From f35a6ede9a4341e1c8b184d98feeb17ef86f85f7 Mon Sep 17 00:00:00 2001
From: Alexandre Roulois <alexandre@roulois.fr>
Date: Fri, 20 Jan 2023 09:07:56 +0100
Subject: [PATCH] Section Simpson paradox

---
 .../machine-learning/1.machine-learning.ipynb |  44 ++++++++++--------
 .../images/penguins-by-sex-simpson.png        | Bin 0 -> 36622 bytes
 .../images/penguins-by-specy-simpson.png      | Bin 0 -> 23348 bytes
 .../images/penguins-simpson.png               | Bin 0 -> 28590 bytes
 4 files changed, 25 insertions(+), 19 deletions(-)
 create mode 100644 notebooks/machine-learning/images/penguins-by-sex-simpson.png
 create mode 100644 notebooks/machine-learning/images/penguins-by-specy-simpson.png
 create mode 100644 notebooks/machine-learning/images/penguins-simpson.png

diff --git a/notebooks/machine-learning/1.machine-learning.ipynb b/notebooks/machine-learning/1.machine-learning.ipynb
index d2b8044..93769e6 100644
--- a/notebooks/machine-learning/1.machine-learning.ipynb
+++ b/notebooks/machine-learning/1.machine-learning.ipynb
@@ -423,23 +423,13 @@
    "id": "60535d0b-2290-4c80-84c5-7f5ffedaa475",
    "metadata": {},
    "source": [
-    "Toujours sur les mêmes données de l’évolution des cas d’autisme, les courbes sur les graphiques ci-dessous semblenet montrer que le secteur de l’agriculture biologique augmente de manière parralèle au nombre de cas d’autisme recensés, tandis que la part d’OGM dans les cultures reste stable, à un seuil proche de zéro."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "359ded53-45c2-4ded-b8ce-f24d88b61eb4",
-   "metadata": {},
-   "source": [
-    "![](./images/evolution-autism-no-scale.png)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7bf4368d-a951-4685-8dd8-10742da9c5be",
-   "metadata": {},
-   "source": [
-    "Cette interprétation est bien évidemment fausse. Tout d’abord, nous l’avons vu, il n’existe aucune causalité entre les volumes de vente de l’agriculture biologique ou la part d’OGM dans les surfaces agricoles et les cas d’autisme ; ensuite, l'échelle de mesure n’est pas du tout la même : quand la courbe des OGM est exprimée en pourcentages, sur une échelle de 0 à 100, celle des volumes de vente s’échelonne entre 10 000 et 30 000, et celle des cas d’autisme commence à 160 000 pour terminer à près de 500 000."
+    "Toujours sur les mêmes données de l’évolution des cas d’autisme, les courbes sur les graphiques ci-dessous semblent montrer que le secteur de l’agriculture biologique augmente de manière parralèle au nombre de cas d’autisme recensés, tandis que la part d’OGM dans les cultures reste stable, à un seuil proche de zéro.\n",
+    "\n",
+    "![Données sur des échelles différentes](./images/evolution-autism-no-scale.png)\n",
+    "\n",
+    "Cette interprétation est bien évidemment fausse. Tout d’abord, nous l’avons vu, il n’existe aucune causalité entre les volumes de vente de l’agriculture biologique ou la part d’OGM dans les surfaces agricoles et les cas d’autisme ; ensuite, l'échelle de mesure n’est pas du tout la même : quand la courbe des OGM est exprimée en pourcentages, sur une échelle de 0 à 100, celle des volumes de vente s’échelonne entre 10 000 et 30 000, et celle des cas d’autisme commence à 160 000 pour terminer à près de 500 000.\n",
+    "\n",
+    "Pour cette raison, si vous voulez montrer l’évolution de deux courbes, vous devez d’abord passer leurs données sur la même échelle, en adoptant l’une des deux méthodes privilégiées : **la standardisation** (*Z score normalization*) ou **la normalisation** (*Min-Max normalization*)."
    ]
   },
   {
@@ -455,7 +445,23 @@
    "id": "8d179735-20b4-4eca-bcf1-c0bf250a4fb1",
    "metadata": {},
    "source": [
-    "Bien plus difficile à détecter, le paradoxe de Simpson, du nom du statisticien Edward Simpson qui l’a décrit en 1951, est une bizarrerie mathématique qui montre que, combinés, les résultats de plusieurs groupes sont inversés par rapport à leurs résultats individuels."
+    "Bien plus difficile à détecter, une bizarrerie mathématique qui montre que, combinés, les résultats de plusieurs groupes sont inversés par rapport à leurs résultats individuels. Il s’agit du paradoxe de Simpson, du nom du statisticien Edward Simpson qui l’a décrit en 1951.\n",
+    "\n",
+    "Prenons un exemple issu [du recensement des manchots en Antarctique](./0.about-datasets.ipynb#Size-measurements-for-adult-foraging-penguins-near-Palmer-Station,-Antarctica) (Gorman, 2014). Le graphique ci-dessous montre la corrélation entre la masse corporelle d’un manchot et la taille de son bec.\n",
+    "\n",
+    "![Le paradoxe de Simpson](./images/penguins-simpson.png)\n",
+    "\n",
+    "La droite de régression ne laisse aucun doute : les becs des manchots rétrécissent à mesure qu’ils prennent du poids. Une conclusion contre-intuitive, non ? On penserait plutôt l’inverse d’un individu lambda, qu’il existe une corrélation positive entre le poids et les autres caractéristiques physiques. Quelle erreur avons-nous commise ici ?\n",
+    "\n",
+    "Sur le graphique se distinguent nettement deux groupes de manchots, une observation qui nous laisse penser que nous avons négligé un critère dans notre analyse. Regardons ce qu’il en est pour les manchots mâles et les manchots femelles :\n",
+    "\n",
+    "![Le paradoxe de Simpson : hypothèse de facteur de confusion](./images/penguins-by-sex-simpson.png)\n",
+    "\n",
+    "Notre hypothèse ne fait que renforcer la conclusion, aussi, les manchots seraient-ils la première espèce animale à voire leur silhouette s’affiner avec la prise de masse ? Définitivement, non. Pour s’en assurer, on devrait plutôt s’intéresser aux différentes espèces qui composent la grande famille des manchots et à leurs disparités physiques :\n",
+    "\n",
+    "![Le paradoxe de Simpson : effet inverse sur les sous-groupes](./images/penguins-by-specy-simpson.png)\n",
+    "\n",
+    "C’est l’illustration du paradoxe de Simpson, où l’espèce des manchots influe autant sur la cause (masse plus ou moins importante) que sur la conséquence (longueur du bec variant également selon l’espèce). On parle alors de **facteur de confusion**."
    ]
   },
   {
@@ -471,7 +477,7 @@
    "id": "615d9158-4103-4bf4-8087-8972c838e217",
    "metadata": {},
    "source": [
-    "Les systèmes sont tout autant soumis au problème du sur-entraînement (*overfitting*) ou du sous-entraînement (*underfitting*). Un algorithme trop simple ne pourra mettre en évidence la structure des données quand un algorithme trop compliqué – parce que parfaitement ajusté aux données sur lesquelles il s’est entraîné – provoquera des erreurs de généralisation importantes.\n",
+    "Les systèmes sont tout autant soumis au problème du **sur-entraînement** (*overfitting*) qu’à celui du **sous-entraînement** (*underfitting*). Un algorithme trop simple ne pourra mettre en évidence la structure des données quand un algorithme trop compliqué – parce que parfaitement ajusté aux données sur lesquelles il s’est entraîné – provoquera des erreurs de généralisation importantes.\n",
     "\n",
     "On peut estimer par exemple qu’un modèle linéaire sous-ajustera systématiquement par rapport à la réalité et que, a contrario, un modèle polynomial de très haut degré sur-ajustera tellement que ses prédictions se révéleront toutes fausses."
    ]
diff --git a/notebooks/machine-learning/images/penguins-by-sex-simpson.png b/notebooks/machine-learning/images/penguins-by-sex-simpson.png
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-- 
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