Performance of different ML algorithms for fitting functions

metamodelling.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rereference\t\n",
    "- Jin, Ruichen, Wei Chen, and Timothy W. Simpson. \"Comparative studies of metamodelling techniques under multiple modelling criteria.\" Structural and multidisciplinary optimization 23.1 (2001): 1-13."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f4(x1, x2):\n",
    "    y = (30+x1*np.sin(x1))*(4+np.exp(-x2**2))\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x1, x2 = np.meshgrid(np.linspace(0,10),\n",
    "                     np.linspace(0,6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = f4(x1, x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x11b197e48>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b009a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.contourf(x1, x2, y)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2500, 2)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.stack([x1.ravel(), x2.ravel()], axis=1)\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2500,)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = y.ravel()\n",
    "Y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ANN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.neural_network import MLPRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nn = MLPRegressor(hidden_layer_sizes=(20, 20), \n",
    "                  activation='tanh', solver='lbfgs', max_iter=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 47.8 s, sys: 7.52 s, total: 55.3 s\n",
      "Wall time: 28.3 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "MLPRegressor(activation='tanh', alpha=0.0001, batch_size='auto', beta_1=0.9,\n",
       "       beta_2=0.999, early_stopping=False, epsilon=1e-08,\n",
       "       hidden_layer_sizes=(20, 20), learning_rate='constant',\n",
       "       learning_rate_init=0.001, max_iter=10000, momentum=0.9,\n",
       "       nesterovs_momentum=True, power_t=0.5, random_state=None,\n",
       "       shuffle=True, solver='lbfgs', tol=0.0001, validation_fraction=0.1,\n",
       "       verbose=False, warm_start=False)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time nn.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.074035161840334568"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nn.loss_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred_nn = nn.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.96 ms ± 332 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit y_pred_nn = nn.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99954188355407192"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(y_pred_nn, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1183c3f60>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rbaW/jdtfPhN4yV++0xhTAEwA1rRZj0WkUU2tslmZ7+b+17ew8s5pYV9z1iMrmDw8Mzjy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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1183c3d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Y, Y, color='k', linewidth=1)\n",
    "plt.scatter(Y, y_pred_nn, alpha=0.5, s=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x11a832828>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Ia8PDC9YVn8bZm7qG30tvfo0Fu4v1zYruaxjmbSgi1nWYvWGG5W8Fbu2mDfd0bSgMspfb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\nZmYJOXTNzBL6Z+w+ylDnpGqPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1183c35f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.contourf(x1, x2, y_pred_nn.reshape(50,50))\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SVM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.svm import SVR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVR(C=10000000000.0, cache_size=200, coef0=0.0, degree=3, epsilon=0.1,\n",
       "  gamma='auto', kernel='rbf', max_iter=-1, shrinking=True, tol=0.001,\n",
       "  verbose=False)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf = SVR(C=1e10)\n",
    "clf.fit(X, Y) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred_svm = clf.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.59 ms ± 208 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit clf.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99998705295039281"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(y_pred_svm, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x11aee8978>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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tB1YA93bankPXKqPpoV7G5blVvCS4yv9nSRuBLwArJU1IejPwQeB44K7sNghXA0TENuAm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\nzCyh/wMBILatJQecmQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a95a198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.contourf(x1, x2, y_pred_svm.reshape(50,50))\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# RF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.ensemble import RandomForestRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rf = RandomForestRegressor(n_estimators=5, n_jobs=5, \n",
    "                           max_leaf_nodes=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestRegressor(bootstrap=True, criterion='mse', max_depth=None,\n",
       "           max_features='auto', max_leaf_nodes=200,\n",
       "           min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "           min_samples_leaf=1, min_samples_split=2,\n",
       "           min_weight_fraction_leaf=0.0, n_estimators=5, n_jobs=5,\n",
       "           oob_score=False, random_state=None, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rf.fit(X, Y) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99868159386253585"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred_rf = rf.predict(X)\n",
    "r2_score(y_pred_rf, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x11b19c550>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hm8bqIq48tS61ylUhLzIxCno5IkNftF5z1mIaq4oy9o5v6vATisTGHKpJWtNQ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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b172438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Y, Y, color='k', linewidth=1)\n",
    "plt.scatter(Y, y_pred_rf, alpha=0.5, s=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "104 ms ± 508 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit rf.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x11b45cfd0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VSuiOsCY+vBhk8A5q3wv9OyVsBmMcX7y7ZXgh+jbuT5pxVGaYoa1DXlVLT3fEtf1QncVK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\nJXQjImqU0I2IqFFCNyKiRv8fzgIAAvfsLvkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b172390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.contourf(x1, x2, y_pred_rf.reshape(50,50))\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pytorch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch.autograd import Variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = Variable(torch.from_numpy(X).type(torch.FloatTensor))\n",
    "y = Variable(torch.from_numpy(Y.reshape(-1,1)).type(torch.FloatTensor))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "H1, H2 = 20, 20\n",
    "\n",
    "model = torch.nn.Sequential(\n",
    "    torch.nn.Linear(2, H1),\n",
    "    torch.nn.BatchNorm1d(H1),\n",
    "    #torch.nn.Dropout(),\n",
    "    torch.nn.Tanh(),\n",
    "    torch.nn.Linear(H1, H2),\n",
    "    torch.nn.BatchNorm1d(H2),\n",
    "    #torch.nn.Dropout(),\n",
    "    torch.nn.Tanh(),\n",
    "    torch.nn.Linear(H2, 1)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50 3.1374166011810303\n",
      "100 0.6595962643623352\n",
      "150 0.23710793256759644\n",
      "200 0.08169987797737122\n",
      "250 0.034176066517829895\n",
      "300 0.022618694230914116\n",
      "350 0.013968806713819504\n",
      "400 0.00791569147258997\n",
      "450 0.0064892577938735485\n",
      "500 0.00543169304728508\n"
     ]
    }
   ],
   "source": [
    "loss_fn = torch.nn.MSELoss()\n",
    "\n",
    "# LBFGS can make error very small\n",
    "optimizer = torch.optim.LBFGS(model.parameters(), lr=0.1)\n",
    "#optimizer = torch.optim.Adam(model.parameters(), lr = 0.01)\n",
    "\n",
    "for t in range(500):\n",
    "    \n",
    "    def closure():\n",
    "        optimizer.zero_grad()\n",
    "        y_pred = model(x)\n",
    "        loss = loss_fn(y_pred, y)\n",
    "        loss.backward()\n",
    "        return loss\n",
    "    optimizer.step(closure)\n",
    "    \n",
    "    if (t+1)%50==0:\n",
    "        y_pred = model(x)\n",
    "        loss = loss_fn(y_pred, y)\n",
    "        print(t+1, loss.data[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred = model(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.42 ms ± 96 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit model(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99998320023540554"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(y_pred.data.numpy(), Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x122c08978>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NqKl9918UFvLZ04Yw+ZweCnkRkYCE2AJBu0uKiJQt7kf0IiJSPgW9iEiCU9CL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x122c085c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Y, Y, color='k', linewidth=1)\n",
    "plt.scatter(y_pred.data.numpy(), Y, alpha=0.5, s=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Keras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import keras\n",
    "from keras import models\n",
    "from keras import layers\n",
    "from keras import regularizers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /Users/zhuangjw/Research/Computing/miniconda3/envs/geo/lib/python3.6/site-packages/tensorflow/python/ops/nn_impl.py:667: calling reduce_mean (from tensorflow.python.ops.math_ops) with keep_dims is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "keep_dims is deprecated, use keepdims instead\n"
     ]
    }
   ],
   "source": [
    "network = models.Sequential()\n",
    "network.add(layers.Dense(20, activation='tanh', input_shape=(2,)))\n",
    "network.add(layers.BatchNormalization())\n",
    "network.add(layers.Dense(20, activation='tanh'))\n",
    "network.add(layers.BatchNormalization())\n",
    "network.add(layers.Dense(1, activation=None))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "network.compile(optimizer=keras.optimizers.Adam(lr=0.01), \n",
    "                loss='mse')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/3\n",
      "1000/1000 [==============================] - 5s 5ms/step - loss: 1618.2311\n",
      "Epoch 2/3\n",
      "1000/1000 [==============================] - 4s 4ms/step - loss: 0.0568\n",
      "Epoch 3/3\n",
      "1000/1000 [==============================] - 4s 4ms/step - loss: 0.0470\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x1337cfa58>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "network.fit(X, Y, epochs=3, steps_per_epoch=1000, verbose=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred = network.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "35.6 ms ± 3.33 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit network.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99348591424505939"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(y_pred, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1337cf320>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XXXRR3M+UbXyh1xefAGZMSOfu1TOHs9lCjBsS9GJUba+q52dbD3Ci1YvZaKQ4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\nCCES3P8Ha3DuPfGcTksAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1337cf358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Y, Y, color='k', linewidth=1)\n",
    "plt.scatter(y_pred, Y, alpha=0.5, s=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x1345ca668>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x134370b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.contourf(x1, x2, y_pred.reshape(50,50))\n",
    "plt.colorbar()"
   ]
  }
 ],
 "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": "3.6.2"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": "block",
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}