iaroslav-ai/Disballanced Learning.ipynb

## Disballanced Learning.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example learning with disballanced dataset\n",
    "\n",
    "ML with disballanced dataset is not an issue in case of separable classes. In this example, a model learns to separate perfectly both classes, even though the ratio of class instances is ~ 1000 to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Positive instances: 118\n",
      "Negative instances: 99882\n",
      "Positive to negative class ratio: 0.0011813940449730681\n",
      "Model test accuracy: 1.0 (1.0 is perfectly accurate)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/iaroslav/.local/lib/python3.5/site-packages/sklearn/svm/base.py:922: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
      "  \"the number of iterations.\", ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.svm import LinearSVC\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X = np.random.rand(100000, 2)\n",
    "y = np.sum(np.abs(X), axis=-1) < 0.05\n",
    "X = (X.T - 0.1*y.T).T # perfectly separable classes.\n",
    "\n",
    "print('Positive instances: %s' % np.sum(y==True))\n",
    "print('Negative instances: %s' % np.sum(y==False))\n",
    "print('Positive to negative class ratio: %s' % (np.sum(y==True) / np.sum(y==False)))\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y)\n",
    "\n",
    "# Appropriate selection of parameter C should be done\n",
    "model = LinearSVC(C=10000.0)\n",
    "model.fit(X_train, y_train)\n",
    "y_pred = model.predict(X_test)\n",
    "score = model.score(X_test, y_test)\n",
    "print(\"Model test accuracy: %s (1.0 is perfectly accurate)\" % score)\n",
    "\n",
    "# visualize data and predictions\n",
    "def plot_data(X, y, title):\n",
    "    plt.title(title)\n",
    "    plt.scatter(X[~y, 0], X[~y, 1])\n",
    "    plt.scatter(X[y, 0], X[y, 1])\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.subplot(1, 3, 1)\n",
    "plot_data(X_train, y_train, 'Training data')\n",
    "plt.subplot(1, 3, 2)\n",
    "plot_data(X_test, y_test, 'Testing data')\n",
    "plt.subplot(1, 3, 3)\n",
    "plot_data(X_test, y_pred, 'Model predictions')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"# Example learning with disballanced dataset\n",
	"\n",
	"ML with disballanced dataset is not an issue in case of separable classes. In this example, a model learns to separate perfectly both classes, even though the ratio of class instances is ~ 1000 to 1."
	]
	},
	{
	"cell_type": "code",
	"execution_count": 2,
	"metadata": {},
	"outputs": [
	{
	"name": "stdout",
	"output_type": "stream",
	"text": [
	"Positive instances: 118\n",
	"Negative instances: 99882\n",
	"Positive to negative class ratio: 0.0011813940449730681\n",
	"Model test accuracy: 1.0 (1.0 is perfectly accurate)\n"
	]
	},
	{
	"name": "stderr",
	"output_type": "stream",
	"text": [
	"/home/iaroslav/.local/lib/python3.5/site-packages/sklearn/svm/base.py:922: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
	" \"the number of iterations.\", ConvergenceWarning)\n"
	]
	},
	{
	"data": {
	"image/png": 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\n",
	"text/plain": [
	"<Figure size 720x288 with 3 Axes>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"import numpy as np\n",
	"import matplotlib.pyplot as plt\n",
	"from sklearn.svm import LinearSVC\n",
	"from sklearn.model_selection import train_test_split\n",
	"\n",
	"X = np.random.rand(100000, 2)\n",
	"y = np.sum(np.abs(X), axis=-1) < 0.05\n",
	"X = (X.T - 0.1*y.T).T # perfectly separable classes.\n",
	"\n",
	"print('Positive instances: %s' % np.sum(y==True))\n",
	"print('Negative instances: %s' % np.sum(y==False))\n",
	"print('Positive to negative class ratio: %s' % (np.sum(y==True) / np.sum(y==False)))\n",
	"\n",
	"X_train, X_test, y_train, y_test = train_test_split(X, y)\n",
	"\n",
	"# Appropriate selection of parameter C should be done\n",
	"model = LinearSVC(C=10000.0)\n",
	"model.fit(X_train, y_train)\n",
	"y_pred = model.predict(X_test)\n",
	"score = model.score(X_test, y_test)\n",
	"print(\"Model test accuracy: %s (1.0 is perfectly accurate)\" % score)\n",
	"\n",
	"# visualize data and predictions\n",
	"def plot_data(X, y, title):\n",
	" plt.title(title)\n",
	" plt.scatter(X[~y, 0], X[~y, 1])\n",
	" plt.scatter(X[y, 0], X[y, 1])\n",
	"\n",
	"plt.figure(figsize=(10, 4))\n",
	"plt.subplot(1, 3, 1)\n",
	"plot_data(X_train, y_train, 'Training data')\n",
	"plt.subplot(1, 3, 2)\n",
	"plot_data(X_test, y_test, 'Testing data')\n",
	"plt.subplot(1, 3, 3)\n",
	"plot_data(X_test, y_pred, 'Model predictions')\n",
	"plt.show()"
	]
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "Python 3",
	"language": "python",
	"name": "python3"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 3
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython3",
	"version": "3.5.2"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 2
	}