzWU089ZXr06GElXzfccINlNLKDtD5yQrUJg4l0C+N+2YVXH7XXWioCioAioAgoArWN\nQFMxWKi/YKg4yBl7rCuvvNKqBmu7i/Kr3R577GGOPPJIM2/ePINEC2ZLSRFQBBQBRUARUATK\nR6BpGKxnnnnGHnh83nnnWTcFHM2DgXezEy4qttpqK3P//fdbuyyVZDX7G6HtVwQUAUVAEcgC\ngcwZrHfffddwaPLMmTPt7rqkSn7++ed2cp86daohbZbELjzqsvvuu9s/mKxdd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MqWW27Zamcfu+MgdsblyWDhYgE1HZ7PUQExObIdf5tt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NM0O7xjKCuYKTx/mlYAgWGAGixhJ8/WpH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\nCvyNAux7zI8g5tz8m+8bNmwY/cM//EPSKnzgAx/YxC420orXBvID4vYtM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0hTFx9lEy8zhCyBMJKAOGrbjEPy2BaGGUYLuyXvfaDe2kNb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\nSvn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8TuJGDu0dhiefHFF48w+CZpp9pI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\nTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "GGally::ggpairs(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Let's try a few standard prediction algorithms**" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "1.99132408234604" ], "text/latex": [ "1.99132408234604" ], "text/markdown": [ "1.99132408234604" ], "text/plain": [ "[1] 1.991324" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Intercept GLM\n", "mean_fit <- mean(y)\n", "mean_pred <- rep(mean_fit, length(y))\n", "(mse_mean <- mean((y - mean_pred)^2))" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "1.13997134197425" ], "text/latex": [ "1.13997134197425" ], "text/markdown": [ "1.13997134197425" ], "text/plain": [ "[1] 1.139971" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Simple GLM\n", "glm_fit <- glm(Y ~ ., data = data)\n", "glm_pred <- predict(glm_fit)\n", "(mse_glm <- mean((y - glm_pred)^2))" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "1.62097295787779" ], "text/latex": [ "1.62097295787779" ], "text/markdown": [ "1.62097295787779" ], "text/plain": [ "[1] 1.620973" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Ridge (L2-penalized) regression\n", "ridge_fit <- glmnet(x = x, y = y, alpha = 0)\n", "ridge_pred <- predict(ridge_fit, newx = x)\n", "(mse_ridge <- mean((y - ridge_pred)^2))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "1.24130069217104" ], "text/latex": [ "1.24130069217104" ], "text/markdown": [ "1.24130069217104" ], "text/plain": [ "[1] 1.241301" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Lasso (L1-penalized) regression\n", "lasso_fit <- glmnet(x = x, y = y, alpha = 1)\n", "lasso_pred <- predict(lasso_fit, newx = x)\n", "(mse_lasso <- mean((y - lasso_pred)^2))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.547326292503409" ], "text/latex": [ "0.547326292503409" ], "text/markdown": [ "0.547326292503409" ], "text/plain": [ "[1] 0.5473263" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Multivariate Adaptive Regression Splines (MARS)\n", "mars_fit <- earth(Y ~ ., data = data)\n", "mars_pred <- predict(mars_fit)\n", "(mse_mars <- mean((y - mars_pred)^2))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.548685008416127" ], "text/latex": [ "0.548685008416127" ], "text/markdown": [ "0.548685008416127" ], "text/plain": [ "[1] 0.548685" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Random Forest\n", "rf_fit <- randomForest(Y ~ ., data = data)\n", "rf_pred <- predict(rf_fit)\n", "(mse_rf <- mean((y - rf_pred)^2))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1] \"Good morning, Dave.\"\n" ] }, { "data": { "text/html": [ "0.0840655961849102" ], "text/latex": [ "0.0840655961849102" ], "text/markdown": [ "0.0840655961849102" ], "text/plain": [ "[1] 0.0840656" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Highly Adaptive LASSO (HAL)\n", "hal_fit <- fit_hal(X = x, Y = y)\n", "hal_pred <- predict(hal_fit, new_data = x)\n", "(mse_hal <- mean((y - hal_pred)^2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model Ensembling with `sl3`\n", "\n", "Now that we've generate some data, we will generate an `Task` object for use with `sl3`:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "A sl3 Task with 1000 obs and these nodes:\n", "$covariates\n", "[1] \"X1\" \"X2\" \"X3\" \"X4\"\n", "\n", "$outcome\n", "[1] \"Y\"\n", "\n", "$id\n", "NULL\n", "\n", "$weights\n", "NULL\n", "\n", "$offset\n", "NULL\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "task <- sl3_Task$new(data, covariates = c(paste0(\"X\", seq_len(p + 1))), outcome = \"Y\")\n", "task" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Easily and flexibly build a stack** _(n.b., this is the `sl3` idiom for the `SL.library` of `SuperLearner`)_" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1] \"Lrnr_mean\"\n", "[1] \"Lrnr_glm_fast_TRUE_Cholesky\"\n", "[1] \"Lrnr_randomForest_100_TRUE_5_NULL_FALSE\"\n", "[[1]]\n", "[1] \"Lrnr_mean\"\n", "\n", "[[2]]\n", "NULL\n", "\n", "[[3]]\n", "NULL\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lrnr_stack <- make_learner_stack(\"Lrnr_mean\", \"Lrnr_glm_fast\", \"Lrnr_randomForest\")\n", "lrnr_stack" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Next, we'll train the Super Learner and predict on the observed data**" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.0406695846361075" ], "text/latex": [ "0.0406695846361075" ], "text/markdown": [ "0.0406695846361075" ], "text/plain": [ "[1] 0.04066958" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sl <- Lrnr_sl$new(learners = list(lrnr_stack), metalearner = Lrnr_nnls$new())\n", "sl_fit <- sl$train(task)\n", "preds_sl <- sl_fit$predict()\n", "(mse_sl <- mean((y - preds_sl)^2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**What's the stacked ensemble look like?**" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1] \"SuperLearner:\"\n", "List of 1\n", " $ : chr \"Stack\"\n", "[1] \"Lrnr_nnls\"\n", " lrnrs weights\n", "1: Lrnr_mean 0.00000\n", "2: Lrnr_glm_fast_TRUE_Cholesky 0.00000\n", "3: Lrnr_randomForest_100_TRUE_5_NULL_FALSE 1.03947\n", "[1] \"Cross-validated risk (MSE, squared error loss):\"\n", " learner coefficients mean_risk SE_risk\n", "1: Lrnr_mean 0.00000 1.9951799 0.14827550\n", "2: Lrnr_glm_fast_TRUE_Cholesky 0.00000 1.1664105 0.09117183\n", "3: Lrnr_randomForest_100_TRUE_5_NULL_FALSE 1.03947 0.2158630 0.01532222\n", "4: SuperLearner NA 0.2129381 0.01503779\n", " fold_SD fold_min_risk fold_max_risk\n", "1: 0.68348784 1.2554075 3.0880768\n", "2: 0.37317242 0.6950223 1.7927896\n", "3: 0.04590635 0.1337699 0.2771392\n", "4: 0.04479534 0.1417545 0.2834144" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sl_fit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**What happens when we add HAL to the stacked ensemble?**\n", "\n", "Yes, there's a `Lrnr_hal9001` now!" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.052777555469573" ], "text/latex": [ "0.052777555469573" ], "text/markdown": [ "0.052777555469573" ], "text/plain": [ "[1] 0.05277756" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lrnr_stack_hal <- make_learner_stack(\"Lrnr_mean\", \"Lrnr_glm_fast\", \"Lrnr_randomForest\",\n", " \"Lrnr_hal9001\")\n", "sl_hal <- Lrnr_sl$new(learners = list(lrnr_stack_hal), metalearner = Lrnr_nnls$new())\n", "sl_hal_fit <- sl_hal$train(task)\n", "preds_sl_hal <- sl_hal_fit$predict()\n", "(mse_sl_hal <- mean((y - preds_sl_hal)^2))" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1] \"SuperLearner:\"\n", "List of 1\n", " $ : chr \"Stack\"\n", "[1] \"Lrnr_nnls\"\n", " lrnrs weights\n", "1: Lrnr_mean 0.0000000\n", "2: Lrnr_glm_fast_TRUE_Cholesky 0.0000000\n", "3: Lrnr_randomForest_100_TRUE_5_NULL_FALSE 0.5168892\n", "4: Lrnr_hal9001_NULL_glmnet_10_TRUE 0.5030761\n", "[1] \"Cross-validated risk (MSE, squared error loss):\"\n", " learner coefficients mean_risk SE_risk\n", "1: Lrnr_mean 0.0000000 1.9951799 0.14827550\n", "2: Lrnr_glm_fast_TRUE_Cholesky 0.0000000 1.1664105 0.09117183\n", "3: Lrnr_randomForest_100_TRUE_5_NULL_FALSE 0.5168892 0.2197907 0.01535048\n", "4: Lrnr_hal9001_NULL_glmnet_10_TRUE 0.5030761 0.2166624 0.02211670\n", "5: SuperLearner NA 0.1862682 0.01446540\n", " fold_SD fold_min_risk fold_max_risk\n", "1: 0.68348784 1.2554075 3.0880768\n", "2: 0.37317242 0.6950223 1.7927896\n", "3: 0.04455936 0.1359939 0.2765591\n", "4: 0.06755858 0.1352412 0.3725420\n", "5: 0.03469860 0.1249777 0.2387863" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sl_hal_fit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### _Reminder:_ Homwork #3, Question 2: Contributing to `sl3`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Update: Homework #3 is now officially due Friday, 06 April, by 3pm**\n", "\n", "What learners to contribute: https://github.com/tlverse/sl3/issues/114\n", "How do learners work: https://sl3.tlverse.org/articles/custom_lrnrs.html\n", "\n", "Tips and best practices:\n", "* For the `sl3` repo from https://github.com/tlverse/sl3\n", "* Using git, create a new branch for your proposed contribution (e.g., `Lrnr_ranger`)\n", "* Generate a template for your new learner via `sl3::write_learner_template(here::here(\"R\", \"Lrnr_ranger.R\"))`\n", "* Fill out the template based on the properties of your new learner. Try looking at already written learners to get a better idea of how to fill out the various methods slots.\n", "* Write a set of unit tests under `tests/testthat/test_Lrnr_ranger.R` that ensure that your new learner works as intended/expected.\n", "* For a guide on how to write unit tests properly, try looking at the numerous unit tests that already exist inside the `sl3` package.\n", "* For background on unit testing in R, take a look here: http://r-pkgs.had.co.nz/tests.html\n", "* The `tlverse` ecosystem uses the [\"`Tidyverse` Style Guide\"](http://style.tidyverse.org/). Make sure to follow the formatting guidelines for your code and for pull requests. You can use the [`styler` R package](https://cran.r-project.org/web/packages/styler/index.html) to automatically reformat your code." ] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "3.4.4" } }, "nbformat": 4, "nbformat_minor": 2 }