{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nonparametric Density Estimation with `condensier`\n",
    "\n",
    "## Lab 07 for PH 290: Targeted Learning in Biomedical Big Data\n",
    "\n",
    "### Author: [Nima Hejazi](https://nimahejazi.org)\n",
    "\n",
    "### Date: 28 February 2018"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# I. Nonparametric Density Estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a moment, we will go back to simple data structures: we have observations which are realizations of univariate random variables,\n",
    "$$X_1, \\ldots, X_n \\sim F,$$\n",
    "where $F$ denotes an unknown cumulative distribution function (CDF). The goal is to estimate the distribution $F$. In particular, we are interested in estimating the density $f = F′$ , assuming that it exists.\n",
    "\n",
    "### Histograms\n",
    "\n",
    "The histogram is the oldest and most popular density estimator. We need to specify an \"origin\" $x_0$ and the class width $h$ for the specifications of the intervals:\n",
    "$$I_j =(x_0 + j \\cdot h,x_0 + (j + 1) \\cdot h),  (j = \\ldots, −1, 0, 1, \\ldots)$$\n",
    "\n",
    "### The Naïve Kernel Estimator\n",
    "\n",
    "$$\\hat{f}(x) = \\frac{1}{nh} \\sum_{i = 1}^{n} w \\left(\\frac{x - X_i}{h}\\right),$$\n",
    "where $w(x) = \\frac{1}{2}, \\mid X \\mid \\leq 1; 0, \\text{otherwise}$. This is merely a simple weight function that places a rectangular box around each interval $(x - h, x + h)$.\n",
    "\n",
    "By replaceing $w$ with a generalized smooth kernel function, we get the definition of the _kernel density estimator_:\n",
    "$$\\hat{f}(x) = \\frac{1}{nh} \\sum_{i = 1}^{n} K \\left(\\frac{x - X_i}{h}\\right),$$\n",
    "where $$K(x) \\geq 0, \\int_{-\\infty}^{\\infty} K(x) dx = 1, K(x) = K(-x).$$\n",
    "\n",
    "The positivity of the kernel function $K(\\cdot)$ guarantees a positive density estimate $f(\\cdot)$ and the normalization $K(x)dx = 1$ implies that $f(x)dx = 1$, which is necessary for $f(\\cdot)$ to be a density.\n",
    "Typically, the kernel function $K(\\cdot)$ is chosen as a probability density which is symmetric around $0$. Additionally, the smoothness of $f(\\cdot)$ is inherited from the smoothness of the kernel.\n",
    "\n",
    "In the above definition, we leave the bandwidth $h$ as a _tuning parameter_, which can be chosen so as to minimize an arbitrary distance metric that ensures the estimated function is optimal, given the available data. For large bandwidth $h$, the estimate $f(x)$ tends to be very slowly varying as a function of $x$, while small bandwidths will produce a more variable function estimate.\n",
    "\n",
    "### The Bandwidth $h$\n",
    "\n",
    "The bandwidth h is often also called the \"smoothing parameter\". It should be clear that for $h \\to 0$, we will have spikes at every observation $X_i$, whereas $f(\\cdot) = fh(\\cdot)$ becomes smoother as $h$ is increasing. In the above, we use a global bandwidth, which we might choose optimally using cross-validation, but, we can also use variable bandwidths (locally changing bandwidths $h(x)$), with the general idea her being to use a large bandwidth for regions where the data is sparse. With respect to the _bias-variance tradeoff_: **the (absolute value of the) bias of $\\hat{f}$ increases and the variance of $\\hat{f}$ decreases as $h$ increases**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (!) Exercise\n",
    "\n",
    "Propose a specific approach to choosing a locally changing bandwidth $h(x)$ for kernel density estimation. For your chosen approach, provide a single advantage and a single disadvantage for your given approach."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# II. Density Estimation with `condensier`"
   ]
  },
  {
   "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": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Changing active project to lab_07\n",
      "✔ Writing a sentinel file '.here'\n",
      "● Build robust paths within your project via `here::here()`\n",
      "● Learn more at https://krlmlr.github.io/here/\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "here() starts at /Users/nimahejazi/Dropbox/UC_Berkeley-grad/teaching/tlbbd-labs/lab_07\n",
      "── 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 1.3.0     \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",
      "condensier\n",
      "The condensier package is still in beta testing. Interpret results with caution.\n"
     ]
    }
   ],
   "source": [
    "library(usethis)\n",
    "usethis::create_project(\".\")\n",
    "library(here)\n",
    "library(tidyverse)\n",
    "library(data.table)\n",
    "library(simcausal)\n",
    "library(condensier)\n",
    "library(data.table)\n",
    "library(sl3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We begin by simulating a simple data set and illustrating a simple execution of how to use `condensier` to perform conditional density estimation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "...automatically assigning order attribute to some nodes...\n",
      "node W1, order:1\n",
      "node W2, order:2\n",
      "node W3, order:3\n",
      "node A, order:4\n"
     ]
    }
   ],
   "source": [
    "library(\"simcausal\")\n",
    "D <- DAG.empty()\n",
    "D <- D + node(\"W1\", distr = \"rbern\", prob = 0.5) +\n",
    "         node(\"W2\", distr = \"rbern\", prob = 0.3) +\n",
    "         node(\"W3\", distr = \"rbern\", prob = 0.3) +\n",
    "         node(\"A\", distr = \"rnorm\", mean = (0.98 * W1 + 0.58 * W2 + 0.33 * W3), sd = 1)\n",
    "D <- set.DAG(D, n.test = 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "using the following vertex attributes: \n",
      "120.8NAdarkbluenone0\n",
      "using the following edge attributes: \n",
      "0.50.40.8black1\n"
     ]
    },
    {
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BAgQIAAAQIECBAgQIAAAQIECBAgQIAA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",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotDAG(D, xjitter = 0.3, yjitter = 0.04, edge_attrs = list(width = 0.5, arrow.width = 0.4, arrow.size = 0.8), vertex_attrs = list(size = 12, label.cex = 0.8))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've taken a look at the structure of the data-generating process (the DAG), let's generate some data and take a quick look at the data set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "simulating observed dataset from the DAG object\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>ID</th><th scope=col>W1</th><th scope=col>W2</th><th scope=col>W3</th><th scope=col>A</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1         </td><td>1         </td><td>0         </td><td>0         </td><td> 0.7075761</td></tr>\n",
       "\t<tr><td>2         </td><td>1         </td><td>0         </td><td>1         </td><td> 1.5157866</td></tr>\n",
       "\t<tr><td>3         </td><td>1         </td><td>1         </td><td>1         </td><td> 0.8108074</td></tr>\n",
       "\t<tr><td>4         </td><td>1         </td><td>1         </td><td>1         </td><td> 2.4268503</td></tr>\n",
       "\t<tr><td>5         </td><td>0         </td><td>0         </td><td>0         </td><td>-0.8857180</td></tr>\n",
       "\t<tr><td>6         </td><td>0         </td><td>0         </td><td>1         </td><td>-0.3614194</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       " ID & W1 & W2 & W3 & A\\\\\n",
       "\\hline\n",
       "\t 1          & 1          & 0          & 0          &  0.7075761\\\\\n",
       "\t 2          & 1          & 0          & 1          &  1.5157866\\\\\n",
       "\t 3          & 1          & 1          & 1          &  0.8108074\\\\\n",
       "\t 4          & 1          & 1          & 1          &  2.4268503\\\\\n",
       "\t 5          & 0          & 0          & 0          & -0.8857180\\\\\n",
       "\t 6          & 0          & 0          & 1          & -0.3614194\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "ID | W1 | W2 | W3 | A | \n",
       "|---|---|---|---|---|---|\n",
       "| 1          | 1          | 0          | 0          |  0.7075761 | \n",
       "| 2          | 1          | 0          | 1          |  1.5157866 | \n",
       "| 3          | 1          | 1          | 1          |  0.8108074 | \n",
       "| 4          | 1          | 1          | 1          |  2.4268503 | \n",
       "| 5          | 0          | 0          | 0          | -0.8857180 | \n",
       "| 6          | 0          | 0          | 1          | -0.3614194 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  ID W1 W2 W3 A         \n",
       "1 1  1  0  0   0.7075761\n",
       "2 2  1  0  1   1.5157866\n",
       "3 3  1  1  1   0.8108074\n",
       "4 4  1  1  1   2.4268503\n",
       "5 5  0  0  0  -0.8857180\n",
       "6 6  0  0  1  -0.3614194"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_O <- as.data.table(sim(D, n = 10000, rndseed = 12345))\n",
    "head(data_O)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "newdata <- data_O[seq_len(100), c(\"W1\", \"W2\", \"W3\", \"A\"), with = FALSE]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've generate some data, we can try to estimate the conditional distribution $P(A \\mid W)$, using the observed data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dens_fit <- fit_density(\n",
    "    X = c(\"W1\", \"W2\", \"W3\"), \n",
    "    Y = \"A\", \n",
    "    input_data = data_O, \n",
    "    nbins = 40, \n",
    "    bin_method = \"equal.mass\",\n",
    "    bin_estimator = speedglmR6$new())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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cuWmx3DDgQQ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\nIIAAAgggYHOB/wPDJGeARNmlQQAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "preds_1 <- sample_value(model_fit = dens_fit, newdata = newdata)\n",
    "\n",
    "p1_A_given_W <- as_tibble(preds_1) %>%\n",
    "  ggplot(., aes(x = value)) +\n",
    "  geom_histogram(aes(y = ..density..), binwidth = 0.1, alpha = 0.8,\n",
    "                 position = \"identity\") +\n",
    "  geom_density(alpha = 0.2) +\n",
    "  ggtitle(\"Conditional Density: p(A | W)\") + theme_bw()\n",
    "\n",
    "p1_A_given_W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dens_fit <- fit_density(\n",
    "    X = c(\"W1\", \"W2\", \"W3\"), \n",
    "    Y = \"A\", \n",
    "    input_data = data_O, \n",
    "    nbins = 40, \n",
    "    bin_method = \"equal.len\",\n",
    "    bin_estimator = speedglmR6$new())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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S9OOukkN+df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\nAAEEEEDA5gL/DxgClpVWm6R0AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "preds_2 <- sample_value(model_fit = dens_fit, newdata = newdata)\n",
    "\n",
    "p2_A_given_W <- as_tibble(preds_2) %>%\n",
    "  ggplot(., aes(x = value)) +\n",
    "  geom_histogram(aes(y = ..density..), binwidth = 0.1, alpha = 0.8,\n",
    "                 position = \"identity\") +\n",
    "  geom_density(alpha = 0.2) +\n",
    "  ggtitle(\"Conditional Density: p(A | W)\") + theme_bw()\n",
    "\n",
    "p2_A_given_W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dens_fit <- fit_density(\n",
    "    X = c(\"W1\", \"W2\", \"W3\"), \n",
    "    Y = \"A\", \n",
    "    input_data = data_O, \n",
    "    nbins = 25, \n",
    "    bin_method = \"dhist\",\n",
    "    bin_estimator = speedglmR6$new())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AIIIIAAAgjE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\n5861c1HIOwIIIBCnAAFSnDQ8gQAC/gjo1L/Lli0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WLFmQQQABBGwroMFRv3795NSpU7Qi2bYWyTgCzhMgQHJenVIiBwvo1LibN2+Wnj17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\nAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "preds_3 <- sample_value(model_fit = dens_fit, newdata = newdata)\n",
    "\n",
    "p3_A_given_W <- as_tibble(preds_3) %>%\n",
    "  ggplot(., aes(x = value)) +\n",
    "  geom_histogram(aes(y = ..density..), binwidth = 0.1, alpha = 0.8,\n",
    "                 position = \"identity\") +\n",
    "  geom_density(alpha = 0.2) +\n",
    "  ggtitle(\"Conditional Density: p(A | W)\") + theme_bw()\n",
    "\n",
    "p3_A_given_W"
   ]
  }
 ],
 "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}