Bayesian Optimization with Hyperopt.ipynb

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    "## Bayesian Optimization using Hyperopt\n",
    "\n",
    "#### This notebook is about the basics of [Bayesian Model-Based Optimization](https://sigopt.com/static/pdf/SigOpt_Bayesian_Optimization_Primer.pdf) using [Hyperopt](https://jaberg.github.io/hyperopt/) to find the minimum of a function. \n",
    "After we are familiar with the basic concepts, we can use these methods to solve [hyperparamter optimization](https://en.wikipedia.org/wiki/Hyperparameter_optimization) of machine learning models. "
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    "## Introduction to Bayesian Model-Based Optimization\n",
    "\n",
    "There are four parts to an optimization problem:\n",
    "\n",
    "1. Objective function: what we want to minimize\n",
    "2. Domain space: values of the parameters over which to minimize the objective\n",
    "3. Hyperparameter optimization function: constructs the surrogate function and chooses next values to evaluate\n",
    "4. Trials: score, parameter pairs recorded each time we evaluate the objective function\n",
    "\n",
    "Evaluating the objective function is the expensive part of optimization, so ideally we want to limit calls to this function. One way we can limit calls is by choosing the next values to try in the objective function based on the past results. \n",
    "Bayesian optimization differs from random or grid search by doing exactly this: rather than just selecting from a grid __uninformed__ by past objective function evaluations, Bayesian methods take into account the previous results to try more promising values. They work by constructing a probability model of the objective function (called a surrogate function) $p(\\text{score} | \\text{parameters})$ which is much easier to optimize than the actual objective function. \n",
    "\n",
    "After each evaluation of the objective function, the algorithm updates the probability model (usually given as $p(y | x)$) incorporating the new results. [Sequential Model-Based Optimization (SMBO) methods are a formalization of Bayesian optimization](https://papers.nips.cc/paper/4443-algorithms-for-hyper-parameter-optimization.pdf) that update the probability model sequentially: every evaluation of the objective function with a set of values updates the model with the idea that eventually the model will come to represent the true objective function. This is an application of Bayesian Reasoning. The algorithm forms an initial idea of the objective function and updates it with each new piece of evidence.\n",
    "\n",
    "The next values to try in the objective function are selected by the algorithm optmizing the probability model (surrogate function) usually with a criteria known as Expected Improvement. Finding the values that will yield the greatest expected improvement in the surrogate function is much cheaper than evaluating the objective function itself. By choosing the next values based on a model rather than randomly, the hope is that the algorithm with converge to the true best values much quicker. The overall goal is to evaluate the objective function fewer times by spending a little more time choosing the next values.\n",
    "\n",
    "<span style=\"color:green\">=======================================================================================================================\n",
    "\n",
    "<span style=\"color:green\"> <b>It has been argued that Bayesian Optimization (and SMBO methods in general):\n",
    "\n",
    "<span style=\"color:green\"> 1. Converge to a lower score of the objective function than random search\n",
    "    \n",
    "<span style=\"color:green\"> 2. Require far less time to find the optimum of the objective function\n",
    "\n",
    "<span style=\"color:green\">So, one would get both faster optimization and a better result. These are both two desirable outcomes especially when working with hyperparameter tuning of machine learning models! \n",
    "\n",
    "<span style=\"color:green\">In this notebook I am trying to verify this claim!</span></b>\n",
    "\n",
    "<span style=\"color:green\">=======================================================================================================================\n",
    "    \n",
    "    \n",
    "\n",
    "### Sequential Model Based Optimization using the Tree Parzen Estimator\n",
    "\n",
    "SMBO methods differ in part 3, the algorithm used to construct the probability model (also called the Surrogate Function). Several options are for the surrogate function are:\n",
    "\n",
    "* Gaussian Processes\n",
    "* Tree-structured Parzen Estimator\n",
    "* Random Forest Regression\n",
    "\n",
    "\n",
    "## Hyperopt\n",
    "\n",
    "Hyperopt is an open-source Python library for Bayesian optimization that implements SMBO using the Tree-structured Parzen Estimator. There are other open-source libraries which use a Gaussian Process or a Random Forest regression for the surrogate function (probability model). \n",
    "\n",
    "In this notebook, both random search (Hyperopt has a method for this) as well as the Tree Parzen Estimator are implemented. This is just a simple example which would allow us to learn the basics.\n",
    "\n",
    "#### Resources\n",
    "\n",
    "For more details on Bayesian Model Based Optimization, here are some good articles:\n",
    "\n",
    "* Algorithms for Hyper-Parameter Optimization [Link](https://papers.nips.cc/paper/4443-algorithms-for-hyper-parameter-optimization.pdf)\n",
    "* Making a Science of Model Search: Hyperparameter Optimization in Hundreds of Dimensions for Vision Architectures [Link](http://proceedings.mlr.press/v28/bergstra13.pdf)\n",
    "* Bayesian Optimization Primer [Link](https://sigopt.com/static/pdf/SigOpt_Bayesian_Optimization_Primer.pdf)\n",
    "* Taking the Human Out of the Loop: A Review of Bayesian Optimization [Link](https://www.cs.ox.ac.uk/people/nando.defreitas/publications/BayesOptLoop.pdf)\n",
    "* Hyperparameter Optimization-a short review (https://medium.com/criteo-labs/hyper-parameter-optimization-algorithms-2fe447525903)"
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    "# Good old pandas and numpy\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# Unfortunately I'm still using matplotlib for graphs\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
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    "## Objective Function\n",
    "\n",
    "\n",
    "For the objective function, a simple polynomial function is used with the goal being to find the minimum value. This function has one global minimum over the range we define it as well as one local minimum.\n",
    "\n",
    "When we define the objective function, we must make sure it returns a single real-value number to _minimize_. If we use a metric such as accuracy, then we would have to return the _negative_ of accuracy to tell our model to find a better accuracy! "
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   "source": [
    "def objective(x):\n",
    "    \"\"\"Objective function to minimize\"\"\"\n",
    "    \n",
    "    # Create the polynomial object\n",
    "    f = np.poly1d([1, -2, -28, 28, 12, -26, 100])\n",
    "\n",
    "    # Return the value of the polynomial\n",
    "    return f(x) * 0.05"
   ]
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum of -219.8012 occurs at 4.8779\n"
     ]
    },
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Space over which to evluate the function is -5 to 6\n",
    "x = np.linspace(-5, 6, 10000)\n",
    "y = objective(x)\n",
    "\n",
    "miny = min(y)\n",
    "minx = x[np.argmin(y)]\n",
    "\n",
    "# Visualize the function\n",
    "plt.figure(figsize = (8, 6))\n",
    "plt.style.use('fivethirtyeight')\n",
    "plt.title('Objective Function'); plt.xlabel('x'); plt.ylabel('f(x)')\n",
    "plt.vlines(minx, min(y)- 50, max(y), linestyles = '--', colors = 'r')\n",
    "plt.plot(x, y);\n",
    "\n",
    "# Print out the minimum of the function and value\n",
    "print('Minimum of %0.4f occurs at %0.4f' % (miny, minx))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "# Domain\n",
    "\n",
    "The domain is the values of x over which we evaluate the function. First we can use a uniform distribution over the space our function is defined."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "from hyperopt import hp\n",
    "\n",
    "# Create the domain space\n",
    "space = hp.uniform('x', -5, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "We can draw samples from the space using a Hyperopt utility. This is useful for visualizing a distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from hyperopt.pyll.stochastic import sample\n",
    "\n",
    "\n",
    "samples = []\n",
    "\n",
    "# Sample 10000 values from the range\n",
    "for _ in range(10000):\n",
    "    samples.append(sample(space))\n",
    "    \n",
    "\n",
    "# Histogram of the values\n",
    "plt.hist(samples, bins = 20, edgecolor = 'black'); \n",
    "plt.xlabel('x'); plt.ylabel('Frequency'); plt.title('Domain Space');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "When running, our algorithm will sample values from this distribution, initially at random as it explores the domain space, but then over time, it will \"focus\" on the most promising values. Therefore, the algorithm should more values around 4.9, the minimum of the function. We can compare this to random search which should try values evenly from the entire distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "# Hyperparameter Optimization Algorithm\n",
    "\n",
    "There are two choices for a hyperparameter optimization algorithm in Hyperopt: random and Tree Parzen Estimator. We can use both and compare the results. Using the `suggest` algorithm in these families automatically configures the algorithm for us. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "from hyperopt import rand, tpe\n",
    "\n",
    "# Create the algorithms\n",
    "tpe_algo = tpe.suggest\n",
    "rand_algo = rand.suggest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "# Trials\n",
    "\n",
    "Storing the history can be done by using a `Trials` object that we pass into the function call. This is not strictly necessary, but it gives us information that we can use to understand what the algorithm is doing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "from hyperopt import Trials\n",
    "\n",
    "# Create two trials objects\n",
    "tpe_trials = Trials()\n",
    "rand_trials = Trials()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "# Run the Optimization\n",
    "\n",
    "\n",
    "The `fmin` function implements the actual optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100%|████████████████████| 500/500 [00:02<00:00, 179.94it/s, best loss: -219.80120399695434]\n",
      "{'x': 4.878123889530553}\n",
      "100%|████████████████████| 500/500 [00:00<00:00, 987.40it/s, best loss: -219.80120237695547]\n"
     ]
    }
   ],
   "source": [
    "from hyperopt import fmin\n",
    "\n",
    "# Run 2000 evals with the tpe algorithm\n",
    "tpe_best = fmin(fn=objective, space=space, algo=tpe_algo, trials=tpe_trials, \n",
    "                max_evals=1500, rstate= np.random.RandomState(50))\n",
    "\n",
    "print(tpe_best)\n",
    "\n",
    "# Run 2000 evals with the random algorithm\n",
    "rand_best = fmin(fn=objective, space=space, algo=rand_algo, trials=rand_trials, \n",
    "                 max_evals=1500, rstate= np.random.RandomState(50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum loss attained with TPE:    -219.8009\n",
      "Minimum loss attained with random: -219.8012\n",
      "Actual minimum of f(x):            -219.8012\n",
      "\n",
      "Number of trials needed to attain minimum with TPE:    161\n",
      "Number of trials needed to attain minimum with random: 235\n",
      "\n",
      "Best value of x from TPE:    4.8796\n",
      "Best value of x from random: 4.8776\n",
      "Actual best value of x:      4.8779\n"
     ]
    }
   ],
   "source": [
    "# Print out information about losses\n",
    "print('Minimum loss attained with TPE:    {:.4f}'.format(tpe_trials.best_trial['result']['loss']))\n",
    "print('Minimum loss attained with random: {:.4f}'.format(rand_trials.best_trial['result']['loss']))\n",
    "print('Actual minimum of f(x):            {:.4f}'.format(miny))\n",
    "\n",
    "# Print out information about number of trials\n",
    "print('\\nNumber of trials needed to attain minimum with TPE:    {}'.format(tpe_trials.best_trial['misc']['idxs']['x'][0]))\n",
    "print('Number of trials needed to attain minimum with random: {}'.format(rand_trials.best_trial['misc']['idxs']['x'][0]))\n",
    "\n",
    "# Print out information about value of x\n",
    "print('\\nBest value of x from TPE:    {:.4f}'.format(tpe_best['x']))\n",
    "print('Best value of x from random: {:.4f}'.format(rand_best['x']))\n",
    "print('Actual best value of x:      {:.4f}'.format(minx))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that TPE found the minimum in much less number of iterations. (After finding this minimum, we could probably have stopped running the algorith!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'state': 2,\n",
       " 'tid': 161,\n",
       " 'spec': None,\n",
       " 'result': {'loss': -219.80091884578985, 'status': 'ok'},\n",
       " 'misc': {'tid': 161,\n",
       "  'cmd': ('domain_attachment', 'FMinIter_Domain'),\n",
       "  'workdir': None,\n",
       "  'idxs': {'x': [161]},\n",
       "  'vals': {'x': [4.87961354557523]}},\n",
       " 'exp_key': None,\n",
       " 'owner': None,\n",
       " 'version': 0,\n",
       " 'book_time': datetime.datetime(2020, 1, 3, 21, 15, 55, 204000),\n",
       " 'refresh_time': datetime.datetime(2020, 1, 3, 21, 15, 55, 204000)}"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tpe_trials.best_trial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       " {'loss': -74.90909381113913, 'status': 'ok'},\n",
       " {'loss': -217.12718113366174, 'status': 'ok'},\n",
       " {'loss': -219.75078530825414, 'status': 'ok'},\n",
       " {'loss': -219.5020102608001, 'status': 'ok'},\n",
       " {'loss': -20.680026567522784, 'status': 'ok'},\n",
       " {'loss': -138.6878612022831, 'status': 'ok'},\n",
       " {'loss': -20.579777438518793, 'status': 'ok'},\n",
       " {'loss': -207.02030704357523, 'status': 'ok'},\n",
       " {'loss': 5.161423679293265, 'status': 'ok'},\n",
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       " {'loss': 51.68301846280438, 'status': 'ok'},\n",
       " {'loss': -188.11427932387846, 'status': 'ok'},\n",
       " {'loss': -217.6198588755022, 'status': 'ok'},\n",
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       " {'loss': -173.9686344098449, 'status': 'ok'},\n",
       " {'loss': -216.66551268741793, 'status': 'ok'},\n",
       " {'loss': -200.308407092077, 'status': 'ok'},\n",
       " {'loss': -124.96664183789728, 'status': 'ok'},\n",
       " {'loss': -133.24760180206314, 'status': 'ok'},\n",
       " {'loss': -218.7866912279256, 'status': 'ok'},\n",
       " {'loss': -194.96557363880382, 'status': 'ok'},\n",
       " {'loss': -13.350660192763208, 'status': 'ok'},\n",
       " {'loss': -32.79927452271819, 'status': 'ok'},\n",
       " {'loss': -210.70294176960635, 'status': 'ok'},\n",
       " {'loss': -88.49459375843153, 'status': 'ok'},\n",
       " {'loss': -161.82622342511968, 'status': 'ok'},\n",
       " {'loss': 4.002255202813365, 'status': 'ok'},\n",
       " {'loss': -214.79747060459897, 'status': 'ok'},\n",
       " {'loss': 52.2176672938167, 'status': 'ok'},\n",
       " {'loss': 4.62191343853469, 'status': 'ok'},\n",
       " {'loss': -112.0355662156279, 'status': 'ok'},\n",
       " {'loss': -199.75625330552245, 'status': 'ok'},\n",
       " {'loss': -121.54127043476109, 'status': 'ok'},\n",
       " {'loss': -204.97658154240312, 'status': 'ok'},\n",
       " {'loss': -219.19786198844884, 'status': 'ok'},\n",
       " {'loss': -176.80130688392202, 'status': 'ok'},\n",
       " ...]"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tpe_trials.results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "#### Comparing the runtime\n",
    "Let's see if there is any difference in time between the two methods. We can use the built in Jupyter magic command for timing (running the function 3 times)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100%|████████████████████| 200/200 [00:00<00:00, 626.63it/s, best loss: -219.80119510864662]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 644.02it/s, best loss: -219.77922879440348]\n",
      "100%|█████████████████████| 200/200 [00:00<00:00, 673.10it/s, best loss: -219.7965648294202]\n",
      "100%|█████████████████████| 200/200 [00:00<00:00, 667.39it/s, best loss: -219.7878676074405]\n",
      "100%|█████████████████████| 200/200 [00:00<00:00, 670.72it/s, best loss: -219.7812865952979]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 673.44it/s, best loss: -219.79784190572974]\n",
      "100%|█████████████████████| 200/200 [00:00<00:00, 672.30it/s, best loss: -219.8005832793272]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 674.16it/s, best loss: -219.77351523047992]\n",
      "100%|█████████████████████| 200/200 [00:00<00:00, 672.84it/s, best loss: -219.7971612672311]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 660.95it/s, best loss: -219.79055607937664]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 675.45it/s, best loss: -219.80082453589745]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 672.69it/s, best loss: -219.80102353832322]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 671.16it/s, best loss: -219.80108917837003]\n",
      "100%|█████████████████████| 200/200 [00:00<00:00, 679.04it/s, best loss: -219.7882355834006]\n",
      "100%|█████████████████████| 200/200 [00:00<00:00, 668.82it/s, best loss: -219.8011540734563]\n",
      "100%|█████████████████████| 200/200 [00:00<00:00, 673.26it/s, best loss: -219.8008204117683]\n",
      "100%|█████████████████████| 200/200 [00:00<00:00, 671.17it/s, best loss: -219.8011536484438]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 670.11it/s, best loss: -219.79149980731654]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 669.06it/s, best loss: -219.79964999747173]\n",
      "100%|█████████████████████| 200/200 [00:00<00:00, 674.56it/s, best loss: -219.8010925104688]\n",
      "100%|█████████████████████| 200/200 [00:00<00:00, 678.16it/s, best loss: -219.8012021933123]\n",
      "304 ms ± 4.94 ms per loop (mean ± std. dev. of 7 runs, 3 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit -n 3\n",
    "# Run 2000 evals with the tpe algorithm\n",
    "best = fmin(fn=objective, space=space, algo=tpe_algo, max_evals=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100%|███████████████████| 200/200 [00:00<00:00, 2653.09it/s, best loss: -219.44628524260153]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2939.09it/s, best loss: -219.24051657674764]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2851.92it/s, best loss: -219.71229467594358]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2958.83it/s, best loss: -219.80079647596054]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 2825.27it/s, best loss: -219.7889504951636]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2960.20it/s, best loss: -219.78622773689915]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 3093.32it/s, best loss: -219.7826295341539]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2954.81it/s, best loss: -219.76753782465045]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2894.95it/s, best loss: -219.77964996105698]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 3008.06it/s, best loss: -219.47949038500525]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2855.88it/s, best loss: -219.75246372796465]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 2910.87it/s, best loss: -219.6367530872941]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2899.59it/s, best loss: -219.71375348308817]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 2954.01it/s, best loss: -219.6939865225582]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2961.03it/s, best loss: -219.68501842694778]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2805.98it/s, best loss: -219.79632456530786]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2844.70it/s, best loss: -219.78253290795638]\n",
      "100%|████████████████████| 200/200 [00:00<00:00, 2762.64it/s, best loss: -219.7819817651158]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2819.52it/s, best loss: -219.34649672325224]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2977.02it/s, best loss: -219.37976900872383]\n",
      "100%|███████████████████| 200/200 [00:00<00:00, 2825.19it/s, best loss: -219.51307990653027]\n",
      "73.8 ms ± 1.54 ms per loop (mean ± std. dev. of 7 runs, 3 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit -n 3\n",
    "\n",
    "# Run 2000 evals with the random algorithm\n",
    "best = fmin(fn=objective, space=space, algo=rand_algo, max_evals=200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "As a point of interest, the random algorithm ran much faster than the tpe algorithm. This shows that the TPE method is taking more time to propose the next set of parameters while the random method is just choosing from the space randomly. But perhaps we could say that the extra time to choose the next parmaeters is made up for by choosing better parameters that should let us make fewer overall calls to the objective function (which is the most expensive part of optimization). Here we ran the same number of totals calls, but this was probably not necessary because the Tree Parzen Estimator will converge on the optimum quickly without the need for more iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "# Results\n",
    "\n",
    "We see that both models returned optimal or nearly optimal values. We can investigate ow they differ in the search procedure by making use of the trials objects. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false,
    "scrolled": true
   },
   "outputs": [
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   "source": [
    "tpe_results = pd.DataFrame({'loss': [x['loss'] for x in tpe_trials.results], 'iteration': tpe_trials.idxs_vals[0]['x'],\n",
    "                            'x': tpe_trials.idxs_vals[1]['x']})\n",
    "                            \n",
    "tpe_results.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
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   "source": [
    "### Plotting the values that were evaluated over time. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
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     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "tpe_results['rolling_average_x'] = tpe_results['x'].rolling(10).mean().fillna(method = 'bfill')\n",
    "tpe_results['rolling_average_loss'] = tpe_results['loss'].rolling(10).mean().fillna(method = 'bfill')\n",
    "tpe_results.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
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    "hidePrompt": false,
    "scrolled": true
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   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10, 8))\n",
    "plt.plot(tpe_results['iteration'], tpe_results['x'],  'bo', alpha = 0.5);\n",
    "plt.xlabel('Iteration', size = 22); plt.ylabel('x value', size = 22); plt.title('TPE Sequence of Values', size = 24);\n",
    "plt.hlines(minx, 0, tpe_results.shape[0], linestyles = '--', colors = 'r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "We can see that over time, the algorithm tended to try values closer to 4.9. The local minimum around -4 likely threw off the algorithm initially, but the points tend to cluster around the actual minimum as the algorithm progresses. \n",
    "\n",
    "We can also plot the histogram to see the distribution of values tried."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (8, 6))\n",
    "plt.hist(tpe_results['x'], bins = 50, edgecolor = 'k');\n",
    "plt.title('Histogram of TPE Values'); plt.xlabel('Value of x'); plt.ylabel('Count');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "Sure enough, the algorithm tried many values closer to 4.9 that anywhere else! This clearly shows the benefits of choosing the next values based on the past values: more evaluations of promising values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Loss of -219.8009 occured at iteration 161\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sort with best loss first\n",
    "tpe_results = tpe_results.sort_values('loss', ascending = True).reset_index()\n",
    "\n",
    "plt.plot(tpe_results['iteration'], tpe_results['loss'], 'bo', alpha = 0.3);\n",
    "plt.xlabel('iteration'); plt.ylabel('loss'); plt.title('TPE Sequence of Losses');\n",
    "\n",
    "print('Best Loss of {:.4f} occured at iteration {}'.format(tpe_results['loss'][0], tpe_results['iteration'][0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "### Random Results\n",
    "\n",
    "We should contrast the TPE results with those from random search. Here we do not expect to see any trend in values evaluated over time because the values are selected randomly. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>loss</th>\n",
       "      <th>iteration</th>\n",
       "      <th>x</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>36.210073</td>\n",
       "      <td>0</td>\n",
       "      <td>5.957885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-202.384052</td>\n",
       "      <td>1</td>\n",
       "      <td>4.470885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-75.519449</td>\n",
       "      <td>2</td>\n",
       "      <td>3.218963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.543552</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.515859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>35.078011</td>\n",
       "      <td>4</td>\n",
       "      <td>-4.916832</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         loss  iteration         x\n",
       "0   36.210073          0  5.957885\n",
       "1 -202.384052          1  4.470885\n",
       "2  -75.519449          2  3.218963\n",
       "3    5.543552          3 -0.515859\n",
       "4   35.078011          4 -4.916832"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand_results = pd.DataFrame({'loss': [x['loss'] for x in rand_trials.results], 'iteration': rand_trials.idxs_vals[0]['x'],\n",
    "                            'x': rand_trials.idxs_vals[1]['x']})\n",
    "                            \n",
    "rand_results.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10, 8))\n",
    "plt.plot(rand_results['iteration'], rand_results['x'],  'bo', alpha = 0.5);\n",
    "plt.xlabel('Iteration', size = 22); plt.ylabel('x value', size = 22); plt.title('Random Sequence of Values', size = 24);\n",
    "plt.hlines(minx, 0, 2000, linestyles = '--', colors = 'r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "Clearly, the random algorithm is just \"randomly\" choosing the next set of values to try! There is no logical order here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Loss of -219.8012 occured at iteration 735\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sort with best loss first\n",
    "rand_results = rand_results.sort_values('loss', ascending = True).reset_index()\n",
    "\n",
    "plt.figure(figsize = (8, 6))\n",
    "plt.hist(rand_results['x'], bins = 50, edgecolor = 'k');\n",
    "plt.title('Histogram of Random Values'); plt.xlabel('Value of x'); plt.ylabel('Count');\n",
    "\n",
    "# Print information\n",
    "print('Best Loss of {:.4f} occured at iteration {}'.format(rand_results['loss'][0], rand_results['iteration'][0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "Again, there is no discernable clustering because this method is choosing the next values randomly. In this case, it happended across the minimum of the function because it was a relatively simple problem and we used many iterations. This would not likely be the case when we are optimizing more complex functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "# Some upgrades!\n",
    "\n",
    "We will make two upgrades:\n",
    "\n",
    "* Smarter domain space over which to search\n",
    "* Return more useful information from the objective function\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "### Better Domain Space\n",
    "\n",
    "In this problem, we can cheat because we know where the minimum is and therefore can define a region of higher probability around this value of x. In more complicated problems, we don't have a graph to show us the minimum, but we can probably use experience and domain knowledge to inform our choice of a domain space. \n",
    "\n",
    "Here we will make a normally distributed domain space around the value where the minimum of the objective function occurs, around 4.9. This is simple to do in Hyperopt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "# Normally distributed space\n",
    "space = hp.normal('x', 4.9, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples = []\n",
    "\n",
    "# Sample 10000 values from the range\n",
    "for _ in range(10000):\n",
    "    samples.append(sample(space))\n",
    "    \n",
    "\n",
    "# Histogram of the values\n",
    "plt.hist(samples, bins = 20, edgecolor = 'black'); \n",
    "plt.xlabel('x'); plt.ylabel('Frequency'); plt.title('Domain Space');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "Much closer to the true value! This could help both the random search and the TPE find the minimum quicker (for random search it would help because we are concentrating the possible values around the optimum)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "## More Useful Trials Object\n",
    "\n",
    "Another modification to make is to return more useful information from the objective function. We do this using a dictionary with any information we want included. The only requirements are that the dictionary must contain a single real-valued metric to minimize stored under a `\"loss\"` key and whether the function sucessfully ran, stored under a `\"status\"` key. Here we make the modifications to the objective to store the value of x as well as the time to evaluate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "from hyperopt import STATUS_OK\n",
    "from timeit import default_timer as timer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "def objective(x):\n",
    "    \"\"\"Objective function to minimize with smarter return values\"\"\"\n",
    "    \n",
    "    # Create the polynomial object\n",
    "    f = np.poly1d([1, -2, -28, 28, 12, -26, 100])\n",
    "\n",
    "    # Evaluate the function\n",
    "    start = timer()\n",
    "    loss = f(x) * 0.05\n",
    "    end = timer()\n",
    "    \n",
    "    # Calculate time to evaluate\n",
    "    time_elapsed = end - start\n",
    "    \n",
    "    results = {'loss': loss, 'status': STATUS_OK, 'x': x, 'time': time_elapsed}\n",
    "    \n",
    "    # Return dictionary\n",
    "    return results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "We run the algorithm the same as before. We'll create a new `Trials` object to save new results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100%|██████████████████| 1000/1000 [00:02<00:00, 396.49it/s, best loss: -219.80120399695434]\n",
      "100%|█████████████████| 1000/1000 [00:00<00:00, 1765.13it/s, best loss: -219.80120237695547]\n"
     ]
    }
   ],
   "source": [
    "# New trials object\n",
    "tpe_trials = Trials()\n",
    "rand_trials = Trials()\n",
    "\n",
    "# Run 2000 evals with the tpe algorithm\n",
    "best_tpe = fmin(fn=objective, space=space, algo=tpe_algo, trials=tpe_trials, \n",
    "                max_evals=1000, rstate= np.random.RandomState(20))\n",
    "\n",
    "best_random = fmin(fn=objective, space=space, algo=rand_algo, trials=rand_trials, \n",
    "                max_evals=1000, rstate= np.random.RandomState(20))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "This time our trials object will have all of our information in the `results` attribute. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'loss': -206.64173845639232,\n",
       "  'status': 'ok',\n",
       "  'x': 4.529591650773245,\n",
       "  'time': 4.153400004724972e-05},\n",
       " {'loss': -187.12552636817037,\n",
       "  'status': 'ok',\n",
       "  'x': 5.326534118359849,\n",
       "  'time': 1.8123999780073063e-05}]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = tpe_trials.results\n",
    "results[:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "This time we have more information from the results. We can extract the results into a dataframe for inspect and plotting if we like. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>loss</th>\n",
       "      <th>x</th>\n",
       "      <th>iteration</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>882</th>\n",
       "      <td>0.000015</td>\n",
       "      <td>-219.801204</td>\n",
       "      <td>4.878124</td>\n",
       "      <td>882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>579</th>\n",
       "      <td>0.000025</td>\n",
       "      <td>-219.801204</td>\n",
       "      <td>4.878183</td>\n",
       "      <td>579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>520</th>\n",
       "      <td>0.000015</td>\n",
       "      <td>-219.801202</td>\n",
       "      <td>4.878260</td>\n",
       "      <td>520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>401</th>\n",
       "      <td>0.000015</td>\n",
       "      <td>-219.801201</td>\n",
       "      <td>4.878285</td>\n",
       "      <td>401</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>772</th>\n",
       "      <td>0.000016</td>\n",
       "      <td>-219.801197</td>\n",
       "      <td>4.878359</td>\n",
       "      <td>772</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         time        loss         x  iteration\n",
       "882  0.000015 -219.801204  4.878124        882\n",
       "579  0.000025 -219.801204  4.878183        579\n",
       "520  0.000015 -219.801202  4.878260        520\n",
       "401  0.000015 -219.801201  4.878285        401\n",
       "772  0.000016 -219.801197  4.878359        772"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Results into a dataframe\n",
    "results_df = pd.DataFrame({'time': [x['time'] for x in results], \n",
    "                           'loss': [x['loss'] for x in results],\n",
    "                           'x': [x['x'] for x in results],\n",
    "                            'iteration': list(range(len(results)))})\n",
    "\n",
    "# Sort with lowest loss on top\n",
    "results_df = results_df.sort_values('loss', ascending = True)\n",
    "results_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "This was a simple optimization problem, so the lowest score obtained does not really differ from that with the uniform distribution. It took around the same number of iterations to converge. We can compare the distribution though to see if better values were tried."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(results_df['x'], bins = 50, edgecolor = 'k');\n",
    "plt.title('Histogram of TPE Values'); plt.xlabel('Value of x'); plt.ylabel('Count');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "Indeed the values of x evaluated cluster much closer to the optimum! The algorithm spend much more time around the best value than searching the domain space. We can compare this distribution to that attained with the TPE algorithm on the uniform domain using a Kernel Density Estimate Plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(results_df['x'], label = 'Normal Domain')\n",
    "sns.kdeplot(tpe_results['x'], label = 'Uniform Domain')\n",
    "plt.legend(); plt.xlabel('Value of x'); plt.ylabel('Density'); plt.title('Comparison of Domain Choice using TPE');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lowest Value of the Objective Function = -219.8012 at x = 4.8781 found in 882 iterations.\n"
     ]
    }
   ],
   "source": [
    "print('Lowest Value of the Objective Function = {:.4f} at x = {:.4f} found in {:.0f} iterations.'.format(results_df['loss'].min(),\n",
    "                                                                             results_df.loc[results_df['loss'].idxmin()]['x'],\n",
    "                                                                             results_df.loc[results_df['loss'].idxmin()]['iteration']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "Well that definitely shows the value of choosing a good prior! When it comes to hyperparameter tuning, we often do not know ahead of time what values to concentrate around but we can try to use past experience or the work of others to inform our search spaces. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### One-Line Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████| 2000/2000 [00:09<00:00, 218.92it/s, best loss: -219.80120388782132]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'x': 4.8781018775165474}"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Just because you can do it in one line doesn't mean you should! \n",
    "best = fmin(fn = lambda x: np.poly1d([1, -2, -28, 28, 12, -26, 100])(x) * 0.05,\n",
    "            space = hp.normal('x', 4.9, 0.5), algo=tpe.suggest, \n",
    "            max_evals = 2000)\n",
    "\n",
    "best"
   ]
  },
  {
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   "source": [
    "# Conclusions\n",
    "\n",
    "This notebook showed a the basic implementation of Bayesian Model-Based optimization using Hyperopt. We can see some of the advantages of Bayesian Optimization over Random (or grid) search. \n",
    "\n",
    "The differences between random search and and Sequential Model-Based Optimization is clear: random search is _uninformed_ and therefore requires more trials to minimize the objective function. The Tree Parzen Estimator, an algorithm used for SMBO, spends more time choosing the next values, but overall requires fewer evaluations of the objective function because it is able to _reason_ about the next values to evaluate. Over many iterations, SMBO algorithms concentrate the search around the most promising values.\n"
   ]
  }
 ],
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