{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Nonlinear regression for inverse dynamics\n",
    "\n",
    "In this question, we fit a model which can predict what torques a robot needs to apply in order to make its arm reach a desired point in space. The data was collected from a SARCOS robot arm with $7$ degrees of freedom. The input vector $x \\in \\mathbb{R}^{21}$ encodes the desired position, velocity and accelaration of the $7$ joints. The output vector $y \\in \\mathbb{R}^7$ encodes the torques that should be applied to the joints to reach that point. The mapping from $x$ to $y$ is highly nonlinear.\n",
    "\n",
    "We can find the data at [http://www.gaussianprocess.org/gpml/data/](http://www.gaussianprocess.org/gpml/data/). Obviously the first step is to read this data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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       "      <td>-11.415526</td>\n",
       "      <td>37.354858</td>\n",
       "      <td>-20.809343</td>\n",
       "      <td>12.379975</td>\n",
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       "      <td>-1.700880</td>\n",
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       "      <td>-5.772058</td>\n",
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       "      <td>-2.143370</td>\n",
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       "         x1        x2        x3        x4        x5        x6        x7  \\\n",
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       "3  0.016273 -0.145307  0.029072  1.566855  0.307628  0.059027  0.080321   \n",
       "4  0.017279 -0.150051  0.031083  1.584416  0.314162  0.059027  0.058840   \n",
       "\n",
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       "3  0.053238 -0.460963  0.188013    ...     10.309203  0.921360  -5.772058   \n",
       "4  0.133810 -0.462264  0.263975    ...      2.868096  1.059957  -0.491542   \n",
       "\n",
       "          y1         y2         y3         y4        y5        y6        y7  \n",
       "0  50.292652 -36.971897  20.937170  47.821712 -0.424812 -0.907553  8.090739  \n",
       "1  44.104164 -28.851845  16.230194  43.194073 -0.228739 -1.235817  7.762475  \n",
       "2  37.354858 -20.809343  12.379975  39.386017  0.244491 -1.700880  7.289678  \n",
       "3  30.676065 -13.963816   7.702940  36.478813 -0.182062 -2.143370  6.410800  \n",
       "4  25.920128 -11.178479   5.643934  34.773911 -1.031687 -2.355776  5.792892  \n",
       "\n",
       "[5 rows x 28 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import time\n",
    "from util import read_all_sarcos_data, TARGET_COLUMN\n",
    "\n",
    "training_data, test_data = read_all_sarcos_data()\n",
    "training_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's standardize our data by making each column have mean $0$ and unit variance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression\n",
    "\n",
    "Now, the first order of business is to fit a standard linear regression. I'll just use the `sklearn` implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import preprocessing\n",
    "def standardize_data(data):\n",
    "    feature_column_names = [column_name for column_name in all_data.columns if 'x' in column_name]\n",
    "    features = data[feature_column_names]\n",
    "    # only care about the first output for this problem\n",
    "    target = data[TARGET_COLUMN]\n",
    "    X = features.as_matrix()\n",
    "    Y = target.as_matrix()\n",
    "    X_scaled = preprocessing.scale(X, axis = 0, with_mean = True, with_std = True, copy = True)\n",
    "    # only standardize inputs\n",
    "    # Y_scaled = preprocessing.scale(Y, axis = 0, with_mean = True, with_std = True, copy = True)\n",
    "    return X_scaled, Y\n",
    "# standardize together and separate\n",
    "all_data = pd.concat([training_data, test_data], axis = 0)\n",
    "standardize_data(all_data)\n",
    "X, Y = standardize_data(all_data)\n",
    "X_scaled, Y_scaled = X[:len(training_data)], Y[:len(training_data)]\n",
    "X_scaled_test, Y_scaled_test = X[len(training_data):], Y[len(training_data):]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/site-packages/scipy/linalg/basic.py:1018: RuntimeWarning: internal gelsd driver lwork query error, required iwork dimension not returned. This is likely the result of LAPACK bug 0038, fixed in LAPACK 3.2.2 (released July 21, 2010). Falling back to 'gelss' driver.\n",
      "  warnings.warn(mesg, RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.92494581827142286"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "## since data is already normalized\n",
    "linearRegressor = linear_model.LinearRegression(fit_intercept = True, normalize = False)\n",
    "linearRegressor.fit(X_scaled, Y_scaled)\n",
    "linearRegressor.score(X_scaled_test, Y_scaled_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the problem, we should be able to get a standardized mean squared error (SMSE) of 0.075. We define\n",
    "\n",
    "\\begin{equation}\n",
    "SMSE = \\left(\\frac{1}{N_{test}}\\sum_{i=1}^{N_{test}}\\left(y_i - \\hat{y}_i\\right)^2\\right)/\\sigma^2,\n",
    "\\end{equation}\n",
    "\n",
    "where \n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma^2 = \\frac{1}{N_{train}}\\sum_{i=1}^{N_{train}}\\left(y_i - \\bar{y}\\right)^2.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE: 31.0857592861\n",
      "SMSE: 0.0742260930\n"
     ]
    }
   ],
   "source": [
    "def compute_mse(prediction, labels):\n",
    "    return (sum((labels - prediction)**2)/len(prediction))\n",
    "def compute_model_mse(model, X, y):\n",
    "    predicted_y = model.predict(X)\n",
    "    return compute_mse(predicted_y, y)\n",
    "def log_mse(mse):\n",
    "    print('MSE: {:.10f}'.format(mse))\n",
    "    print('SMSE: {:.10f}'.format(mse/np.var(Y_scaled, ddof = 0)))\n",
    "\n",
    "test_mse = compute_model_mse(linearRegressor, X_scaled_test, Y_scaled_test)\n",
    "\n",
    "log_mse(test_mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like we got the correct result. Yay! \n",
    "\n",
    "## Radial Basis Function Network\n",
    "\n",
    "Next, we'll try using a radial basis function (RBF) network. First, we need to do some K-means clustering. We'll pick the number of clusters with the qualitative kink, knee, or elbow method (three different names for the same method). The book says to use cross-validation, but that's nonsense since the book itself says that using cross-validation is not possible for non-probablistic methods. I guess we could use a Gaussian Mixture Model if we want to do cross-validation?\n",
    "\n",
    "We'll fit the model with various values of $k$ and look at the reconstruction error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time elapsed: 963.612736572999\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[93511.741947211151,\n",
       " 65971.803182832591,\n",
       " 52906.722708804191,\n",
       " 45695.425134108205,\n",
       " 40914.984232328658,\n",
       " 37248.225253985787,\n",
       " 34558.310657963739,\n",
       " 32687.881212347915,\n",
       " 30928.954367901584,\n",
       " 29095.062690792329,\n",
       " 28426.793310216104,\n",
       " 26914.31468947696,\n",
       " 25975.490225306414,\n",
       " 25435.360392172126,\n",
       " 24836.868461234892,\n",
       " 24133.903034204865,\n",
       " 23626.584694583617,\n",
       " 23060.447629759739,\n",
       " 22521.141339972521,\n",
       " 21986.600362484041,\n",
       " 21708.632679338189,\n",
       " 21322.262079304437,\n",
       " 20787.919953330376,\n",
       " 20624.359384467432,\n",
       " 20029.795155720603,\n",
       " 19853.067069977682,\n",
       " 19440.537303560875,\n",
       " 19233.056525067761,\n",
       " 18875.450036315928,\n",
       " 18604.189801324806,\n",
       " 18443.502619621235,\n",
       " 18096.416501089247,\n",
       " 17887.377666428139,\n",
       " 17637.052858147334,\n",
       " 17348.111435998861,\n",
       " 17166.150898743901]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import cluster\n",
    "from joblib import Parallel, delayed\n",
    "\n",
    "k_range = np.arange(1, 107, 3)\n",
    "def score_k(k):\n",
    "    kMeansModel = cluster.KMeans(n_clusters = k, init = 'k-means++', algorithm = 'elkan', precompute_distances = True)\n",
    "    kMeansModel.fit(X_scaled)\n",
    "    return -kMeansModel.score(X_scaled_test)\n",
    "start = time.perf_counter() ## time how long it takes\n",
    "reconstruction_error = Parallel(n_jobs = 2, backend='threading')(delayed(score_k)(k) for k in k_range)\n",
    "print('Time elapsed: ' + str(time.perf_counter() - start))\n",
    "reconstruction_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the reconstruction error to find the kink."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/site-packages/matplotlib/figure.py:397: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
      "  \"matplotlib is currently using a non-GUI backend, \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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MgMyAzIAaKTKz7Bq2KSK+DazPzP9TtewqoDsz31F5fx/wicz8TOX9JGAD8M7M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FAAAI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\nSZLUQSZ7kiRJktRB/wdfbeiCmUFQDQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1178ef2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reconstruction_error = np.array(reconstruction_error, dtype = np.float64)\n",
    "fig = plt.figure(figsize=(10,6))\n",
    "ax = plt.gca()\n",
    "ax.plot(k_range, reconstruction_error, '.k-')\n",
    "ax.grid(True)\n",
    "ax.set_ylabel('Reconstruction error')\n",
    "ax.set_xlabel('$k$ - the number of clusters')\n",
    "ax.set_title('Test Data Reconstruction Error versus $k$')\n",
    "ax.get_yaxis().set_major_formatter(\n",
    "    matplotlib.ticker.FuncFormatter(lambda y, pos : format(int(y), ',')))\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Qualitatively, $100$ looks good to me. Now, let's fit our RBF network, which is a super simple [neural network](https://en.wikipedia.org/wiki/Radial_basis_function_network). We have 1 hidden layer of 100 units with the RBF activation function, and we run a linear regression on that hidden layer. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_clusters = 100\n",
    "kMeansModel = cluster.KMeans(n_clusters = n_clusters, init = 'k-means++', algorithm = 'elkan', precompute_distances = True)\n",
    "kMeansModel.fit(X_scaled)\n",
    "prototypes = kMeansModel.cluster_centers_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The RBF kerneal is\n",
    "\n",
    "\\begin{equation}\n",
    "\\kappa(\\mathbf{x}, \\mathbf{x}^\\prime) = \\exp\\left(-\\frac{\\lVert\\mathbf{x}-\\mathbf{x}^\\prime\\rVert^2}{2\\sigma^2}\\right),\n",
    "\\end{equation}\n",
    "\n",
    "so we'll perform our linear regression with design matrix $\\Phi$, where rows of $\\Phi$ are\n",
    "\n",
    "\\begin{equation}\n",
    "\\phi(\\mathbf{x}) = \\begin{pmatrix}\n",
    "\\kappa(\\mathbf{x}, \\boldsymbol\\mu_1) & \\kappa(\\mathbf{x}, \\boldsymbol\\mu_2) & \\cdots \n",
    "& \\kappa(\\mathbf{x}, \\boldsymbol\\mu_{k})\n",
    "\\end{pmatrix},\n",
    "\\end{equation}\n",
    "\n",
    "where the $\\boldsymbol\\mu_j$ for $j = 1,2,\\ldots,k$ are our cluster centers. $\\sigma^2$ is parameter called *bandwidth* that we'll have to find with cross-validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bandwidth</th>\n",
       "      <th>mean_test_score</th>\n",
       "      <th>mean_train_score</th>\n",
       "      <th>std_test_score</th>\n",
       "      <th>std_train_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>-267.152902</td>\n",
       "      <td>-265.932425</td>\n",
       "      <td>15.279617</td>\n",
       "      <td>3.813405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>-188.522188</td>\n",
       "      <td>-187.648077</td>\n",
       "      <td>11.168259</td>\n",
       "      <td>2.790824</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>-122.894823</td>\n",
       "      <td>-122.112400</td>\n",
       "      <td>6.091327</td>\n",
       "      <td>1.522200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8</td>\n",
       "      <td>-72.431290</td>\n",
       "      <td>-71.858192</td>\n",
       "      <td>2.480018</td>\n",
       "      <td>0.620141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>16</td>\n",
       "      <td>-40.163809</td>\n",
       "      <td>-39.825444</td>\n",
       "      <td>0.767083</td>\n",
       "      <td>0.193418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>32</td>\n",
       "      <td>-25.264711</td>\n",
       "      <td>-25.057333</td>\n",
       "      <td>0.227940</td>\n",
       "      <td>0.056388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>64</td>\n",
       "      <td>-20.167603</td>\n",
       "      <td>-20.004292</td>\n",
       "      <td>0.097739</td>\n",
       "      <td>0.025807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>128</td>\n",
       "      <td>-18.716779</td>\n",
       "      <td>-18.568064</td>\n",
       "      <td>0.192818</td>\n",
       "      <td>0.049968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>256</td>\n",
       "      <td>-18.422612</td>\n",
       "      <td>-18.277355</td>\n",
       "      <td>0.228230</td>\n",
       "      <td>0.058791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>512</td>\n",
       "      <td>-18.432984</td>\n",
       "      <td>-18.287904</td>\n",
       "      <td>0.238813</td>\n",
       "      <td>0.061415</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   bandwidth  mean_test_score  mean_train_score  std_test_score  \\\n",
       "0          1      -267.152902       -265.932425       15.279617   \n",
       "1          2      -188.522188       -187.648077       11.168259   \n",
       "2          4      -122.894823       -122.112400        6.091327   \n",
       "3          8       -72.431290        -71.858192        2.480018   \n",
       "4         16       -40.163809        -39.825444        0.767083   \n",
       "5         32       -25.264711        -25.057333        0.227940   \n",
       "6         64       -20.167603        -20.004292        0.097739   \n",
       "7        128       -18.716779        -18.568064        0.192818   \n",
       "8        256       -18.422612        -18.277355        0.228230   \n",
       "9        512       -18.432984        -18.287904        0.238813   \n",
       "\n",
       "   std_train_score  \n",
       "0         3.813405  \n",
       "1         2.790824  \n",
       "2         1.522200  \n",
       "3         0.620141  \n",
       "4         0.193418  \n",
       "5         0.056388  \n",
       "6         0.025807  \n",
       "7         0.049968  \n",
       "8         0.058791  \n",
       "9         0.061415  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import model_selection\n",
    "\n",
    "class RBFNetwork:\n",
    "    \"\"\"\n",
    "    Implements RBFNetwork as a special case of linear regression.\n",
    "    \"\"\"\n",
    "    def __init__(self, mu, sigma2):\n",
    "        self.linearRegressor = linear_model.LinearRegression(fit_intercept = True, normalize = False)\n",
    "        self.mu = mu\n",
    "        self.sigma2 = sigma2\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        Phi = self.rbf_transform(X, self.mu, self.sigma2)\n",
    "        linearRegressor.fit(Phi, y)\n",
    "        return self\n",
    "    \n",
    "    def predict(self, X):\n",
    "        Phi = self.rbf_transform(X, self.mu, self.sigma2)\n",
    "        return linearRegressor.predict(Phi)\n",
    "        \n",
    "    def score(self, X, y):\n",
    "        predicted_y = self.predict(X)\n",
    "        return -(sum((y - predicted_y)**2)/len(y))[0]         \n",
    "    \n",
    "    def get_params(self, deep = True):\n",
    "        return {'mu': self.mu, 'sigma2': self.sigma2}\n",
    "    \n",
    "    def set_params(self, **params):\n",
    "        if 'mu' in params:\n",
    "            self.mu = params['mu']\n",
    "        if 'sigma2' in params:\n",
    "            self.sigma2 = params['sigma2']\n",
    "        return self\n",
    "    \n",
    "    @staticmethod\n",
    "    def rbf(x1, x2, sigma2):\n",
    "        deltaX = (x1 - x2)\n",
    "        distX = sum(deltaX*deltaX)\n",
    "        return np.exp(-distX/2/sigma2)\n",
    "    \n",
    "    @staticmethod\n",
    "    def phi(x, mu, sigma2):\n",
    "        return np.apply_along_axis(func1d = RBFNetwork.rbf, axis = 1, arr = mu, x2 = x, sigma2 = sigma2)\n",
    "    \n",
    "    @staticmethod\n",
    "    def rbf_transform(X, mu, sigma2):\n",
    "        return np.apply_along_axis(func1d = RBFNetwork.phi, axis = 1, arr = X, mu = mu, sigma2 = sigma2)\n",
    "\n",
    "\n",
    "bandwidths = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]\n",
    "gridSearchCV = model_selection.GridSearchCV(RBFNetwork(mu = prototypes, sigma2 = 1024),\n",
    "                                            param_grid = {'sigma2': bandwidths},\n",
    "                                            cv = model_selection.KFold(n_splits = 5, shuffle = True, random_state = 2016),\n",
    "                                            n_jobs = 1) ## parallel jobs are broken for a reason that I don't feel like debugging\n",
    "gridSearchCV.fit(X_scaled, Y_scaled)\n",
    "cv_results = pd.DataFrame({'bandwidth': bandwidths,\n",
    "                           'mean_test_score': gridSearchCV.cv_results_['mean_test_score'],\n",
    "                           'std_test_score': gridSearchCV.cv_results_['std_test_score'],\n",
    "                           'mean_train_score': gridSearchCV.cv_results_['mean_train_score'],\n",
    "                           'std_train_score': gridSearchCV.cv_results_['std_train_score']})\n",
    "cv_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/site-packages/matplotlib/figure.py:397: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
      "  \"matplotlib is currently using a non-GUI backend, \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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XP5SrH8rVj6lTpyZsLDVkErq8vLywS0hKytUP5eqHcvVDufqhXP1Qrn4oVz8mTpyYsLF0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\nt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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1153cca20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.gca()\n",
    "test_error_bars = ax.errorbar(cv_results['bandwidth'], cv_results['mean_test_score'], cv_results['std_test_score'],\n",
    "                              linestyle='-', marker='.', color='b', capsize=5)\n",
    "train_error_bars = ax.errorbar(cv_results['bandwidth'], cv_results['mean_train_score'], cv_results['std_train_score'],\n",
    "                              linestyle='-', marker='.', color='r', capsize=5)\n",
    "ax.grid(True)\n",
    "ax.legend([test_error_bars, train_error_bars], ['Test Set', 'Training Set'], loc='lower right')\n",
    "ax.set_xscale('log', basex = 2)\n",
    "ax.set_xlabel('Bandwidth ($\\sigma^2$)')\n",
    "ax.set_ylabel('Score (negative MSE)')\n",
    "ax.set_title('Score versus Bandwidth')\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like the best model has a bandwidth of about $2^{8}$. Let's compute its SMSE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.042844306703931787"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rBFNetwork = RBFNetwork(mu = prototypes, sigma2 = 2**8)\n",
    "rBFNetwork.fit(X_scaled, Y_scaled)\n",
    "-rBFNetwork.score(X_scaled_test, Y_scaled_test)/np.var(Y_scaled, ddof=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seems that we can only get down to an SMSE of 0.043. The next step is to try a neural network. This has more parameters to choose. In particular, we're interested in the number of hidden units, layers, and the L2 regularization parameter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural Networks with TensorFlow\n",
    "\n",
    "Since I work at Google, I thought that I would demonstrate constructing a neural network in [TensorFlow](https://www.tensorflow.org/). Since I'm doing this with the intent of learning the details of the models, I'm going to eschew the high-level APIs and construct the graph mostly by hand. Much of the code is imported from [`sarco_train.py`](https://github.com/ppham27/MLaPP-solutions/blob/master/chap16/sarco_train.py).\n",
    "\n",
    "First, we'll set up our features which need to normalized. We make it so that the input has mean 0 and variance 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "from sarco_train import create_feature_columns\n",
    "\n",
    "feature_columns = create_feature_columns(pd.concat([training_data, test_data]))\n",
    "\n",
    "def get_feature_data(data, feature_columns):\n",
    "    graph = tf.Graph()\n",
    "    with graph.as_default():\n",
    "        features = {column: tf.constant(column_data, dtype=tf.float32)\n",
    "                    for column, column_data in data.to_dict('list').items()}\n",
    "        input_layer = tf.feature_column.input_layer(\n",
    "            features=features, feature_columns=feature_columns)\n",
    "    with tf.Session(graph=graph) as sess:\n",
    "        input_data = sess.run(input_layer)\n",
    "    return input_data, data[TARGET_COLUMN].astype(np.float32)\n",
    "\n",
    "training_input_data, training_target_data = get_feature_data(training_data, feature_columns)\n",
    "test_input_data, test_target_data = get_feature_data(test_data, feature_columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building the Graph\n",
    "\n",
    "Everything in TensorFlow is a graph. We build build it layer by layer.\n",
    "\n",
    "### Input Layer\n",
    "\n",
    "Here, we extract the features from the training data and test data and apply the feature columns to the two datasets.\n",
    "\n",
    "### Inference Layer\n",
    "\n",
    "Now, we can think about the inference layer. To keep things rather simple, I'll only use two layers. The weights and biases are initialize with noise, ReLU is used as the activation function. The first layer has 70 units, and the second layer has 50 units. Since we have an input of 21 features, the total number of weight parameters in a fully connected network are $21 \\times 70 + 70 \\times 50 + 50 \\times 1$, and we have also have $70 + 50 + 1$ bias parameters. The number of units was chosen arbitrarily. I was too lazy to implement and cross validation strategy.\n",
    "\n",
    "### Loss Layer\n",
    "\n",
    "For loss, we minimize mean squared error. This is we'll compare models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sarco_train import inference, HIDDEN1_UNITS, HIDDEN2_UNITS\n",
    "\n",
    "eval_graph = tf.Graph()\n",
    "with eval_graph.as_default():    \n",
    "    input = tf.placeholder(dtype=tf.float32, shape=(None, len(feature_columns)))\n",
    "    prediction = inference(input, HIDDEN1_UNITS, HIDDEN2_UNITS)\n",
    "    \n",
    "    labels = tf.placeholder(dtype=tf.float32, shape=(None,))\n",
    "    mse = tf.losses.mean_squared_error(labels=labels, predictions=prediction, reduction=tf.losses.Reduction.MEAN)\n",
    "        \n",
    "    tf.summary.scalar('mse', mse)\n",
    "    \n",
    "    summary_op = tf.summary.merge_all()\n",
    "# Reset evaluation process\n",
    "last_checkpoint_summarized = None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training the Model\n",
    "\n",
    "Training the model is done in [`sarco_train.py`](https://github.com/ppham27/MLaPP-solutions/blob/master/chap16/sarco_train.py). The script was run with the command:\n",
    "\n",
    "`python3 sarco_train.py --restart --log_level=INFO --log_dir /Users/phillypham/tmp/sarco/logs`\n",
    "\n",
    "Input is fetched from a queue to avoid blocking the thread doing the training. 1024 examples are processed in each training step. In addition to minimize mean squared error, we add $L^1$ and $L^2$ regularization to deal with the large number of parameters. The scale parameter for $L^1$ was $1.0$. The scale parameter for $L^2$ is $14.0$. The variation of gradient descent that we'll use is [Adam Optimizer](https://arxiv.org/abs/1412.6980) with a learning rate of $0.01$.\n",
    "\n",
    "While the training script is running, this code runs in a separate process to periodically evaluate the model. We calculate mean squared error against the entire training set and entire test set. We can see these plotted by running `tensorboard --logdir=/Users/phillypham/tmp/sarco/logs` and visiting [TensorBoard](http://localhost:6006).\n",
    "\n",
    "Since we're using a [Monitored Session](https://www.tensorflow.org/versions/master/api_docs/python/tf/train/MonitoredSession), we can continue training from where left off by running\n",
    "\n",
    "`python3 sarco_train.py --log_level=INFO --log_dir /Users/phillypham/tmp/sarco/logs`\n",
    "\n",
    "and restarting the evaluation code below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Writing summary for step 297332\n",
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      "INFO:tensorflow:Writing summary for step 298176\n",
      "INFO:tensorflow:Training stopped.\n"
     ]
    }
   ],
   "source": [
    "from sarco_train import CHECKPOINT_INTERVAL_SECS\n",
    "\n",
    "CHECKPOINT_DIR = '/Users/phillypham/tmp/sarco/logs'\n",
    "EVAL_DIR = CHECKPOINT_DIR + '/eval'\n",
    "\n",
    "with eval_graph.as_default():\n",
    "    saver = tf.train.Saver(tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES))\n",
    "    \n",
    "    training_writer = tf.summary.FileWriter(EVAL_DIR + '/training', eval_graph)\n",
    "    test_writer = tf.summary.FileWriter(EVAL_DIR + '/test', eval_graph)\n",
    "    with tf.Session() as sess:           \n",
    "        def write_summary(step):\n",
    "            def write_mse(writer, features, target):\n",
    "                summary = sess.run(summary_op, feed_dict={input: features, labels: target})\n",
    "                writer.add_summary(summary, step)\n",
    "                writer.flush()\n",
    "            tf.logging.info('Writing summary for step {:d}'.format(step))\n",
    "            write_mse(test_writer, test_input_data, test_target_data)\n",
    "            write_mse(training_writer, training_input_data, training_target_data)\n",
    "        while True:\n",
    "            checkpoint_state = tf.train.get_checkpoint_state(CHECKPOINT_DIR)\n",
    "            checkpoint_path = checkpoint_state.model_checkpoint_path\n",
    "            # Stop running when no more new checkpoints are being generated.\n",
    "            if checkpoint_path == last_checkpoint_summarized:\n",
    "                break\n",
    "            saver.restore(sess, checkpoint_state.model_checkpoint_path)\n",
    "            global_step = int(checkpoint_state.model_checkpoint_path.split('/')[-1].split('-')[-1])                   \n",
    "            write_summary(global_step)\n",
    "            last_checkpoint_summarized = checkpoint_path\n",
    "            time.sleep(CHECKPOINT_INTERVAL_SECS)\n",
    "        tf.logging.info('Training stopped.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Monitoring the training process\n",
    "\n",
    "In TensorBoard, I've been summarizing loss and the mean squared error on checkpoints as the model is training. Here's the loss plotted.\n",
    "\n",
    "![Batch Loss](nn_batch_loss.png)\n",
    "\n",
    "You can see that the model has more or less by converged 50,000 training steps. Because we're sampling batches of data, there's a lot of noise.\n",
    "\n",
    "The loss includes the regularization penalty, so when evaluating the model on the test data, it may be more helpful to look at mean squared error. The various mean squared errors are:\n",
    "- **Orange**: Batch that we're training on\n",
    "- **Blue**: The test set\n",
    "- **Purple**: The training set\n",
    "\n",
    "![MSE](nn_mse_all.png)\n",
    "\n",
    "## Selecting a model\n",
    "\n",
    "Of course, this isn't very helpful because of how noisy the MSE of the training batch set is. It's more helpful to look at just the MSEs from the evaluation process.\n",
    "\n",
    "![Evaluation MSEs](nn_mse_eval.png)\n",
    "\n",
    "After the model converged, there's a lot of random noise. We may possibly be overfitting by training this long. The MSE on the training and test set stay pretty close together, however. It looks like the lowest MSE is obtained by the model at step 188,939. Let's calculate the SMSE for this model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from /Users/phillypham/tmp/sarco/logs/model.ckpt-188939\n",
      "MSE: 9.1203241348\n",
      "SMSE: 0.0217773683\n"
     ]
    }
   ],
   "source": [
    "SELECTED_MODEL = CHECKPOINT_DIR + '/model.ckpt-188939'\n",
    "\n",
    "with eval_graph.as_default():\n",
    "    with tf.Session() as sess:\n",
    "        saver.restore(sess, SELECTED_MODEL)\n",
    "        test_mse = sess.run(mse, feed_dict={input: test_input_data, labels: test_target_data})\n",
    "        log_mse(test_mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nice. Neural networks achieve the best standarded mean squared error. Of course, training this model took the longest, and the details of why it works are already obscure after only two layers."
   ]
  }
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