t81_558_class_04_5_rmse_logloss.ipynb

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   "source": [
    "# T81-558: Applications of Deep Neural Networks\n",
    "**Module 4: Training for Tabular Data**\n",
    "* Instructor: [Jeff Heaton](https://sites.wustl.edu/jeffheaton/), McKelvey School of Engineering, [Washington University in St. Louis](https://engineering.wustl.edu/Programs/Pages/default.aspx)\n",
    "* For more information visit the [class website](https://sites.wustl.edu/jeffheaton/t81-558/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Module 4 Material\n",
    "\n",
    "* Part 4.1: Encoding a Feature Vector for Keras Deep Learning [[Video]](https://www.youtube.com/watch?v=Vxz-gfs9nMQ&list=PLjy4p-07OYzulelvJ5KVaT2pDlxivl_BN) [[Notebook]](t81_558_class_04_1_feature_encode.ipynb)\n",
    "* Part 4.2: Keras Multiclass Classification for Deep Neural Networks with ROC and AUC [[Video]](https://www.youtube.com/watch?v=-f3bg9dLMks&list=PLjy4p-07OYzulelvJ5KVaT2pDlxivl_BN) [[Notebook]](t81_558_class_04_2_multi_class.ipynb)\n",
    "* Part 4.3: Keras Regression for Deep Neural Networks with RMSE [[Video]](https://www.youtube.com/watch?v=wNhBUC6X5-E&list=PLjy4p-07OYzulelvJ5KVaT2pDlxivl_BN) [[Notebook]](t81_558_class_04_3_regression.ipynb)\n",
    "* Part 4.4: Backpropagation, Nesterov Momentum, and ADAM Neural Network Training [[Video]](https://www.youtube.com/watch?v=VbDg8aBgpck&list=PLjy4p-07OYzulelvJ5KVaT2pDlxivl_BN) [[Notebook]](t81_558_class_04_4_backprop.ipynb)\n",
    "* **Part 4.5: Neural Network RMSE and Log Loss Error Calculation from Scratch** [[Video]](https://www.youtube.com/watch?v=wmQX1t2PHJc&list=PLjy4p-07OYzulelvJ5KVaT2pDlxivl_BN) [[Notebook]](t81_558_class_04_5_rmse_logloss.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 4.5: Error Calculation from Scratch\n",
    "\n",
    "We will now look at how to calculate RMSE and logloss by hand.  \n",
    "\n",
    "\n",
    "### Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score (MSE): 0.14200000000000007\n",
      "Score (RMSE): 0.37682887362833556\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "import numpy as np\n",
    "\n",
    "predicted = [1.1,1.9,3.4,4.2,4.3]\n",
    "expected = [1,2,3,4,5]\n",
    "\n",
    "score_mse = metrics.mean_squared_error(predicted,expected)\n",
    "score_rmse = np.sqrt(score_mse)\n",
    "print(\"Score (MSE): {}\".format(score_mse))\n",
    "print(\"Score (RMSE): {}\".format(score_rmse))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score (MSE): 0.14200000000000007\n",
      "Score (RMSE): 0.37682887362833556\n"
     ]
    }
   ],
   "source": [
    "score_mse = ((predicted[0]-expected[0])**2 + (predicted[1]-expected[1])**2 \n",
    "+ (predicted[2]-expected[2])**2 + (predicted[3]-expected[3])**2\n",
    "+ (predicted[4]-expected[4])**2)/len(predicted)\n",
    "score_rmse = np.sqrt(score_mse)\n",
    "    \n",
    "print(\"Score (MSE): {}\".format(score_mse))\n",
    "print(\"Score (RMSE): {}\".format(score_rmse))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classification\n",
    "\n",
    "We will now look at how to calculate a logloss by hand. For this we look at a binary prediction. The expected is always 0 or 1. The predicted is some number between 0-1 that indicates the probability true (1). Therefore, a prediction of 1.0 is completely correct if the expected is 1 and completely wrong if the expected is 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.06678801305495843\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "\n",
    "expected = [1,1,0,0,0]\n",
    "predicted = [0.9,0.99,0.1,0.05,0.06]\n",
    "\n",
    "print(metrics.log_loss(expected,predicted))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we attempt to calculate the same logloss manually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score Logloss 0.06678801305495843\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "score_logloss = (np.log(1.0-np.abs(expected[0]-predicted[0]))+\\\n",
    "np.log(1.0-np.abs(expected[1]-predicted[1]))+\\\n",
    "np.log(1.0-np.abs(expected[2]-predicted[2]))+\\\n",
    "np.log(1.0-np.abs(expected[3]-predicted[3]))+\\\n",
    "np.log(1.0-np.abs(expected[4]-predicted[4])))\\\n",
    "*(-1/len(predicted))\n",
    "\n",
    "print(f'Score Logloss {score_logloss}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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