{
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   "source": [
    "## Bias-Variance Tradeoff and Cross-Validation\n",
    "\n",
    "## Lab 04 for PH 290: Targeted Learning in Biomedical Big Data\n",
    "\n",
    "### Author: [Nima Hejazi](https://nimahejazi.org)\n",
    "\n",
    "### Date: 07 February 2018\n",
    "\n",
    "### Attribution: adapted from source materials by [David Benkeser](https://www.benkeserstatistics.com/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "── Attaching packages ─────────────────────────────────────── tidyverse 1.2.1 ──\n",
      "✔ ggplot2 2.2.1.9000     ✔ purrr   0.2.4     \n",
      "✔ tibble  1.4.2          ✔ dplyr   0.7.4     \n",
      "✔ tidyr   0.8.0          ✔ stringr 1.2.0.9000\n",
      "✔ readr   1.1.1          ✔ forcats 0.2.0     \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",
      "origami: Generalized Cross-Validation Framework\n",
      "Version: 1.0.0\n"
     ]
    }
   ],
   "source": [
    "options(repr.plot.width = 4, repr.plot.height = 3)  ## resizing plots\n",
    "options(scipen = 999)  ## has scientific notation ever annoyed you?\n",
    "library(tidyverse)\n",
    "library(data.table)\n",
    "library(origami)\n",
    "library(ggsci)\n",
    "set.seed(76548208)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## I. Introduction\n",
    "In class we have been working through the roadmap to targeted learning. This started with defining a statistical model,\n",
    "defined as the set of all possible data generating distributions. The statistical target parameter was defined as a function\n",
    "of a probability distribution, or in other words, a summary measure of the population of interest. We then saw how the interpretation\n",
    "of some statistical target parameters could be enriched by making untestable assumptions via a structural causal model. Conversely,\n",
    "we could start with the structural causal model and determine what interventions are of scientific interest. A causal parameter can\n",
    "be defined on the post-intervention distribution that is equal (under assumptions) to some statistical target parameter. If the\n",
    "assumptions do not hold, then the causal interpretation is not justified, but nevertheless the statistical target parameter may\n",
    "be an interesting object to study. \n",
    "\n",
    "What we have often seen in class is that many statistical target parameters that are motivated causal parameters involve some \n",
    "possibly high dimensional object. For example, in the setting where $O = (W, A, Y)$ and our interest is in estimating the counterfactual parameter $E_0(Y_1)$, we found that the statistical target parameter $E_0(E_0(Y \\ \\mid \\ A = 1, W))$ was equal to \n",
    "the counterfactual parameter under the assumption of randomization and positivity. Thus far in lab, we have been computing these statistical target parameters using an (effectively) infinite sample. However, in practice we rarely get to see a truly infinite sample size, which is why we have to consider the problem of statistical estimation. That is, how can be get the best estimate of the target parameter $E_0(E_0(Y \\ \\mid \\ A = 1, W))$ when we don't get to observe the whole population."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## II. Example with a Simple SCM\n",
    "Let's consider the following SCM:\n",
    "\\begin{align*}\n",
    "U_W &\\sim \\mbox{Discrete Uniform}(0,50)\\\\\n",
    "U_A &\\sim \\mbox{Normal}(0,1) \\\\\n",
    "U_Y &\\sim \\mbox{Normal}(0,3^2) \\ ,\n",
    "\\end{align*}\n",
    "and structural equations \\begin{align*}\n",
    "f_{W}(U_{W}) &= U_{W} \\\\\n",
    "f_A(W, U_A) &= I(\\mbox{expit}(0.02 W + U_A) > 0.5)\\\\\n",
    "f_Y(W, A, U_Y) &= -W + 10 A - U_Y \\ . \n",
    "\\end{align*}\n",
    "\n",
    "As with the last lab, we can explicity code this distribution in `R`. First, we write functions to represent each structural equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# structural equation for W\n",
    "f_W <- function(U_W) {\n",
    "    return(U_W)\n",
    "}\n",
    "\n",
    "# structural equation for A\n",
    "f_A <- function(W, U_A) {\n",
    "    return(as.numeric(plogis(0.02 * W + U_A) > 0.25))\n",
    "}\n",
    "\n",
    "# structural equation for Y\n",
    "f_Y <- function(W, A, U_Y) {\n",
    "    return(-W + 10 * A - U_Y)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now define a function to generate an observation from this SCM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# function to draw n observations from an scm\n",
    "# n = the number of observations to draw\n",
    "# returns a tibble with named columns\n",
    "simObsSCM <- function(n) {\n",
    "    ## first we draw the errors\n",
    "    # draw Uniform(-0.5, 50.5) and round\n",
    "    U_W <- round(runif(n, -0.5, 50.5))\n",
    "    # draw U_A\n",
    "    U_A <- rnorm(n, 0, 1)\n",
    "    # draw U_Y\n",
    "    U_Y <- rnorm(n, 0, 3)\n",
    "\n",
    "\t#evaluate the observations sequentially\n",
    "    # evaluate W\n",
    "    W <- f_W(U_W)\n",
    "    # evaluate A\n",
    "    A <- f_A(W = W, U_A = U_A)\n",
    "    # evaluate Y\n",
    "    Y <- f_Y(W = W, A = A, U_Y = U_Y)\n",
    "\n",
    "    ## return a data.frame object\n",
    "    out <- as.data.table(cbind(W = W, A = A, Y = Y))\n",
    "    return(out)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similar to the last lab, we can write a function that intervenes on the SCM in order to calculate the true value of the counterfactual parameter, which we will need to benchmark our estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# function that draws n observations from an SCM that is \n",
    "# intervened on to set A = setA\n",
    "# n = number of observations\n",
    "# setA = the value to set A equal to (0 or 1)\n",
    "# returns a data.frame of coutnerfactual observations\n",
    "simIntSCM <- function(n, set_A = 1) {\n",
    "\t## first we draw the errors\n",
    "    # draw Uniform(-0.5,50.5) and round\n",
    "    U_W <- round(runif(n, -0.5, 50.5))\n",
    "    # draw U_A\n",
    "    U_A <- rnorm(n, 0, 1)\n",
    "    # draw U_Y\n",
    "    U_Y <- rnorm(n, 0, 1)\n",
    "\n",
    "\t# evaluate the observations sequentially\n",
    "    # evaluate W\n",
    "    W <- f_W(U_W)\n",
    "    # evaluate A\n",
    "    A <- rep(set_A, n)\n",
    "    # evaluate Y\n",
    "    Y <- f_Y(W = W, A = A, U_Y = U_Y)\n",
    "\n",
    "    ## return a data.frame object\n",
    "    out <- as.data.table(cbind(W = W, A = A, Y = Y))\n",
    "    return(out)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compute the true value by simulating a large sample using `simIntSCM`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "int_big_samp <- simIntSCM(n = 1e6, set_A = 1)\n",
    "E0Y1 <- mean(int_big_samp$Y)\n",
    "round(E0Y1, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The true value of $E_0(Y_1)$ is given above. In the last lab, we computed the true value of a causal effect when $W$ only assumed four unique values. In this example, $W$ assumes fifty one unique values. However, our identification result did not rely on $W$ being discrete or low-dimensional, so we can numerically confirm that indeed $E_0(Y_1) = E_0(E_0(Y \\mid A = 1, W))$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "# let's go ahead and write a function that takes as input\n",
    "# a data frame from the observed SCM and computes the \n",
    "# mean in each strata and returns it as a vector\n",
    "getStratEst <- function(data, strata = (seq_len(51) - 1)) {\n",
    "    est <- rep(NA, length(strata))\n",
    "    # over each unique value of W compute the mean of Y in the A=1 grp\n",
    "    for (w in strata) {\n",
    "         # let's check to make sure someone is in each strata\n",
    "        if (sum(data$A == 1 & data$W == w) > 0) {\n",
    "            est[w + 1] <- mean(data$Y[data$A == 1 & data$W == w])\n",
    "        } else {\n",
    "            est[w + 1] <- NA\n",
    "        }\n",
    "    }\n",
    "    # return the vector\n",
    "    est\n",
    "}\n",
    "\n",
    "# simulate very large data set from the observed SCM\n",
    "big_obs <- simObsSCM(n = 5e6)\n",
    "\n",
    "# get the stratified estimate \n",
    "E0Y_A1Ww <- getStratEst(data = big_obs)\n",
    "\n",
    "# we know the probability that W=w, it's 1/51\n",
    "pw <- rep(1/51, 51)\n",
    "\n",
    "# sum over all the strata to get E_0(E_0(Y | A = 1, W))\n",
    "E0_E0Y_A1Ww <- sum(pw * E0Y_A1Ww)\n",
    "\n",
    "# the statistical target parameter\n",
    "E0_E0Y_A1Ww <- sum(pw * E0Y_A1Ww)\n",
    "E0_E0Y_A1Ww"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, we have confirmed that because the randomization and positivity assumptions hold in this example the statistical parameter is equal to the counterfactual parameter. \n",
    "\n",
    "However, we have been working with an effectively infinite sample size, which may not be available in practice. This enormous sample allows us to compute stable estimates of $E_0(Y \\mid A = 1, W = w)$ for every stratum $w$. Let's plot the \"estimated\" (using the huge sample) values and the true values, which we know because we simulated the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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J8E1oXyXJ+c8TJeZcQEWxlrM+E274Xp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\nSUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# vector of all w values, makes it easier to plot\n",
    "allw <- (seq_len(51) - 1)\n",
    "\n",
    "# plot \"estimated\" values\n",
    "plot(E0Y_A1Ww ~ allw, bty=\"n\",\n",
    "     xlab=\"w\", \n",
    "     ylab = expression(E[0]*\"(Y | A=1, W)\")) \n",
    "\n",
    "# add true values\n",
    "E0Y_A1Ww_true <- -allw + 10\n",
    "\n",
    "points(E0Y_A1Ww_true ~ allw, pch=3)\n",
    "# add legend\n",
    "legend(x=30, y=10, bty=\"n\", pch = c(1,3),\n",
    "       legend = c(\"'Estimated'\", \"True\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see what happens when we don't use an infinite sample size. Here's the same code run, but now only simulating $5,000$ observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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do1bbL+EHwXbPf1X8Hly67nBRg3Qa9TlDeVgA9i3syQiIEYiIEOMdDa/5NHh/xY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\ngg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simulate n=5,000 observations from the observed SCM\n",
    "smallerObs <- simObsSCM(n = 5e3)\n",
    "\n",
    "# get stratified estimates \n",
    "EhatY_A1Ww <- getStratEst(data = smallerObs)\n",
    "\n",
    "# plot stratified-estimated values\n",
    "plot(EhatY_A1Ww ~ allw, bty=\"n\", xlab=\"w\", \n",
    "     ylab=expression(hat(E)*\"(Y | A=1, W)\"),\n",
    "     mgp = c(2.1,0.5,0))\n",
    "# add true values\n",
    "points(E0Y_A1Ww_true ~ allw, pch=3) \n",
    "# add legend\n",
    "legend(x=30, y=10, bty=\"n\", pch = c(1,3),\n",
    "       legend = c(\"Estimated\", \"True\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What about with only $500$ observations?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zpSLsJyJWw97wUuP1+pTBkDMRADfdnAIWz8DjBXX96Jbt72JODRC7b7+K/gDZzD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\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simulate n=5,000 observations from the observed SCM\n",
    "smallerObs <- simObsSCM(n = 5e2)\n",
    "\n",
    "# get stratified estimates \n",
    "EhatY_A1Ww <- getStratEst(data = smallerObs)\n",
    "\n",
    "# plot stratified-estimated values\n",
    "plot(EhatY_A1Ww ~ allw, bty=\"n\", xlab=\"w\", \n",
    "     ylab=expression(hat(E)*\"(Y | A=1, W)\"),\n",
    "     mgp = c(2.1,0.5,0))\n",
    "# add true values\n",
    "points(E0Y_A1Ww_true ~ allw, pch=3) \n",
    "# add legend\n",
    "legend(x=30, y=10, bty=\"n\", pch = c(1,3),\n",
    "       legend = c(\"Estimated\", \"True\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What about only $100$ observations?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lfBXudx8BlwyH47+CWY0L4I58J3oISjB+vCKbBaqWT6FgyruIvpfeDz3knhc7Ae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\nMRADMRADMRADMRADvW3g/wG8J2C3TdoYpAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simulate n=5,000 observations from the observed SCM\n",
    "smallerObs <- simObsSCM(n = 1e2)\n",
    "\n",
    "# get stratified estimates \n",
    "EhatY_A1Ww <- getStratEst(data = smallerObs)\n",
    "\n",
    "# plot stratified-estimated values\n",
    "plot(EhatY_A1Ww ~ allw, bty=\"n\", xlab=\"w\", \n",
    "     ylab=expression(hat(E)*\"(Y | A=1, W)\"),\n",
    "     mgp = c(2.1,0.5,0))\n",
    "# add true values\n",
    "points(E0Y_A1Ww_true ~ allw, pch=3) \n",
    "# add legend\n",
    "legend(x=30, y=10, bty=\"n\", pch = c(1,3),\n",
    "       legend = c(\"Estimated\", \"True\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we see problems arise with the stratified estimator. \n",
    "\n",
    "1. When there are few observations in each strata, the estimator will have high variance. \n",
    "\n",
    "2. When there are no observations in a stratum, the estimator is not well defined. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## III. Simple kernel regression\n",
    "In this section we will start to explore solutions the problems with stratified estimators that we explored in the previous section. We will move into the even harder problem where $W$ is a continuous variable. With continuous variables there is no hope of constructing a stratified estimator because the probability that $W=w$ for any choice of $w$ is 0. Let's modify some of the functions from the first section to a new SCM. \n",
    "\n",
    "Let's consider the following SCM:\n",
    "\\begin{align*}\n",
    "U_W &\\sim \\mbox{Uniform}(0,50)\\\\\n",
    "U_A &\\sim \\mbox{Normal}(0,1) \\\\\n",
    "U_Y &\\sim \\mbox{Normal}(0,3^2) \\ ,\n",
    "\\end{align*}\n",
    "and structural equations \\begin{align*}\n",
    "f_{W}(U_{W}) &= U_{W} \\\\\n",
    "f_A(W, U_A) &= I(\\mbox{expit}(0.02 W + U_A) > 0.5)\\\\\n",
    "f_Y(W, A, U_Y) &= -W + 10 A - U_Y \\ . \n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# function to draw n observations from an scm\n",
    "# n = the number of observations to draw\n",
    "# returns a data.frame with named columns\n",
    "simObsSCM <- function(n){\n",
    "    ## first we draw the errors\n",
    "    # draw Uniform(-0.5,50.5) and round\n",
    "    U_W <- runif(n,0,50)\n",
    "    # draw U_A\n",
    "    U_A <- rnorm(n,0,1)\n",
    "    # draw U_Y\n",
    "    U_Y <- rnorm(n,0,3)\n",
    "\n",
    "\t#evaluate the observations sequentially\n",
    "    # evaluate W\n",
    "    W <- f_W(U_W)\n",
    "    # evaluate A\n",
    "    A <- f_A(W = W, U_A = U_A)\n",
    "    # evaluate Y\n",
    "    Y <- f_Y(W = W, A = A, U_Y = U_Y)\n",
    "\n",
    "    ## return a data.frame object\n",
    "    out <- data.frame(W = W, A = A, Y = Y)\n",
    "    return(out)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To solve this problem, we might begin by thinking that people in strata $w$ probably aren't that different than people in strata $w + h/2$ or people in strata $w - h/2$ for some small number $h$. For example, do we think that people with $W = 10$ differ significantly in their outcome than people with $W = 10.01$ or people with $W = 9.99$? Therefore, we might think we could obtain a good estimate by using a moving average. That is, we pick a window around each $w$ of width $h$ and then estimate the function $E_0(Y | A=1, W=w)$ with the average outcome for observations in that window."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# this function takes as input a dataframe of observations\n",
    "# and computes the moving window average of the mean of Y\n",
    "# given W at each value of the vector wValues \n",
    "# the function returns a data.frame with columns w (wValues)\n",
    "simpleKern <- function(\n",
    "    dat, # data.frame of observations\n",
    "    h, # the size of the window\n",
    "    wValues # values at which to return kernel predictions\n",
    "    ){\n",
    "    # for each value in wValues, compute the mean of the observed\n",
    "    # data with A = 1 in that window \n",
    "    # empty vector of results\n",
    "    EhatY <- rep(NA, length(wValues))\n",
    "    ct <- 0\n",
    "    for(w in wValues){\n",
    "        ct <- ct + 1\n",
    "        EhatY[ct] <- \n",
    "            mean(dat$Y[dat$A == 1 & dat$W < w + h/2 & dat$W > w - h/2])\n",
    "    }\n",
    "    \n",
    "    return(data.frame(\n",
    "        w = wValues,\n",
    "        EhatY = EhatY\n",
    "    ))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try out this function for a couple choices of bandwidth. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HDiXq2MH+wg1CWQZFptK4I4rxDfAelm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\nAiZgAiZgAnlN4P8Bm2Rldv0pFeEAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# try it out\n",
    "dat <- simObsSCM(n=200)\n",
    "\n",
    "# for window size 2\n",
    "fit2 <- simpleKern(dat = dat, \n",
    "                  h = 2, # window of size 2\n",
    "                  wValues = seq(0,50, length = 200)) # evenly spaced from 0,50\n",
    "fit20 <- simpleKern(dat = dat, \n",
    "                  h = 20, # window of size 20\n",
    "                  wValues = seq(0,50, length = 200)) # evenly spaced from 0,50\n",
    "\n",
    "plot(fit2$EhatY ~ fit2$w, bty=\"n\",xlab=\"w\", type=\"l\",\n",
    "     ylab=expression(hat(E)*\"(Y | A = 1, W =w)\"),\n",
    "     mgp = c(2.1, 0.5, 0),lwd=2)\n",
    "lines(fit20$EhatY ~ fit20$w,lwd=2, lty=2)\n",
    "points(dat$Y ~ dat$W, col=\"gray75\")\n",
    "legend(x=\"topright\", lty=c(1,2), title=\"h\", legend = c(2,20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can already see the bias/variance tradeoff in play here. The small bandwidth ($h=2$) results in a jagged fit that appears to have smaller bias, but we expect there to be more variance. The larger bandwidth ($h=20$) has bias (look at the tails), but we expect has less variance. We can confirm these by writing a function that computes a Monte Carlo estimate of the bias and variance at several points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "getBiasVariance <- function(\n",
    "    estimator, # a function that takes as input a data set and \n",
    "               # vector of w values called 'wValues' and outputs\n",
    "               # a value for the estimator at w\n",
    "    truth, # a function that takes as input a vector wValues and outputs the\n",
    "           # true value at those values\n",
    "    n, # sample size\n",
    "    wValues, # vector of strata to compute bias and variance \n",
    "    nSim = 100, # number of repeated draws to compute bias and variance\n",
    "    getMSE = FALSE, # should bias and variance be returned or MSE?\n",
    "    ... # other args passed to estimator (e.g., h)\n",
    "){\n",
    "    estMat <- NULL\n",
    "    for(i in 1:nSim){\n",
    "        dat <- simObsSCM(n = n)\n",
    "        est <- do.call(estimator, \n",
    "                       args = c(list(dat = dat, wValues = wValues),\n",
    "                                 list(...)))\n",
    "        estMat <- rbind(estMat, est$EhatY)\n",
    "    }\n",
    "    trueValues <- do.call(truth, args = list(wValues = wValues))\n",
    "    if(!getMSE){\n",
    "       # compute the bias and variance\n",
    "        if(is.matrix(estMat)){\n",
    "            bias <- colMeans(estMat, na.rm=TRUE) - trueValues\n",
    "            variance <- apply(estMat, 2, var)\n",
    "        }else{\n",
    "            bias <- mean(estMat, na.rm = TRUE) - trueValues\n",
    "            variance <- var(estMat, na.rm = TRUE)\n",
    "        }\n",
    "        names(bias) <- wValues\n",
    "        names(variance) <- wValues\n",
    "       # return a list\n",
    "        out <- list(bias = bias, variance = variance)\n",
    "    }else{\n",
    "        mse <- apply(matrix(1:ncol(estMat)), 1, function(i){\n",
    "            mean((estMat[,i] - trueValues[i])^2)\n",
    "        })\n",
    "        names(mse) <- wValues\n",
    "        out <- list(mse = mse)\n",
    "    }\n",
    "    out\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try out the function to see what it does. Here we call the function to get the Monte Carlo estimated bias and variance of $\\hat{E}(Y | A=1, W=w)$ for $w \\in \\{5,25,45\\}$, where the estimate is computed using our function `simpleKern` with $h=5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$bias</dt>\n",
       "\t\t<dd><dl class=dl-horizontal>\n",
       "\t<dt>5</dt>\n",
       "\t\t<dd>0.00283780554063373</dd>\n",
       "\t<dt>25</dt>\n",
       "\t\t<dd>0.0266405922461388</dd>\n",
       "\t<dt>45</dt>\n",
       "\t\t<dd>-0.0173187921432216</dd>\n",
       "</dl>\n",
       "</dd>\n",
       "\t<dt>$variance</dt>\n",
       "\t\t<dd><dl class=dl-horizontal>\n",
       "\t<dt>5</dt>\n",
       "\t\t<dd>0.267944741307965</dd>\n",
       "\t<dt>25</dt>\n",
       "\t\t<dd>0.258542394379207</dd>\n",
       "\t<dt>45</dt>\n",
       "\t\t<dd>0.251427002237634</dd>\n",
       "</dl>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$bias] \\begin{description*}\n",
       "\\item[5] 0.00283780554063373\n",
       "\\item[25] 0.0266405922461388\n",
       "\\item[45] -0.0173187921432216\n",
       "\\end{description*}\n",
       "\n",
       "\\item[\\$variance] \\begin{description*}\n",
       "\\item[5] 0.267944741307965\n",
       "\\item[25] 0.258542394379207\n",
       "\\item[45] 0.251427002237634\n",
       "\\end{description*}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$bias\n",
       ":   5\n",
       ":   0.0028378055406337325\n",
       ":   0.026640592246138845\n",
       ":   -0.0173187921432216\n",
       "\n",
       "\n",
       "$variance\n",
       ":   5\n",
       ":   0.26794474130796525\n",
       ":   0.25854239437920745\n",
       ":   0.251427002237634\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$bias\n",
       "           5           25           45 \n",
       " 0.002837806  0.026640592 -0.017318792 \n",
       "\n",
       "$variance\n",
       "        5        25        45 \n",
       "0.2679447 0.2585424 0.2514270 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# call the function to get the estimated bias and variance of \n",
    "# \\hat{E}\n",
    "getBiasVariance(\n",
    "    estimator = \"simpleKern\", # estimation function to use\n",
    "    truth = function(wValues){ -wValues + 10 }, # the true value\n",
    "    n = 500, # sample size\n",
    "    wValues = c(5, 25, 45),\n",
    "    nSim = 1000,\n",
    "    h = 5\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or alternatively, we could directly study the mean squared-error, which is a combination of bias and variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>$mse</strong> = <dl class=dl-horizontal>\n",
       "\t<dt>5</dt>\n",
       "\t\t<dd>0.245507869554723</dd>\n",
       "\t<dt>25</dt>\n",
       "\t\t<dd>0.212455359252484</dd>\n",
       "\t<dt>45</dt>\n",
       "\t\t<dd>0.224877829870996</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\textbf{\\$mse} = \\begin{description*}\n",
       "\\item[5] 0.245507869554723\n",
       "\\item[25] 0.212455359252484\n",
       "\\item[45] 0.224877829870996\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "**$mse** = 5\n",
       ":   0.24550786955472325\n",
       ":   0.21245535925248445\n",
       ":   0.224877829870996\n",
       "\n"
      ],
      "text/plain": [
       "$mse\n",
       "        5        25        45 \n",
       "0.2455079 0.2124554 0.2248778 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# call the function to get the estimated bias and variance of \n",
    "# \\hat{E}\n",
    "getBiasVariance(\n",
    "    estimator = \"simpleKern\", # estimation function to use\n",
    "    truth = function(wValues){ -wValues + 10 }, # the true value\n",
    "    n = 500, # sample size\n",
    "    wValues = c(5, 25, 45),\n",
    "    nSim = 1000,\n",
    "    h = 5, \n",
    "    getMSE = TRUE\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's run for a few different choices of $h$ at a single point $W=25$ to get bias and variances of our simple estimator at that points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6ARaG+UZJ8kBVaF/Yl9jdLHo0tRT/QN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\nerYmkXI8jyJdlJ2MVkS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2snwUYSpnhd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\nJmACJmACnUPg/wG1e1kGlkIJFAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EG4rR7ajzltK/1Mipyux4GvkuzU4p8V1Gafdo5SuHt5UJ8p5yXw+LA/53dazvRZ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\nh/Abi/6X7IhtHqqcK03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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# I'm going to be repeating the same code under several different  \n",
    "# scenarios, so let's go ahead and write a function that takes an input\n",
    "# of h's and outputs a graph of the the Bias^2 and Variance at a particular \n",
    "# point for each of those choices of bandwidth. \n",
    "plotBiasVariance <- function(hGrid, wValue, n, \n",
    "                             estimator = \"simpleKern\",\n",
    "                             plotMSE = FALSE){\n",
    "    rslt <- lapply(split(hGrid, hGrid), getBiasVariance, \n",
    "                   estimator = estimator, \n",
    "                   truth = function(wValues){ f_Y(W=wValues, A=1, U_Y = 0) },\n",
    "                   n = n, getMSE = plotMSE,\n",
    "                   wValues = wValue, \n",
    "                   nSim = 1000)\n",
    "    \n",
    "    if(!plotMSE){\n",
    "       # transform result list into data.frame\n",
    "        biasRslt <- data.frame(h=hGrid, \n",
    "                               bias=unlist(lapply(rslt, function(x){x$bias}),\n",
    "                                           use.names=FALSE))\n",
    "        varRslt <- data.frame(h=hGrid, \n",
    "                              variance=unlist(\n",
    "                                  lapply(rslt, function(x){x$variance}),\n",
    "                                          use.names = FALSE))\n",
    "        # standardize results to put on same graph\n",
    "        biasRslt$bias2_s <- \n",
    "            (biasRslt$bias^2 - min(biasRslt$bias^2))/diff(range(biasRslt$bias^2))\n",
    "      varRslt$variance_s <- \n",
    "            (varRslt$variance -min(varRslt$variance))/diff(range(varRslt$variance))\n",
    "\n",
    "        # plot results\n",
    "        par(mar = c(4.1, 3.1, 0.5, 3.1), mgp = c(1.5, 0.5, 0))\n",
    "        plot(bias2_s ~ h, data = biasRslt, type=\"b\",yaxt=\"n\", \n",
    "             xlab = \"h\", ylab = expression(Bias^2))\n",
    "        points(variance_s ~ h, data = varRslt, type=\"b\", pch=2, lty=2)\n",
    "        axis(side = 2, at = seq(0,1,length = 5), labels = rep(\"\", 5))\n",
    "        axis(side = 4, at = seq(0,1,length = 5), labels = rep(\"\", 5))\n",
    "        mtext(side = 4, line = par()$mgp[1], \"Variance\")\n",
    "        legend(x=\"topleft\", pch = c(1,2), legend = c(\"Bias\", \"Variance\"))\n",
    "    }else{\n",
    "        # mse results list into data.frame\n",
    "        mseRslt <- data.frame(h=hGrid, \n",
    "                              mse=unlist(lapply(rslt, function(x){x$mse}),\n",
    "                                           use.names=FALSE))\n",
    "        # plot results\n",
    "        par(mar = c(4.1, 3.1, 0.5, 3.1), mgp = c(1.5, 0.5, 0))\n",
    "        plot(mse ~ h, data = mseRslt, type=\"b\",\n",
    "             xlab = \"h\", ylab = expression(MSE))\n",
    "        legend(x=\"topleft\", pch = c(1,2), legend = c(\"MSE\"))\n",
    "    }\n",
    "}\n",
    "\n",
    "# run the function to plot bias and variance\n",
    "set.seed(1234)\n",
    "plotBiasVariance(hGrid = seq(1, 30, length = 10), \n",
    "                 wValue = 25, \n",
    "                 n = 500)\n",
    "\n",
    "# run the function plot MSE\n",
    "set.seed(1234)\n",
    "plotBiasVariance(hGrid = seq(1, 30, length = 10), \n",
    "                 wValue = 25, \n",
    "                 n = 500, plotMSE = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks from the results like using a bandwidth of $h=7$ -ish results in the optimal bias-variance trade-off (at least for estimate $E_0(Y | A = 1, W = 25)$). What happens if we change the sample size? Heuristically, we need to be using a smaller and smaller window size to ensure there's no bias. Here are the results for $n=10,000$ and using a smaller set of bandwidths."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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45vkvDfTeIcZQImkA4BjdqtjnQdsHWB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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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F23x6M8S9vJMgacWcaZkPUw2hIVrdkF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\nQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the bias and variance\n",
    "set.seed(1234)\n",
    "plotBiasVariance(hGrid = seq(1, 10, length = 10), \n",
    "                 wValue = 25, \n",
    "                 n = 10000)\n",
    "# plot the mse\n",
    "set.seed(1234)\n",
    "plotBiasVariance(hGrid = seq(1, 10, length = 10), \n",
    "                 wValue = 25, \n",
    "                 n = 10000, plotMSE = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the optimal bandwith appears to be somewhere around $h=5$, as we'd expect. This illustrates a general point that the bandwidth should be shrinking with $n$ to maintain an optimal bias-variance trade-off. \n",
    "\n",
    "But just making the bandwidth get smaller with $n$ is not the whole story. What happens if we change the underlying data-generating mechanism to something that is more smooth, e.g. let's set $$\n",
    "f_Y(W, A, U_Y) = -0.01 W + 10 A - U_Y \\ . \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/kbic6TJX6SyVdMFv5mtG9UifXbAReFLDtfwnjfqnC+fBWrm7F3jps0owf8pujN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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LkoTgkE9tc13LiXSrtJH5fck7xL8pDu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\nSUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# redefine structural equation for Y\n",
    "f_Y <- function(W, A, U_Y){\n",
    "    -0.01*W + 10*A - U_Y\n",
    "}\n",
    "# plot the bias and variance\n",
    "set.seed(1234)\n",
    "plotBiasVariance(hGrid = seq(1, 50, length = 10), \n",
    "                 wValue = 25, \n",
    "                 n = 500)\n",
    "\n",
    "# plot the mse\n",
    "set.seed(1234)\n",
    "plotBiasVariance(hGrid = seq(1, 50, length = 10), \n",
    "                 wValue = 25, \n",
    "                 n = 500, plotMSE = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the optimal bandwidth is much larger. Why?\n",
    "\n",
    "What happens if we make the data generating distribution less smooth?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Qi1fmuZehS0nxzy4jFSq1jxsyGbCXSV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\nQ+D/Aa+UzBSM/5brAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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fiZSvN9yb08owpVMgoDAQg0TaBsDjhc0Xe14a7let3LNyncz38/kzAIlJnAT1R4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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# redefine structural equation for Y\n",
    "f_Y <- function(W, A, U_Y){\n",
    "    10*sin(W/2) + 10*A - U_Y\n",
    "}\n",
    "\n",
    "# plot the bias and variance\n",
    "set.seed(1234)\n",
    "plotBiasVariance(hGrid = seq(1, 20, length = 10), \n",
    "                 wValue = 25, \n",
    "                 n = 2000)\n",
    "\n",
    "# plot the mse\n",
    "set.seed(1234)\n",
    "plotBiasVariance(hGrid = seq(1, 20, length = 10), \n",
    "                 wValue = 25, \n",
    "                 n = 2000, plotMSE = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are still cheating in these examples, because in real life we do not have access to repeated experiments to determine the optimal bandwidth. Even though we might know the rate at which the bandwidth should be decreasing (which, by the way, already requires knowing something about the underlying smoothness), we will not know for a given sample the actual bandwidth to choose. \n",
    "\n",
    "This motivates the use of cross-validation, which mimics repeated experiments through sample splitting. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IV. Other kernels\n",
    "\n",
    "The above function `simpleKern` was an example of kernel regression using a uniform kernel. A kernel can basically be thought of as a weighting function. Above, we gave equal weight to all observations within a specified window. However, it may make more sense to weight observations nearer to the point of interest more heavily than those far away from the point of interest. Below, I write my own kernel regression function to illustrate how this works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0.241970724519143</li>\n",
       "\t<li>0.289691552761483</li>\n",
       "\t<li>0.3332246028918</li>\n",
       "\t<li>0.368270140303323</li>\n",
       "\t<li>0.391042693975456</li>\n",
       "\t<li>0.398942280401433</li>\n",
       "\t<li>0.391042693975456</li>\n",
       "\t<li>0.368270140303323</li>\n",
       "\t<li>0.3332246028918</li>\n",
       "\t<li>0.289691552761483</li>\n",
       "\t<li>0.241970724519143</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.241970724519143\n",
       "\\item 0.289691552761483\n",
       "\\item 0.3332246028918\n",
       "\\item 0.368270140303323\n",
       "\\item 0.391042693975456\n",
       "\\item 0.398942280401433\n",
       "\\item 0.391042693975456\n",
       "\\item 0.368270140303323\n",
       "\\item 0.3332246028918\n",
       "\\item 0.289691552761483\n",
       "\\item 0.241970724519143\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.241970724519143\n",
       "2. 0.289691552761483\n",
       "3. 0.3332246028918\n",
       "4. 0.368270140303323\n",
       "5. 0.391042693975456\n",
       "6. 0.398942280401433\n",
       "7. 0.391042693975456\n",
       "8. 0.368270140303323\n",
       "9. 0.3332246028918\n",
       "10. 0.289691552761483\n",
       "11. 0.241970724519143\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 0.2419707 0.2896916 0.3332246 0.3682701 0.3910427 0.3989423 0.3910427\n",
       " [8] 0.3682701 0.3332246 0.2896916 0.2419707"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# normal kernel. Takes as input a vector of observed points wObs, \n",
    "# a bandwidth h and a single point w and returns the normal kernel \n",
    "# evaluated at each wObs.\n",
    "Knorm <- function(wObs, h, w){\n",
    "    dnorm((w - wObs)/h)\n",
    "}\n",
    "\n",
    "# try it out to see what it does\n",
    "Knorm(wObs = 0:10, h = 5, w = 5)\n",
    "\n",
    "# this function takes as input a dataframe of observations\n",
    "# and computes the moving window average of the mean of Y\n",
    "# given W at each value of the vector wValues \n",
    "# the function returns a data.frame with columns w (wValues)\n",
    "kernReg <- function(\n",
    "    dat, # data.frame of observations\n",
    "    h, # bandwidth\n",
    "    K, # kernel function that takes inputs called wObs, h, and w\n",
    "    wValues # values at which to return kernel predictions\n",
    "    ){\n",
    "    # for each value in wValues, compute the mean of the observed\n",
    "    # data with A = 1 in that window \n",
    "    # empty vector of results\n",
    "    EhatY <- rep(NA, length(wValues))\n",
    "    ct <- 0\n",
    "    for(w in wValues){\n",
    "        ct <- ct + 1\n",
    "        thisK <- do.call(K, args = list(wObs = dat$W, h = h, w = w))\n",
    "        EhatY[ct] <- sum(thisK * dat$Y) / sum(thisK)\n",
    "    }\n",
    "    \n",
    "    return(data.frame(\n",
    "        w = wValues,\n",
    "        EhatY = EhatY\n",
    "    ))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try it out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ypJh1SZRtk7WHQa6j46rfcIu9Ebjt88Zh/aFwoqzNKqElCAfWTVi8kxBgpidAGf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\n6S00A45dDE5awc8cFG5nwh5kNlwHZT2A56A4nK3FzMsXnPLCaz9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IQMpBD9YcMBU8C6qBoA0cf5OkMfA80bWaoUasmXC05AgJa2lZUg/k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KqKJTIA1qwlFep1BSwBrAPABGgpRKsmbn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\nAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “Kernel regression, normal kernel”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# try it out\n",
    "dat <- simObsSCM(n=200)\n",
    "\n",
    "# for window size 2\n",
    "fit2 <- kernReg(dat = dat, K = \"Knorm\",\n",
    "                  h = 2, # window of size 2\n",
    "                  wValues = seq(0,50, length = 200)) # evenly spaced from 0,50\n",
    "fit20 <- kernReg(dat = dat, K = \"Knorm\",\n",
    "                  h = 20, # window of size 20\n",
    "                  wValues = seq(0,50, length = 200)) # evenly spaced from 0,50\n",
    "\n",
    "plot(fit2$EhatY ~ fit2$w, bty=\"n\",xlab=\"w\", type=\"l\",\n",
    "     ylab=expression(hat(E)*\"(Y | A = 1, W =w)\"),\n",
    "     mgp = c(2.1, 0.5, 0),lwd=2, main= \"Kernel regression, normal kernel\")\n",
    "lines(fit20$EhatY ~ fit20$w,lwd=2, lty=2)\n",
    "points(dat$Y ~ dat$W, col=\"gray75\")\n",
    "legend(x=\"topright\", lty=c(1,2), title=\"h\", legend = c(2,20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Epanechnikov kernel is the optimal kernel in the mean-squared error sense. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Epanechnikov</th><th scope=col>Normal</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.00000000</td><td>0.06634167</td></tr>\n",
       "\t<tr><td>0.05454545</td><td>0.07942539</td></tr>\n",
       "\t<tr><td>0.09696970</td><td>0.09136095</td></tr>\n",
       "\t<tr><td>0.12727273</td><td>0.10096946</td></tr>\n",
       "\t<tr><td>0.14545455</td><td>0.10721307</td></tr>\n",
       "\t<tr><td>0.15151515</td><td>0.10937892</td></tr>\n",
       "\t<tr><td>0.14545455</td><td>0.10721307</td></tr>\n",
       "\t<tr><td>0.12727273</td><td>0.10096946</td></tr>\n",
       "\t<tr><td>0.09696970</td><td>0.09136095</td></tr>\n",
       "\t<tr><td>0.05454545</td><td>0.07942539</td></tr>\n",
       "\t<tr><td>0.00000000</td><td>0.06634167</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{ll}\n",
       " Epanechnikov & Normal\\\\\n",
       "\\hline\n",
       "\t 0.00000000 & 0.06634167\\\\\n",
       "\t 0.05454545 & 0.07942539\\\\\n",
       "\t 0.09696970 & 0.09136095\\\\\n",
       "\t 0.12727273 & 0.10096946\\\\\n",
       "\t 0.14545455 & 0.10721307\\\\\n",
       "\t 0.15151515 & 0.10937892\\\\\n",
       "\t 0.14545455 & 0.10721307\\\\\n",
       "\t 0.12727273 & 0.10096946\\\\\n",
       "\t 0.09696970 & 0.09136095\\\\\n",
       "\t 0.05454545 & 0.07942539\\\\\n",
       "\t 0.00000000 & 0.06634167\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Epanechnikov | Normal | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 0.00000000 | 0.06634167 | \n",
       "| 0.05454545 | 0.07942539 | \n",
       "| 0.09696970 | 0.09136095 | \n",
       "| 0.12727273 | 0.10096946 | \n",
       "| 0.14545455 | 0.10721307 | \n",
       "| 0.15151515 | 0.10937892 | \n",
       "| 0.14545455 | 0.10721307 | \n",
       "| 0.12727273 | 0.10096946 | \n",
       "| 0.09696970 | 0.09136095 | \n",
       "| 0.05454545 | 0.07942539 | \n",
       "| 0.00000000 | 0.06634167 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "      Epanechnikov Normal    \n",
       " [1,] 0.00000000   0.06634167\n",
       " [2,] 0.05454545   0.07942539\n",
       " [3,] 0.09696970   0.09136095\n",
       " [4,] 0.12727273   0.10096946\n",
       " [5,] 0.14545455   0.10721307\n",
       " [6,] 0.15151515   0.10937892\n",
       " [7,] 0.14545455   0.10721307\n",
       " [8,] 0.12727273   0.10096946\n",
       " [9,] 0.09696970   0.09136095\n",
       "[10,] 0.05454545   0.07942539\n",
       "[11,] 0.00000000   0.06634167"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# normal kernel. Takes as input a vector of observed points wObs, \n",
    "# a bandwidth h and a single point w and returns the normal kernel \n",
    "# evaluated at each wObs.\n",
    "Kepan <- function(wObs, h, w){\n",
    "    u <- (w - wObs)/h\n",
    "    k <- 3/4 * (1-u^2)*(abs(u)<=1)\n",
    "}\n",
    "\n",
    "# try it out to see what it does\n",
    "Kepan(wObs = 0:10, h = 5, w = 5)\n",
    "\n",
    "# compare to the normal kernal\n",
    "k1 <- Kepan(wObs = 0:10, h = 5, w = 5)\n",
    "k2 <- Knorm(wObs = 0:10, h = 5, w = 5)\n",
    "comp <- cbind(\n",
    "    k1/sum(k1),\n",
    "    k2/sum(k2)\n",
    ")\n",
    "colnames(comp) <- c(\"Epanechnikov\", \"Normal\")\n",
    "comp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One more plot using Epanechnikov kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6FotR0iiYKfp+FiAbzUIU4F/J6hQ7we5fu3NwY/Dz744DGMT4nTkLgtSEdbKh1R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JGXAYwpj0VeLFfX0h51/WUD4NmKVFInRP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\nSl1Wkb4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aQnJujtCOsy8Bkw03nso8F3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",
      "text/plain": [
       "Plot with title “Kernel regression, Epanechnikov kernel”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# try it out\n",
    "dat <- simObsSCM(n=200)\n",
    "\n",
    "# for window size 2\n",
    "fit2 <- kernReg(dat = dat, K = \"Kepan\",\n",
    "                  h = 2, # window of size 2\n",
    "                  wValues = seq(0,50, length = 200)) # evenly spaced from 0,50\n",
    "\n",
    "plot(fit2$EhatY ~ fit2$w, bty=\"n\",xlab=\"w\", type=\"l\",\n",
    "     ylab=expression(hat(E)*\"(Y | A = 1, W =w)\"),\n",
    "     mgp = c(2.1, 0.5, 0),lwd=2, \n",
    "     main= \"Kernel regression, Epanechnikov kernel\")\n",
    "points(dat$Y ~ dat$W, col=\"gray75\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See the `npreg` package for many more kernel regression options (and much more efficient implementation than my own!)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## V. Building R Packages: `origami`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As part of the first homework assignment, you've been asked to build a minimal R package. Today, we'll take a look at the `origami` package -- a simple and completely general package for writing arbitrary cross-validation routines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>mpg</th><th scope=col>cyl</th><th scope=col>disp</th><th scope=col>hp</th><th scope=col>drat</th><th scope=col>wt</th><th scope=col>qsec</th><th scope=col>vs</th><th scope=col>am</th><th scope=col>gear</th><th scope=col>carb</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Mazda RX4</th><td>21.0 </td><td>6    </td><td>160  </td><td>110  </td><td>3.90 </td><td>2.620</td><td>16.46</td><td>0    </td><td>1    </td><td>4    </td><td>4    </td></tr>\n",
       "\t<tr><th scope=row>Mazda RX4 Wag</th><td>21.0 </td><td>6    </td><td>160  </td><td>110  </td><td>3.90 </td><td>2.875</td><td>17.02</td><td>0    </td><td>1    </td><td>4    </td><td>4    </td></tr>\n",
       "\t<tr><th scope=row>Datsun 710</th><td>22.8 </td><td>4    </td><td>108  </td><td> 93  </td><td>3.85 </td><td>2.320</td><td>18.61</td><td>1    </td><td>1    </td><td>4    </td><td>1    </td></tr>\n",
       "\t<tr><th scope=row>Hornet 4 Drive</th><td>21.4 </td><td>6    </td><td>258  </td><td>110  </td><td>3.08 </td><td>3.215</td><td>19.44</td><td>1    </td><td>0    </td><td>3    </td><td>1    </td></tr>\n",
       "\t<tr><th scope=row>Hornet Sportabout</th><td>18.7 </td><td>8    </td><td>360  </td><td>175  </td><td>3.15 </td><td>3.440</td><td>17.02</td><td>0    </td><td>0    </td><td>3    </td><td>2    </td></tr>\n",
       "\t<tr><th scope=row>Valiant</th><td>18.1 </td><td>6    </td><td>225  </td><td>105  </td><td>2.76 </td><td>3.460</td><td>20.22</td><td>1    </td><td>0    </td><td>3    </td><td>1    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllll}\n",
       "  & mpg & cyl & disp & hp & drat & wt & qsec & vs & am & gear & carb\\\\\n",
       "\\hline\n",
       "\tMazda RX4 & 21.0  & 6     & 160   & 110   & 3.90  & 2.620 & 16.46 & 0     & 1     & 4     & 4    \\\\\n",
       "\tMazda RX4 Wag & 21.0  & 6     & 160   & 110   & 3.90  & 2.875 & 17.02 & 0     & 1     & 4     & 4    \\\\\n",
       "\tDatsun 710 & 22.8  & 4     & 108   &  93   & 3.85  & 2.320 & 18.61 & 1     & 1     & 4     & 1    \\\\\n",
       "\tHornet 4 Drive & 21.4  & 6     & 258   & 110   & 3.08  & 3.215 & 19.44 & 1     & 0     & 3     & 1    \\\\\n",
       "\tHornet Sportabout & 18.7  & 8     & 360   & 175   & 3.15  & 3.440 & 17.02 & 0     & 0     & 3     & 2    \\\\\n",
       "\tValiant & 18.1  & 6     & 225   & 105   & 2.76  & 3.460 & 20.22 & 1     & 0     & 3     & 1    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | mpg | cyl | disp | hp | drat | wt | qsec | vs | am | gear | carb | \n",
       "|---|---|---|---|---|---|\n",
       "| Mazda RX4 | 21.0  | 6     | 160   | 110   | 3.90  | 2.620 | 16.46 | 0     | 1     | 4     | 4     | \n",
       "| Mazda RX4 Wag | 21.0  | 6     | 160   | 110   | 3.90  | 2.875 | 17.02 | 0     | 1     | 4     | 4     | \n",
       "| Datsun 710 | 22.8  | 4     | 108   |  93   | 3.85  | 2.320 | 18.61 | 1     | 1     | 4     | 1     | \n",
       "| Hornet 4 Drive | 21.4  | 6     | 258   | 110   | 3.08  | 3.215 | 19.44 | 1     | 0     | 3     | 1     | \n",
       "| Hornet Sportabout | 18.7  | 8     | 360   | 175   | 3.15  | 3.440 | 17.02 | 0     | 0     | 3     | 2     | \n",
       "| Valiant | 18.1  | 6     | 225   | 105   | 2.76  | 3.460 | 20.22 | 1     | 0     | 3     | 1     | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "                  mpg  cyl disp hp  drat wt    qsec  vs am gear carb\n",
       "Mazda RX4         21.0 6   160  110 3.90 2.620 16.46 0  1  4    4   \n",
       "Mazda RX4 Wag     21.0 6   160  110 3.90 2.875 17.02 0  1  4    4   \n",
       "Datsun 710        22.8 4   108   93 3.85 2.320 18.61 1  1  4    1   \n",
       "Hornet 4 Drive    21.4 6   258  110 3.08 3.215 19.44 1  0  3    1   \n",
       "Hornet Sportabout 18.7 8   360  175 3.15 3.440 17.02 0  0  3    2   \n",
       "Valiant           18.1 6   225  105 2.76 3.460 20.22 1  0  3    1   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data(mtcars)\n",
    "head(mtcars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ ., data = mtcars)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-3.4506 -1.6044 -0.1196  1.2193  4.6271 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)\n",
       "(Intercept) 12.30337   18.71788   0.657   0.5181\n",
       "cyl         -0.11144    1.04502  -0.107   0.9161\n",
       "disp         0.01334    0.01786   0.747   0.4635\n",
       "hp          -0.02148    0.02177  -0.987   0.3350\n",
       "drat         0.78711    1.63537   0.481   0.6353\n",
       "wt          -3.71530    1.89441  -1.961   0.0633\n",
       "qsec         0.82104    0.73084   1.123   0.2739\n",
       "vs           0.31776    2.10451   0.151   0.8814\n",
       "am           2.52023    2.05665   1.225   0.2340\n",
       "gear         0.65541    1.49326   0.439   0.6652\n",
       "carb        -0.19942    0.82875  -0.241   0.8122\n",
       "\n",
       "Residual standard error: 2.65 on 21 degrees of freedom\n",
       "Multiple R-squared:  0.869,\tAdjusted R-squared:  0.8066 \n",
       "F-statistic: 13.93 on 10 and 21 DF,  p-value: 0.0000003793\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lm_mod <- lm(mpg ~ ., data = mtcars)\n",
    "summary(lm_mod)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "err <- mean(resid(lm_mod)^2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cv_lm <- function(fold, data, reg_form) {\n",
    "  # get name and index of outcome variable from regression formula\n",
    "  out_var <- as.character(unlist(stringr::str_split(reg_form, \" \"))[1])\n",
    "  out_var_ind <- as.numeric(which(colnames(data) == out_var))\n",
    "\n",
    "  # split up data into training and validation sets\n",
    "  train_data <- origami::training(data)\n",
    "  valid_data <- origami::validation(data)\n",
    "\n",
    "  # fit linear model on training set and predict on validation set\n",
    "  mod <- lm(as.formula(reg_form), data = train_data)\n",
    "  preds <- predict(mod, newdata = valid_data)\n",
    "\n",
    "  # capture results to be returned as output\n",
    "  out <- list(coef = data.frame(t(coef(mod))),\n",
    "              SE = ((preds - valid_data[, out_var_ind])^2))\n",
    "  return(out)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "4.60920093802033"
      ],
      "text/latex": [
       "4.60920093802033"
      ],
      "text/markdown": [
       "4.60920093802033"
      ],
      "text/plain": [
       "[1] 4.609201"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# resubstitution estimate\n",
    "resub <- make_folds(mtcars, fold_fun = folds_resubstitution)[[1]]\n",
    "resub_results <- cv_lm(fold = resub, data = mtcars, reg_form = \"mpg ~ .\")\n",
    "mean(resub_results$SE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "13.2857398744671"
      ],
      "text/latex": [
       "13.2857398744671"
      ],
      "text/markdown": [
       "13.2857398744671"
      ],
      "text/plain": [
       "[1] 13.28574"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# cross-validated estimate\n",
    "folds <- origami::make_folds(mtcars)\n",
    "cvlm_results <- origami::cross_validate(cv_fun = cv_lm,\n",
    "                                        folds = folds, data = mtcars,\n",
    "                                        reg_form = \"mpg ~ .\")\n",
    "mean(cvlm_results$SE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we'll look closely at\n",
    "* What goes in the R/ subdirectory of a package?\n",
    "* How do we document using the Roxygen system?\n",
    "* What does a vignette look like?\n",
    "* What's continuous integration? `.travis.yml`?"
   ]
  }
 ],
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