{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "library(talweg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ts_data = read.csv(system.file(\"extdata\",\"pm10_mesures_H_loc.csv\",package=\"talweg\"))\n",
    "exo_data = read.csv(system.file(\"extdata\",\"meteo_extra_noNAs.csv\",package=\"talweg\"))\n",
    "data = getData(ts_data, exo_data, input_tz = \"Europe/Paris\", working_tz=\"Europe/Paris\", predict_at=13)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "J'ai fait quelques essais dans différentes configurations pour la méthode \"Neighbors\" (la seule dont on a parlé).<br>Il semble que le mieux soit\n",
    "\n",
    " * simtype=\"mix\" : on utilise les similarités endogènes et exogènes (fenêtre optimisée par VC)\n",
    " * same_season=FALSE : les indices pour la validation croisée ne tiennent pas compte des saisons\n",
    " * mix_strategy=\"mult\" : on multiplie les poids (au lieu d'en éteindre)\n",
    "\n",
    "(valeurs par défaut).\n",
    "\n",
    "J'ai systématiquement comparé à deux autres approches : la persistence et la moyennes des lendemains des jours \"similaires\" dans tout le passé ; à chaque fois sans prédiction du saut (sauf pour Neighbors : prédiction basée sur les poids calculés).\n",
    "\n",
    "Ensuite j'affiche les erreurs, quelques courbes prévues/mesurées, quelques filaments puis les histogrammes de quelques poids. Concernant les graphes de filaments, la moitié gauche du graphe correspond aux jours similaires au jour courant, tandis que la moitié droite affiche les lendemains : ce sont donc les voisinages tels qu'utilisés dans l'algorithme.\n",
    "\n",
    "<h2 style=\"color:blue;font-size:2em\">Pollution par chauffage</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "indices_ch = seq(as.Date(\"2015-01-18\"),as.Date(\"2015-01-24\"),\"days\")\n",
    "p_ch_nn = computeForecast(data,indices_ch, \"Neighbors\", \"Neighbors\", simtype=\"mix\")\n",
    "p_ch_pz = computeForecast(data, indices_ch, \"Persistence\", \"Zero\", same_day=TRUE)\n",
    "p_ch_az = computeForecast(data, indices_ch, \"Average\", \"Zero\") #, memory=183)\n",
    "#p_ch_zz = computeForecast(data, indices_ch, \"Zero\", \"Zero\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "e_ch_nn = computeError(data, p_ch_nn)\n",
    "e_ch_pz = computeError(data, p_ch_pz)\n",
    "e_ch_az = computeError(data, p_ch_az)\n",
    "#e_ch_zz = computeError(data, p_ch_zz)\n",
    "options(repr.plot.width=9, repr.plot.height=7)\n",
    "plotError(list(e_ch_nn, e_ch_pz, e_ch_az), cols=c(1,2,colors()[258]))\n",
    "\n",
    "#Noir: neighbors, rouge: persistence, vert: moyenne"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "options(repr.plot.width=9, repr.plot.height=4)\n",
    "plotPredReal(data, p_ch_nn, 3)\n",
    "plotPredReal(data, p_ch_nn, 4)\n",
    "\n",
    "#Bleu: prévue, noir: réalisée"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prédictions très lisses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "plotPredReal(data, p_ch_az, 3)\n",
    "plotPredReal(data, p_ch_az, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "f3_ch = computeFilaments(data, p_ch_nn$getIndexInData(3), plot=TRUE)\n",
    "f4_ch = computeFilaments(data, p_ch_nn$getIndexInData(4), plot=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(2,2))\n",
    "options(repr.plot.width=9, repr.plot.height=7)\n",
    "plotFilamentsBox(data, f3_ch$indices)\n",
    "plotFilamentsBox(data, f3_ch$indices+1)\n",
    "plotFilamentsBox(data, f4_ch$indices)\n",
    "plotFilamentsBox(data, f4_ch$indices+1)\n",
    "\n",
    "#En haut : jour 3 + lendemain (4) ; en bas : jour 4 + lendemain (5)\n",
    "#À gauche : premières 24h ; à droite : 24h suivantes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Peu de voisins, les courbes sont assez isolées (en particulier les lendemains)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "options(repr.plot.width=9, repr.plot.height=4)\n",
    "plotRelativeVariability(data, f3_ch$indices)\n",
    "plotRelativeVariability(data, f4_ch$indices)\n",
    "\n",
    "#Variabilité sur 60 courbes au hasard en rouge ; sur nos 60 voisins (+ lendemains) en noir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il faudrait que la courbe noire soit nettement plus basse que la courbe rouge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "plotSimils(p_ch_nn, 3)\n",
    "plotSimils(p_ch_nn, 4)\n",
    "\n",
    "#Non pollué à gauche, pollué à droite"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Poids plus concentrés autour de 0 pour un jour plus pollué."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Fenêtres sélectionnées dans ]0,10] / endo à gauche, exo à droite\n",
    "p_ch_nn$getParams(3)$window\n",
    "p_ch_nn$getParams(4)$window"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 style=\"color:blue;font-size:2em\">Pollution par épandage</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "indices_ep = seq(as.Date(\"2015-03-15\"),as.Date(\"2015-03-21\"),\"days\")\n",
    "p_ep_nn = computeForecast(data,indices_ep, \"Neighbors\", \"Neighbors\", simtype=\"mix\")\n",
    "p_ep_pz = computeForecast(data, indices_ep, \"Persistence\", \"Zero\", same_day=TRUE)\n",
    "p_ep_az = computeForecast(data, indices_ep, \"Average\", \"Zero\") #, memory=183)\n",
    "#p_ep_zz = computeForecast(data, indices_ep, \"Zero\", \"Zero\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "e_ep_nn = computeError(data, p_ep_nn)\n",
    "e_ep_pz = computeError(data, p_ep_pz)\n",
    "e_ep_az = computeError(data, p_ep_az)\n",
    "#e_ep_zz = computeError(data, p_ep_zz)\n",
    "options(repr.plot.width=9, repr.plot.height=7)\n",
    "plotError(list(e_ep_nn, e_ep_pz, e_ep_az), cols=c(1,2,colors()[258]))\n",
    "\n",
    "#Noir: neighbors, rouge: persistence, vert: moyenne"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Neighbors et Average comparables, Persistence moins performante."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "options(repr.plot.width=9, repr.plot.height=4)\n",
    "plotPredReal(data, p_ep_nn, 6)\n",
    "plotPredReal(data, p_ep_nn, 3)\n",
    "\n",
    "#Bleu: prévue, noir: réalisée"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "À gauche un jour \"bien\" prévu, à droite le pic d'erreur (jour 3)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "plotPredReal(data, p_ep_az, 6)\n",
    "plotPredReal(data, p_ep_az, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Average : autre type de prévision."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "f6_ep = computeFilaments(data, p_ep_nn$getIndexInData(6), plot=TRUE)\n",
    "f3_ep = computeFilaments(data, p_ep_nn$getIndexInData(3), plot=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(2,2))\n",
    "options(repr.plot.width=9, repr.plot.height=7)\n",
    "plotFilamentsBox(data, f6_ep$indices)\n",
    "plotFilamentsBox(data, f6_ep$indices+1)\n",
    "plotFilamentsBox(data, f3_ep$indices)\n",
    "plotFilamentsBox(data, f3_ep$indices+1)\n",
    "\n",
    "#En haut : jour 4 + lendemain (5) ; en bas : jour 6 + lendemain (7)\n",
    "#À gauche : premières 24h ; à droite : 24h suivantes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "options(repr.plot.width=9, repr.plot.height=4)\n",
    "plotRelativeVariability(data, f6_ep$indices)\n",
    "plotRelativeVariability(data, f3_ep$indices)\n",
    "\n",
    "#Variabilité sur 60 courbes au hasard en rouge ; sur nos 60 voisins (+ lendemains) en noir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il faudrait que la courbe noire soit nettement plus basse que la courbe rouge..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "plotSimils(p_ep_nn, 6)\n",
    "plotSimils(p_ep_nn, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Même observation concernant les poids : concentrés près de zéro pour les prédictions avec peu de voisins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Fenêtres sélectionnées dans ]0,10] / endo à gauche, exo à droite\n",
    "p_ep_nn$getParams(6)$window\n",
    "p_ep_nn$getParams(3)$window"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 style=\"color:blue;font-size:2em\">Semaine non polluée</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "indices_np = seq(as.Date(\"2015-04-26\"),as.Date(\"2015-05-02\"),\"days\")\n",
    "p_np_nn = computeForecast(data,indices_np, \"Neighbors\", \"Neighbors\", simtype=\"mix\")\n",
    "p_np_pz = computeForecast(data, indices_np, \"Persistence\", \"Zero\", same_day=FALSE)\n",
    "p_np_az = computeForecast(data, indices_np, \"Average\", \"Zero\") #, memory=183)\n",
    "#p_np_zz = computeForecast(data, indices_np, \"Zero\", \"Zero\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "e_np_nn = computeError(data, p_np_nn)\n",
    "e_np_pz = computeError(data, p_np_pz)\n",
    "e_np_az = computeError(data, p_np_az)\n",
    "#e_np_zz = computeError(data, p_np_zz)\n",
    "options(repr.plot.width=9, repr.plot.height=7)\n",
    "plotError(list(e_np_nn, e_np_pz, e_np_az), cols=c(1,2,colors()[258]))\n",
    "\n",
    "#Noir: neighbors, rouge: persistence, vert: moyenne"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Performances des méthodes \"Average\" et \"Neighbors\" identiques ; mauvais résultats pour la persistence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "options(repr.plot.width=9, repr.plot.height=4)\n",
    "plotPredReal(data, p_np_nn, 5)\n",
    "plotPredReal(data, p_np_nn, 3)\n",
    "\n",
    "#Bleu: prévue, noir: réalisée"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "plotPredReal(data, p_np_az, 5)\n",
    "plotPredReal(data, p_np_az, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "f5_np = computeFilaments(data, p_np_nn$getIndexInData(5), plot=TRUE)\n",
    "f3_np = computeFilaments(data, p_np_nn$getIndexInData(3), plot=TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Jours \"typiques\", donc beaucoup de voisins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(2,2))\n",
    "options(repr.plot.width=9, repr.plot.height=7)\n",
    "plotFilamentsBox(data, f5_np$indices)\n",
    "plotFilamentsBox(data, f5_np$indices+1)\n",
    "plotFilamentsBox(data, f3_np$indices)\n",
    "plotFilamentsBox(data, f3_np$indices+1)\n",
    "\n",
    "#En haut : jour 3 + lendemain (4) ; en bas : jour 6 + lendemain (7)\n",
    "#À gauche : premières 24h ; à droite : 24h suivantes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "options(repr.plot.width=9, repr.plot.height=4)\n",
    "plotRelativeVariability(data, f5_np$indices)\n",
    "plotRelativeVariability(data, f3_np$indices)\n",
    "\n",
    "#Variabilité sur 60 courbes au hasard en rouge ; sur nos 60 voisins (+ lendemains) en noir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Situation meilleure que dans les autres cas, mais assez difficile tout de même."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "par(mfrow=c(1,2))\n",
    "plotSimils(p_np_nn, 5)\n",
    "plotSimils(p_np_nn, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Répartition des poids difficile à interpréter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Fenêtres sélectionnées dans ]0,10] / endo à gauche, exo à droite\n",
    "p_np_nn$getParams(5)$window\n",
    "p_np_nn$getParams(3)$window"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bilan\n",
    "\n",
    "Problème difficile : on ne fait guère mieux qu'une naïve moyenne des lendemains des jours similaires dans le passé, ce qui n'est pas loin de prédire une série constante égale à la dernière valeur observée (méthode \"zéro\"). La persistence donne parfois de bons résultats mais est trop instable (sensibilité à l'argument <code>same_day</code>).\n",
    "\n",
    "Comment améliorer la méthode ?"
   ]
  }
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