{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantized Discrete Parameter Sampling in AzureML HyperDrive\n",
    "> Some examples of the parameter expressions that start with \"q\" when specifying the hyperparameter search space  \n",
    "- toc: true \n",
    "- badges: true\n",
    "- comments: true\n",
    "- categories: [azureml, hyperdrive, parameter expression, qnormal, quniform]\n",
    "- hide: false"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## HyperDrive\n",
    "\n",
    "\n",
    "![hyperdrive](https://raw.githubusercontent.com/pawarbi/blog/master/images/hyperdrive.JPG)\n",
    "\n",
    "Azure ML offers an automated hyperparameter tuning capability at scale using its 'HyperDrive' package. The key word here is 'at scale'. It works similar to Scikit-Learn's [hyperparameter tuning](https://scikit-learn.org/stable/modules/grid_search.html) but HyperDrive can be run on remote compute clusters with multiple nodes to obtain the optimized parameters faster. If your model pipeline has multiple models with different preprocessing steps, you will ikely end up with thousands of parameter combinations. This can take significant amount of time depending on your model pipeline architecture. With HyperDrive, you can submit the run to a managed remote cluster to run all the experiments and obtain the tuned parameters. Depending on the sampling method used, these runs can also be parallelized to run several experiments concurrently.\n",
    "\n",
    "You can follow [this example notebook](https://github.com/Azure/MachineLearningNotebooks/blob/master/how-to-use-azureml/ml-frameworks/scikit-learn/train-hyperparameter-tune-deploy-with-sklearn/train-hyperparameter-tune-deploy-with-sklearn.ipynb) to learn more about how to setup the HyperDrive experiment. I will share my more complex example hopefully in the next couple of blogs.\n",
    "\n",
    "## Parameter Search Space\n",
    "\n",
    "The parameter search space can be defined using discrete or continuous distributions.\n",
    "\n",
    "Discrete parameters are integers or strings (e.g. 1, 50, 'liblinear' etc.), while continuous are floats (e.g. 1.2,0.5). You can read more about it [here on MS Docs](https://docs.microsoft.com/en-us/azure/machine-learning/how-to-tune-hyperparameters). One of the ways you can define the discrete hyperparameters is by using the quantized continuous distributions. These are the parameter expressions that start with 'q', e.g. `quniform()`,`qloguniform()`, `qnormal()` and `qlognormal()`. Note that the 'q' parameters cannot be used for with `GridParameterSampling()` and `BayesianParameterSampling()` only supports `quniform()`.\n",
    "\n",
    "Microsoft documentation doesn't give examples of the search space these 'q' parameters create, so I thought I would provide some examples. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. quniform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`quniform(low, high, q)` creates uniform distriution between low and high values, separated by spacing q. For example, to create a discrete distribution of values between (10,30) that are 2 values values apart you would define : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'param': ['quniform', [10, 30, 2]]}"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from azureml.train.hyperdrive import normal, uniform, choice, quniform, qloguniform, qnormal, qlognormal\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "\n",
    "{\n",
    "    \n",
    "    \"param\" : quniform(10, 30, 2)\n",
    "    \n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is what the search space will look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12., 18., 22., 28.])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#with q = 2\n",
    "param = np.sort(np.unique((np.round(np.random.uniform(low = 10, high = 30, size=10)/2)*2)))\n",
    "\n",
    "param"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[12. 15. 18. 24. 27. 30.]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#with q = 3\n",
    "param = np.sort(np.unique(np.round(np.random.uniform(low = 10, high = 30, size=10)/3)*3))\n",
    "\n",
    "print(param)\n",
    "sns.histplot(param, kde=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see above, qith `q=2` the values are spaced apart by 2 values and with `q=3`, the values are 3 units apart. Note that the values are randomly distributed so you may not see all the values between the specified `low` and `high`. You could specify the same search space by using `choice(12, 15, 17,27)`. But if the search space is large, it's easier to use the quantized version. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. qloguniform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Defined as :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'param': ['qloguniform', [0.01, 5, 3]]}"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{\n",
    "    \n",
    "    \"param\" : qloguniform(0.01, 5, 3)\n",
    "    \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.   2.   3.   4.   5.   7.   9.  10.  11.  17.  18.  19.  37.  47.\n",
      "  50.  57.  59. 102. 141.]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Count'>"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#with q = 3\n",
    "param = np.sort(np.unique(np.round(np.exp(np.random.uniform(0.01,5,30)))/3)*3)\n",
    "\n",
    "print(param)\n",
    "sns.histplot(param, kde=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.qnormal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Values are normally distributed with specified mean and standard deviation. \n",
    "Defined as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'param': ['qnormal', [300, 50, 5]]}"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{\n",
    "    \n",
    "    \"param\" : qnormal(300,50, 5)\n",
    "    \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[196. 199. 200. 236. 241. 255. 257. 258. 260. 261. 274. 277. 278. 280.\n",
      " 284. 285. 286. 287. 291. 296. 298. 300. 302. 303. 305. 306. 307. 310.\n",
      " 312. 314. 317. 319. 323. 324. 331. 338. 341. 345. 350. 372. 395.]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Count'>"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#with mean = 300, std = 50, q = 5\n",
    "param = np.sort(np.unique(np.round((np.random.normal(300,50,50)))/5)*5)\n",
    "\n",
    "print(param)\n",
    "\n",
    "\n",
    "sns.histplot(param, kde=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This would be a good choice for, say `n_estimators()` in tree-based algorithms. You can always adjust the q parameter to define how close the values can be."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4. qlognormal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Values are lognormally distributed with the specified mean and standard deviation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'param': ['qlognormal', [10, 2, 2]]}"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{\n",
    "    \n",
    "    \"param\" : qlognormal(10,0.5, 2)\n",
    "    \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 7426.  9054.  9668. 10800. 10816. 10886. 12758. 14232. 14346. 14838.\n",
      " 15376. 17612. 18320. 19152. 20512. 22676. 25370. 26078. 26398. 32758.\n",
      " 37050. 41412. 43732. 54636. 58332.]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#with mean = 300, std = 50, q = 2\n",
    "param = np.sort(np.unique(np.round(np.exp(np.random.normal(10,0.5,25))/2)*2))\n",
    "\n",
    "print(param)\n",
    "\n",
    "sns.histplot(param, kde=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This would be helpful for creating non-uniform distributin of the parameters that are right-skewed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. https://docs.microsoft.com/en-us/azure/machine-learning/how-to-tune-hyperparameters\n",
    "2. https://docs.microsoft.com/en-us/python/api/azureml-train-core/azureml.train.hyperdrive.parameter_expressions?view=azure-ml-py#azureml_train_hyperdrive_parameter_expressions_uniform\n",
    "\n",
    "3. https://docs.microsoft.com/en-us/python/api/azureml-train-core/azureml.train.hyperdrive.bayesianparametersampling?preserve-view=true&view=azure-ml-py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}