bayesian_deep_learning/uncertainty_estimation/quantile_regression/experiments/01-quantile_regression/02-quantile_regression_loss_function.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Quantile Regression - Pinball Loss function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the [previous notebook](http://localhost:8888/notebooks/bayesian_deep_learning/uncertainty_estimation/quantile_regression/experiments/01-quantile_regression/01-quantile_regression_techniques.ipynb), it has been validated the Pinball/Quantile Loss as a good uncertainty metric for evaluating prediction intervals.\n",
    "\n",
    "The goal of this notebook is to have an intuitive idea of the theory and limitations behind the **quantile loss function**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "import statsmodels.api as sm\n",
    "from scipy.stats import norm\n",
    "from sklearn import ensemble\n",
    "\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "tf.get_logger().setLevel('INFO')\n",
    "\n",
    "mpl.rcParams['figure.figsize'] = 20, 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The notebook is organized in the following two sections:\n",
    "\n",
    "- **Quantile loss formulation**. It is explained the theory and implementation details of the quantile loss formula for evaluating prediction intervals.\n",
    "\n",
    "- **Bayesian interpretation of the quantile loss function**. It is analyzed the assumptions (or beliefs) imposed over the model residual distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantile loss formulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The quantile loss uses the following formulation:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Loss individual data point*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{align}\n",
    "\\mathcal{L}(\\epsilon|\\alpha)=\\begin{cases}\n",
    "\\alpha \\epsilon &\\text{if }\\epsilon\\ge 0, \\\\\n",
    "(\\alpha-1) \\epsilon &\\text{if } \\epsilon< 0.\n",
    "\\end{cases}\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* $\\alpha$: the quantile to be evaluated (a value between 0 and 1)\n",
    "* $\\epsilon$: the residual computed as $\\epsilon = f(\\mathbf{x}_i)$ - y_i \n",
    "    * $f(\\mathbf{x}_i)$ is the predicted (quantile)\n",
    "    * $y_i$ is the true value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Loss global function*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\mathcal{L}(\\mathbf{y},\\mathbf{f}|\\alpha)=\\frac{1}{N} \\sum_{i=1}^N \\mathcal{L}(y_i-f(\\mathbf{x}_i)|\\alpha)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "def quantile_loss(q, y, f):\n",
    "    # q: quantile to be evaluated (represented as alpha in the formula)\n",
    "    # y: true value.\n",
    "    # f: is the predicted quantile\n",
    "    # e: the residual \n",
    "    e = f - y\n",
    "    #e = y - f . NOTE: IMPORTANT!! Sometimes the error is computed in this form \n",
    "    return np.maximum(q * e, (q - 1) * e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Intuitive interpretation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The quantile loss formula have two terms:\n",
    " -  q * e\n",
    " - (q - 1) * e\n",
    "\n",
    "In the practice, only one of the two terms will be applied (the maximum value form both). The term will be applied depending on the sign of prediction residual:\n",
    "\n",
    "* *Over-predicting* f > y. The error will be positive and the first term will dominate \n",
    "* *Under-predicting* f < y. The error will be negative and the second term will dominate\n",
    "\n",
    "Additionally, it is applied different weights to residuals obtained from over-predictions (positive) and under-predictions (negative) depending on the quantile value. Thus, Q is a penalization factor:\n",
    "\n",
    " * q=0.5 under-prediction and over-prediction will be penalized by the same factor, the median is obtained\n",
    " * q=0.75 over-predictions (positive residual) will be penalized by a factor of 0.75, and under-predictions (negative residual) by a factor of 0.25"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following figure it is represented an example. Here, we can see that the model output (prediction) is under the observed true value. Thus, this is a case of **under-predicting**.\n",
    "\n",
    "In this case, if we would like to estimate a quantile of q=0.25, this specific (negative) residual will be penalized more heavily than positive residual. The second term of the loss will become positive and dominate (-0.75 * -e > 0.25 * -e) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"../../img/prediction_interval.png\" width=\"300\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This formula leads us to an **assymmetric form** of the loss function visualized before."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loss function visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, it is artificially generated error values in a interval of [-1,1] in order to understand how the quantile loss function behaves. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [],
   "source": [
    "quantile_loss_error = np.linspace(-1, 1, 1000)\n",
    "quantile_loss_error_loss_10 = quantile_loss(0.1, 0, quantile_loss_error)\n",
    "quantile_loss_error_loss_50 = quantile_loss(0.5, 0, quantile_loss_error)\n",
    "quantile_loss_error_loss_90 = quantile_loss(0.9, 0, quantile_loss_error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "is_executing": false
    }
   },
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with sns.color_palette('Blues', 4):\n",
    "    plt.plot(quantile_loss_error, quantile_loss_error_loss_10)\n",
    "    plt.plot(quantile_loss_error, quantile_loss_error_loss_50)\n",
    "    plt.plot(quantile_loss_error, quantile_loss_error_loss_90)\n",
    "    plt.legend([str(int(q * 100)) + 'th percentile' for q in [0.1, 0.5, 0.9]])\n",
    "    sns.despine(left=True, bottom=True)\n",
    "    plt.xlabel('Error')\n",
    "    plt.ylabel('Quantile loss')\n",
    "    plt.title('Quantile loss by error and quantile', loc='left');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the quantile loss value is dependent on the evaluated quantile. For the case of the quantile 50th the obtained loss is symmetric in both sides of [-1,0] and [0,1] so the errors comming from the predictions of both sides of the true value (overpredictting and underpredictting) are penalized equally. \n",
    "\n",
    "More positive errors are penalized more for higher quantiles and more negative errors are penalized more for lower quantiles. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian interpretation of the quantile loss function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the 'On-the-fly' technique is implemented the mean squared error function for optimizing model paremeters. As we have seen with this technique, this formulation **assumes a gaussian error distribution**. The mode of this distribution (the peak) corresponds to the mean parameter and the variance of the distribution with rmse.\n",
    "\n",
    "In the case of the quantile loss, if we take the negative of the individual loss and exponentiate it, we get the distribution know as the [*Asymmetric Laplace distribution*](https://en.wikipedia.org/wiki/Asymmetric_Laplace_distribution)\n",
    "\n",
    "**Thus, here we are assuming that individual quantiles estimation follows an ALD distribution**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusions\n",
    "\n",
    "Goals achieved in this notebook:\n",
    "  * Gain an intuitive idea of the theory and limitations behind the quantile loss function. \n",
    "  * Bayesian interpretation of the quantile loss function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [Reference post](https://medium.com/analytics-vidhya/prediction-intervals-in-forecasting-quantile-loss-function-18f72501586f) explaning the loss function in forecasting problems\n",
    "* [Reference post](https://www.kdnuggets.com/2018/07/deep-quantile-regression.html) explaning the relationship of the quantile loss function and ALD distirbution"
   ]
  }
 ],
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