Regularization-R.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "suppressMessages(library(tidyverse))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`geom_smooth()` using method = 'loess' and formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using method = 'loess' and formula 'y ~ x'\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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9rr0YJVNaGI1JmdD6guV7X3xG7BqqpQROrL3ge9V6va79FyVXWhiNSV3e9LLFZ1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\nQSRCBIJIhAjk/wE0aHjb9sdlGgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mydata <- read.csv(file=\"Ex1LS.csv\", header=TRUE, sep=\",\")\n",
    "\n",
    "model <- lm( formula = Y ~ X, mydata)\n",
    "modelQ <- lm( formula = Y ~ X + I(X^2), mydata)\n",
    "\n",
    "modData <- mydata\n",
    "modData$newYQ <- predict(modelQ, mydata)\n",
    "\n",
    "modData$newY <- predict(model, mydata)\n",
    "\n",
    "p <- ggplot(modData, aes(x=X, y=Y))+geom_point()  \n",
    "p <- p + geom_point(data = modData, aes(x=X, y = newY), color = 'red')\n",
    "p <- p + geom_smooth(data=modData, aes(X, newY), se=FALSE, color = \"red\", span = 1.5)\n",
    "p <- p + geom_smooth(data=modData, aes(X, newYQ), se=FALSE, color = \"blue\", span = 1.5)\n",
    "p\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`geom_smooth()` using method = 'loess' and formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using method = 'loess' and formula 'y ~ x'\n",
      "\n",
      "`geom_smooth()` using method = 'loess' and formula 'y ~ x'\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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khDoKIeXb8HeMSqupsg0giorEftnx753qSBVXU2QaT+UKmr3s8M8YhVdTdBpO5Q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\n/w9uNReclHzrVAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- mydata$X\n",
    "y <- mydata$Y\n",
    "d <- data.frame(x=x,y=y)\n",
    "\n",
    "# using the quad function above for linear equation \n",
    "# and solving using normal equations (go back to regression 1)\n",
    "\n",
    "\n",
    "m = length(mydata$X) \n",
    "x = matrix(c(rep(1,m), mydata$X, mydata$X^2), ncol=3)\n",
    "n = ncol(x)\n",
    "y = matrix(mydata$Y, ncol=1)\n",
    "\n",
    "\n",
    "# set up 3 different levels of regularization term values 0, 1 and 10\n",
    "\n",
    "\n",
    "lambda = c(0,1,10)\n",
    "d = diag(1,n,n)\n",
    "d[1,1] = 0\n",
    "th = array(0,c(n,length(lambda)))\n",
    "\n",
    "for (i in 1:length(lambda)) {\n",
    "  th[,i] = solve(t(x) %*% x + (lambda[i] * d)) %*% (t(x) %*% y)\n",
    "}\n",
    "\n",
    "nwx = seq(1, 4, len=50)\n",
    "\n",
    "x = matrix(c(rep(1,length(nwx)), nwx, nwx^2), ncol=3)\n",
    "newData <- as.data.frame(nwx)\n",
    "newData$th1 <- (x %*% th[,1])\n",
    "newData$th2 <- (x %*% th[,2])\n",
    "newData$th3 <- (x %*% th[,3])\n",
    "\n",
    "X <- newData$nwx\n",
    "#newData$lm <- predict(model, newData = X)\n",
    "\n",
    "p <- ggplot(mydata, aes(x=X, y=Y))+geom_point() + geom_smooth(method = 'lm', se=FALSE, color = 'black') \n",
    "p <- p+ geom_smooth(data = newData, aes(x=nwx, y = th1), color = 'blue')\n",
    "p <- p+ geom_smooth(data = newData, aes(x=nwx, y = th2), color = 'red')\n",
    "p <- p+ geom_smooth(data = newData, aes(x=nwx, y = th3), color = 'green')\n",
    "p\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R 3.3",
   "language": "R",
   "name": "ir33"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}