test gitlab/jupyter/markdown bug image

b0aa7d8b · Jean-Luc Parouty · 00c17a25 · b0aa7d8b · b0aa7d8b
Commit b0aa7d8b authored 5 years ago by Jean-Luc Parouty
--- a/BHPD/00-Fidle-header-01.png
+++ b/BHPD/00-Fidle-header-01.png
--- a/BHPD/01-DNN-Regression.ipynb
+++ b/BHPD/01-DNN-Regression.ipynb
@@ -4,7 +4,8 @@
   "cell_type": "markdown",
   "metadata": {},
   "source": [
-    "![header1](../fidle/img/00-Fidle-header-01.png)\n",
+    "![Fidle](../fidle/img/00-Fidle-header-01.png)\n",
+    "![Fidle](00-Fidle-header-01.png)\n",
    "\n",
    "# Deep Neural Network (DNN) - BHPD dataset\n",
    "\n",

 %% Cell type:markdown id: tags:
-![header1](../fidle/img/00-Fidle-header-01.png)
+![Fidle](../fidle/img/00-Fidle-header-01.png)
+![Fidle](00-Fidle-header-01.png)
 # Deep Neural Network (DNN) - BHPD dataset
 <!-- INDEX : Simple regression with a Dense Neural Network (DNN) - BHPD dataset -->
 A very simple and classic example of **regression** :
 ## Objectives :
 - Predicts **housing prices** from a set of house features.
 - Understanding the principle and the architecture of a regression with a dense neural network
 The **[Boston Housing Dataset](https://www.cs.toronto.edu/~delve/data/boston/bostonDetail.html)** consists of price of houses in various places in Boston.
 Alongside with price, the dataset also provide information such as Crime, areas of non-retail business in the town,
 age of people who own the house and many other attributes...
 What we're going to do:
 - Retrieve data
 - Preparing the data
 - Build a model
 - Train the model
 - Evaluate the result
 %% Cell type:markdown id: tags:
 ## Step 1 - Import and init
 %% Cell type:code id: tags:
 ``` python
 import tensorflow as tf
 from tensorflow import keras
 import numpy as np
 import matplotlib.pyplot as plt
 import pandas as pd
 import os,sys
 from IPython.display import display, Markdown
 from importlib import reload
 sys.path.append('..')
 import fidle.pwk as ooo
 ooo.init()
 os.makedirs('./run/models',   mode=0o750, exist_ok=True)
 ```
 %% Output
    FIDLE 2020 - Practical Work Module
    Version              : 0.2.9
    Run time             : Tuesday 18 February 2020, 14:42:02
    TensorFlow version   : 2.0.0
    Keras version        : 2.2.4-tf
 %% Cell type:markdown id: tags:
 ## Step 2 - Retrieve data
 ### 2.1 - Option 1  : From Keras
 Boston housing is a famous historic dataset, so we can get it directly from [Keras datasets](https://www.tensorflow.org/api_docs/python/tf/keras/datasets)
 %% Cell type:raw id: tags:
 (x_train, y_train), (x_test, y_test) = keras.datasets.boston_housing.load_data(test_split=0.2, seed=113)
 %% Cell type:markdown id: tags:
 ### 2.2 - Option 2 : From a csv file
 More fun !
 %% Cell type:code id: tags:
 ``` python
 data = pd.read_csv('./data/BostonHousing.csv', header=0)
 display(data.head(5).style.format("{0:.2f}"))
 print('Données manquantes : ',data.isna().sum().sum(), '  Shape is : ', data.shape)
 ```
 %% Output
    Données manquantes :  0   Shape is :  (506, 14)
 %% Cell type:markdown id: tags:
 ## Step 3 - Preparing the data
 ### 3.1 - Split data
 We will use 70% of the data for training and 30% for validation.
 x will be input data and y the expected output
 %% Cell type:code id: tags:
 ``` python
 # ---- Split => train, test
 #
 data_train = data.sample(frac=0.7, axis=0)
 data_test  = data.drop(data_train.index)
 # ---- Split => x,y (medv is price)
 #
 x_train = data_train.drop('medv',  axis=1)
 y_train = data_train['medv']
 x_test  = data_test.drop('medv',   axis=1)
 y_test  = data_test['medv']
 print('Original data shape was : ',data.shape)
 print('x_train : ',x_train.shape, 'y_train : ',y_train.shape)
 print('x_test  : ',x_test.shape,  'y_test  : ',y_test.shape)
 ```
 %% Output
    Original data shape was :  (506, 14)
    x_train :  (354, 13) y_train :  (354,)
    x_test  :  (152, 13) y_test  :  (152,)
 %% Cell type:markdown id: tags:
 ### 3.2 - Data normalization
 **Note :**
 - All input data must be normalized, train and test.
 - To do this we will **subtract the mean** and **divide by the standard deviation**.
 - But test data should not be used in any way, even for normalization.
 - The mean and the standard deviation will therefore only be calculated with the train data.
 %% Cell type:code id: tags:
 ``` python
 display(x_train.describe().style.format("{0:.2f}").set_caption("Before normalization :"))
 mean = x_train.mean()
 std  = x_train.std()
 x_train = (x_train - mean) / std
 x_test  = (x_test  - mean) / std
 display(x_train.describe().style.format("{0:.2f}").set_caption("After normalization :"))
 x_train, y_train = np.array(x_train), np.array(y_train)
 x_test,  y_test  = np.array(x_test),  np.array(y_test)
 ```
 %% Output
 %% Cell type:markdown id: tags:
 ## Step 4 - Build a model
 About informations about :
 - [Optimizer](https://www.tensorflow.org/api_docs/python/tf/keras/optimizers)
 - [Activation](https://www.tensorflow.org/api_docs/python/tf/keras/activations)
 - [Loss](https://www.tensorflow.org/api_docs/python/tf/keras/losses)
 - [Metrics](https://www.tensorflow.org/api_docs/python/tf/keras/metrics)
 %% Cell type:code id: tags:
 ``` python
  def get_model_v1(shape):
    model = keras.models.Sequential()
    model.add(keras.layers.Input(shape, name="InputLayer"))
    model.add(keras.layers.Dense(64, activation='relu', name='Dense_n1'))
    model.add(keras.layers.Dense(64, activation='relu', name='Dense_n2'))
    model.add(keras.layers.Dense(1, name='Output'))
    model.compile(optimizer = 'rmsprop',
                  loss      = 'mse',
                  metrics   = ['mae', 'mse'] )
    return model
 ```
 %% Cell type:markdown id: tags:
 ## Step 5 - Train the model
 ### 5.1 - Get it
 %% Cell type:code id: tags:
 ``` python
 model=get_model_v1( (13,) )
 model.summary()
 keras.utils.plot_model( model, to_file='./run/model.png', show_shapes=True, show_layer_names=True, dpi=96)
 ```
 %% Output
    Model: "sequential"
    _________________________________________________________________
    Layer (type)                 Output Shape              Param #
    =================================================================
    Dense_n1 (Dense)             (None, 64)                896
    _________________________________________________________________
    Dense_n2 (Dense)             (None, 64)                4160
    _________________________________________________________________
    Output (Dense)               (None, 1)                 65
    =================================================================
    Total params: 5,121
    Trainable params: 5,121
    Non-trainable params: 0
    _________________________________________________________________
    <IPython.core.display.Image object>
 %% Cell type:markdown id: tags:
 ### 5.2 - Train it
 %% Cell type:code id: tags:
 ``` python
 history = model.fit(x_train,
                    y_train,
                    epochs          = 100,
                    batch_size      = 10,
                    verbose         = 1,
                    validation_data = (x_test, y_test))
 ```
 %% Output
    Train on 354 samples, validate on 152 samples
    Epoch 1/100
    354/354 [==============================] - 1s 2ms/sample - loss: 414.5603 - mae: 18.2577 - mse: 414.5602 - val_loss: 266.3728 - val_mae: 13.9913 - val_mse: 266.3728
    Epoch 2/100
    354/354 [==============================] - 0s 190us/sample - loss: 165.4507 - mae: 10.4618 - mse: 165.4507 - val_loss: 74.4125 - val_mae: 6.0372 - val_mse: 74.4125
    Epoch 3/100
    354/354 [==============================] - 0s 187us/sample - loss: 54.2313 - mae: 5.3763 - mse: 54.2313 - val_loss: 47.0203 - val_mae: 4.7399 - val_mse: 47.0203
    Epoch 4/100
    354/354 [==============================] - 0s 166us/sample - loss: 32.3303 - mae: 4.2632 - mse: 32.3303 - val_loss: 38.0120 - val_mae: 4.2484 - val_mse: 38.0120
    Epoch 5/100
    354/354 [==============================] - 0s 153us/sample - loss: 25.3763 - mae: 3.7745 - mse: 25.3763 - val_loss: 32.4707 - val_mae: 3.8465 - val_mse: 32.4707
    Epoch 6/100
    354/354 [==============================] - 0s 153us/sample - loss: 22.2331 - mae: 3.4720 - mse: 22.2331 - val_loss: 29.6142 - val_mae: 3.4844 - val_mse: 29.6142
    Epoch 7/100
    354/354 [==============================] - 0s 154us/sample - loss: 19.7834 - mae: 3.2245 - mse: 19.7834 - val_loss: 27.1649 - val_mae: 3.5465 - val_mse: 27.1649
    Epoch 8/100
    354/354 [==============================] - 0s 155us/sample - loss: 18.0991 - mae: 3.0669 - mse: 18.0991 - val_loss: 26.0093 - val_mae: 3.5617 - val_mse: 26.0093
    Epoch 9/100
    354/354 [==============================] - 0s 161us/sample - loss: 16.9247 - mae: 2.9184 - mse: 16.9247 - val_loss: 23.2549 - val_mae: 3.3243 - val_mse: 23.2549
    Epoch 10/100
    354/354 [==============================] - 0s 150us/sample - loss: 16.0827 - mae: 2.8116 - mse: 16.0827 - val_loss: 21.1365 - val_mae: 3.0248 - val_mse: 21.1365
    Epoch 11/100
    354/354 [==============================] - 0s 170us/sample - loss: 15.0334 - mae: 2.7214 - mse: 15.0334 - val_loss: 20.0163 - val_mae: 2.9800 - val_mse: 20.0163
    Epoch 12/100
    354/354 [==============================] - 0s 180us/sample - loss: 14.4011 - mae: 2.6949 - mse: 14.4011 - val_loss: 19.8958 - val_mae: 2.9262 - val_mse: 19.8958
    Epoch 13/100
    354/354 [==============================] - 0s 184us/sample - loss: 13.9168 - mae: 2.5674 - mse: 13.9168 - val_loss: 18.5729 - val_mae: 2.7302 - val_mse: 18.5729
    Epoch 14/100
    354/354 [==============================] - 0s 161us/sample - loss: 13.5575 - mae: 2.5442 - mse: 13.5575 - val_loss: 17.8812 - val_mae: 2.6748 - val_mse: 17.8812
    Epoch 15/100
    354/354 [==============================] - 0s 166us/sample - loss: 12.8689 - mae: 2.4779 - mse: 12.8689 - val_loss: 18.9649 - val_mae: 2.7560 - val_mse: 18.9649
    Epoch 16/100
    354/354 [==============================] - 0s 159us/sample - loss: 12.6470 - mae: 2.4670 - mse: 12.6470 - val_loss: 16.5834 - val_mae: 2.6016 - val_mse: 16.5834
    Epoch 17/100
    354/354 [==============================] - 0s 159us/sample - loss: 12.3566 - mae: 2.4280 - mse: 12.3566 - val_loss: 16.7371 - val_mae: 2.6670 - val_mse: 16.7371
    Epoch 18/100
    354/354 [==============================] - 0s 158us/sample - loss: 12.3328 - mae: 2.4060 - mse: 12.3328 - val_loss: 16.3754 - val_mae: 2.6027 - val_mse: 16.3754
    Epoch 19/100
    354/354 [==============================] - 0s 152us/sample - loss: 11.8357 - mae: 2.3106 - mse: 11.8357 - val_loss: 16.1015 - val_mae: 2.6255 - val_mse: 16.1015
    Epoch 20/100
    354/354 [==============================] - 0s 163us/sample - loss: 11.6722 - mae: 2.3482 - mse: 11.6722 - val_loss: 16.1405 - val_mae: 2.6889 - val_mse: 16.1405
    Epoch 21/100
    354/354 [==============================] - 0s 175us/sample - loss: 11.2774 - mae: 2.3344 - mse: 11.2774 - val_loss: 15.2110 - val_mae: 2.5038 - val_mse: 15.2110
    Epoch 22/100
    354/354 [==============================] - 0s 180us/sample - loss: 11.2491 - mae: 2.3055 - mse: 11.2491 - val_loss: 15.4745 - val_mae: 2.4494 - val_mse: 15.4744
    Epoch 23/100
    354/354 [==============================] - 0s 187us/sample - loss: 10.9102 - mae: 2.2171 - mse: 10.9102 - val_loss: 15.1145 - val_mae: 2.4282 - val_mse: 15.1145
    Epoch 24/100
    354/354 [==============================] - 0s 168us/sample - loss: 10.7952 - mae: 2.2533 - mse: 10.7952 - val_loss: 14.3789 - val_mae: 2.3683 - val_mse: 14.3789
    Epoch 25/100
    354/354 [==============================] - 0s 171us/sample - loss: 10.7250 - mae: 2.2489 - mse: 10.7250 - val_loss: 15.1102 - val_mae: 2.3422 - val_mse: 15.1102
    Epoch 26/100
    354/354 [==============================] - 0s 158us/sample - loss: 10.4010 - mae: 2.1702 - mse: 10.4010 - val_loss: 14.3260 - val_mae: 2.3176 - val_mse: 14.3260
    Epoch 27/100
    354/354 [==============================] - 0s 149us/sample - loss: 10.1442 - mae: 2.1797 - mse: 10.1442 - val_loss: 13.6694 - val_mae: 2.3864 - val_mse: 13.6694
    Epoch 28/100
    354/354 [==============================] - 0s 168us/sample - loss: 10.1391 - mae: 2.1809 - mse: 10.1391 - val_loss: 14.0177 - val_mae: 2.3467 - val_mse: 14.0177
    Epoch 29/100
    354/354 [==============================] - 0s 149us/sample - loss: 9.9119 - mae: 2.1267 - mse: 9.9119 - val_loss: 14.0739 - val_mae: 2.4617 - val_mse: 14.0739
    Epoch 30/100
    354/354 [==============================] - 0s 164us/sample - loss: 10.0176 - mae: 2.1669 - mse: 10.0176 - val_loss: 13.5116 - val_mae: 2.3158 - val_mse: 13.5116
    Epoch 31/100
    354/354 [==============================] - 0s 189us/sample - loss: 9.8259 - mae: 2.1407 - mse: 9.8259 - val_loss: 13.7364 - val_mae: 2.3531 - val_mse: 13.7364
    Epoch 32/100
    354/354 [==============================] - 0s 178us/sample - loss: 9.4495 - mae: 2.0922 - mse: 9.4495 - val_loss: 14.1936 - val_mae: 2.3887 - val_mse: 14.1936
    Epoch 33/100
    354/354 [==============================] - 0s 164us/sample - loss: 9.6721 - mae: 2.0870 - mse: 9.6721 - val_loss: 13.4267 - val_mae: 2.3508 - val_mse: 13.4267
    Epoch 34/100
    354/354 [==============================] - 0s 167us/sample - loss: 9.1042 - mae: 2.0644 - mse: 9.1042 - val_loss: 13.3821 - val_mae: 2.4709 - val_mse: 13.3821
    Epoch 35/100
    354/354 [==============================] - 0s 155us/sample - loss: 9.0129 - mae: 2.0482 - mse: 9.0129 - val_loss: 14.2184 - val_mae: 2.2754 - val_mse: 14.2184
    Epoch 36/100
    354/354 [==============================] - 0s 160us/sample - loss: 9.2470 - mae: 2.0661 - mse: 9.2470 - val_loss: 14.3466 - val_mae: 2.5561 - val_mse: 14.3466
    Epoch 37/100
    354/354 [==============================] - 0s 169us/sample - loss: 9.1695 - mae: 2.0766 - mse: 9.1695 - val_loss: 13.3818 - val_mae: 2.2373 - val_mse: 13.3818
    Epoch 38/100
    354/354 [==============================] - 0s 165us/sample - loss: 9.1663 - mae: 2.0617 - mse: 9.1663 - val_loss: 14.7461 - val_mae: 2.5061 - val_mse: 14.7461
    Epoch 39/100
    354/354 [==============================] - 0s 159us/sample - loss: 8.7273 - mae: 2.0208 - mse: 8.7273 - val_loss: 12.5890 - val_mae: 2.3037 - val_mse: 12.5890
    Epoch 40/100
    354/354 [==============================] - 0s 166us/sample - loss: 8.9038 - mae: 2.0352 - mse: 8.9038 - val_loss: 12.9754 - val_mae: 2.2079 - val_mse: 12.9754
    Epoch 41/100
    354/354 [==============================] - 0s 153us/sample - loss: 8.6155 - mae: 2.0267 - mse: 8.6155 - val_loss: 13.9239 - val_mae: 2.3525 - val_mse: 13.9239
    Epoch 42/100
    354/354 [==============================] - 0s 163us/sample - loss: 8.5479 - mae: 2.0170 - mse: 8.5479 - val_loss: 13.6362 - val_mae: 2.2694 - val_mse: 13.6362
    Epoch 43/100
    354/354 [==============================] - 0s 165us/sample - loss: 8.7087 - mae: 2.0062 - mse: 8.7087 - val_loss: 13.1138 - val_mae: 2.2386 - val_mse: 13.1138
    Epoch 44/100
    354/354 [==============================] - 0s 160us/sample - loss: 8.3942 - mae: 1.9622 - mse: 8.3942 - val_loss: 12.3461 - val_mae: 2.2337 - val_mse: 12.3461
    Epoch 45/100
    354/354 [==============================] - 0s 168us/sample - loss: 8.4101 - mae: 2.0098 - mse: 8.4101 - val_loss: 13.2116 - val_mae: 2.2682 - val_mse: 13.2116
    Epoch 46/100
    354/354 [==============================] - 0s 156us/sample - loss: 8.3264 - mae: 1.9483 - mse: 8.3264 - val_loss: 12.5519 - val_mae: 2.4063 - val_mse: 12.5519
    Epoch 47/100
    354/354 [==============================] - 0s 158us/sample - loss: 8.1445 - mae: 1.9549 - mse: 8.1445 - val_loss: 12.1838 - val_mae: 2.2591 - val_mse: 12.1838
    Epoch 48/100
    354/354 [==============================] - 0s 156us/sample - loss: 8.0389 - mae: 1.9304 - mse: 8.0389 - val_loss: 12.6978 - val_mae: 2.1907 - val_mse: 12.6978
    Epoch 49/100
    354/354 [==============================] - 0s 164us/sample - loss: 8.0705 - mae: 1.9493 - mse: 8.0705 - val_loss: 12.4833 - val_mae: 2.4720 - val_mse: 12.4833
    Epoch 50/100
    354/354 [==============================] - 0s 158us/sample - loss: 8.1872 - mae: 1.9630 - mse: 8.1872 - val_loss: 12.0043 - val_mae: 2.2610 - val_mse: 12.0043
    Epoch 51/100
    354/354 [==============================] - 0s 158us/sample - loss: 8.0357 - mae: 1.8946 - mse: 8.0357 - val_loss: 11.3982 - val_mae: 2.1770 - val_mse: 11.3982
    Epoch 52/100
    354/354 [==============================] - 0s 162us/sample - loss: 7.6882 - mae: 1.8951 - mse: 7.6882 - val_loss: 13.0714 - val_mae: 2.4109 - val_mse: 13.0714
    Epoch 53/100
    354/354 [==============================] - 0s 162us/sample - loss: 7.9639 - mae: 1.9103 - mse: 7.9639 - val_loss: 12.4297 - val_mae: 2.2996 - val_mse: 12.4297
    Epoch 54/100
    354/354 [==============================] - 0s 183us/sample - loss: 7.7929 - mae: 1.8971 - mse: 7.7929 - val_loss: 11.9751 - val_mae: 2.2491 - val_mse: 11.9751
    Epoch 55/100
    354/354 [==============================] - 0s 185us/sample - loss: 7.4411 - mae: 1.8631 - mse: 7.4411 - val_loss: 11.3761 - val_mae: 2.3416 - val_mse: 11.3761
    Epoch 56/100
    354/354 [==============================] - 0s 186us/sample - loss: 7.6105 - mae: 1.9111 - mse: 7.6105 - val_loss: 12.4939 - val_mae: 2.4095 - val_mse: 12.4939
    Epoch 57/100
    354/354 [==============================] - 0s 190us/sample - loss: 7.5013 - mae: 1.9146 - mse: 7.5013 - val_loss: 11.6668 - val_mae: 2.1468 - val_mse: 11.6668
    Epoch 58/100
    354/354 [==============================] - 0s 195us/sample - loss: 7.4096 - mae: 1.8515 - mse: 7.4096 - val_loss: 13.8000 - val_mae: 2.5222 - val_mse: 13.8000
    Epoch 59/100
    354/354 [==============================] - 0s 180us/sample - loss: 7.2263 - mae: 1.8241 - mse: 7.2263 - val_loss: 10.8964 - val_mae: 2.2130 - val_mse: 10.8964
    Epoch 60/100
    354/354 [==============================] - 0s 161us/sample - loss: 7.1773 - mae: 1.8526 - mse: 7.1773 - val_loss: 10.7862 - val_mae: 2.1088 - val_mse: 10.7862
    Epoch 61/100
    354/354 [==============================] - 0s 165us/sample - loss: 7.0812 - mae: 1.8308 - mse: 7.0812 - val_loss: 10.8147 - val_mae: 2.3209 - val_mse: 10.8147
    Epoch 62/100
    354/354 [==============================] - 0s 155us/sample - loss: 7.2235 - mae: 1.8367 - mse: 7.2235 - val_loss: 11.0399 - val_mae: 2.2583 - val_mse: 11.0399
    Epoch 63/100
    354/354 [==============================] - 0s 155us/sample - loss: 7.0341 - mae: 1.8172 - mse: 7.0341 - val_loss: 10.9894 - val_mae: 2.1429 - val_mse: 10.9894
    Epoch 64/100
    354/354 [==============================] - 0s 157us/sample - loss: 6.8729 - mae: 1.7492 - mse: 6.8729 - val_loss: 10.5465 - val_mae: 2.1532 - val_mse: 10.5465
    Epoch 65/100
    354/354 [==============================] - 0s 164us/sample - loss: 6.9345 - mae: 1.7837 - mse: 6.9345 - val_loss: 11.5379 - val_mae: 2.1963 - val_mse: 11.5379
    Epoch 66/100
    354/354 [==============================] - 0s 166us/sample - loss: 6.8218 - mae: 1.7714 - mse: 6.8218 - val_loss: 10.1486 - val_mae: 2.1617 - val_mse: 10.1486
    Epoch 67/100
    354/354 [==============================] - 0s 157us/sample - loss: 6.8711 - mae: 1.8045 - mse: 6.8711 - val_loss: 10.3196 - val_mae: 2.2297 - val_mse: 10.3196
    Epoch 68/100
    354/354 [==============================] - 0s 162us/sample - loss: 6.7281 - mae: 1.7762 - mse: 6.7281 - val_loss: 11.2361 - val_mae: 2.2046 - val_mse: 11.2361
    Epoch 69/100
    354/354 [==============================] - 0s 158us/sample - loss: 6.5518 - mae: 1.7292 - mse: 6.5518 - val_loss: 10.2378 - val_mae: 2.1494 - val_mse: 10.2378
    Epoch 70/100
    354/354 [==============================] - 0s 161us/sample - loss: 6.6489 - mae: 1.7383 - mse: 6.6489 - val_loss: 11.1613 - val_mae: 2.2212 - val_mse: 11.1613
    Epoch 71/100
    354/354 [==============================] - 0s 176us/sample - loss: 6.5827 - mae: 1.7564 - mse: 6.5827 - val_loss: 10.0177 - val_mae: 2.2440 - val_mse: 10.0177
    Epoch 72/100
    354/354 [==============================] - 0s 168us/sample - loss: 6.3411 - mae: 1.7463 - mse: 6.3411 - val_loss: 10.7929 - val_mae: 2.1946 - val_mse: 10.7929
    Epoch 73/100
    354/354 [==============================] - 0s 163us/sample - loss: 6.3621 - mae: 1.7466 - mse: 6.3621 - val_loss: 9.7344 - val_mae: 2.1441 - val_mse: 9.7344
    Epoch 74/100
    354/354 [==============================] - 0s 158us/sample - loss: 6.2298 - mae: 1.7411 - mse: 6.2298 - val_loss: 11.2495 - val_mae: 2.1948 - val_mse: 11.2495
    Epoch 75/100
    354/354 [==============================] - 0s 159us/sample - loss: 6.3037 - mae: 1.7169 - mse: 6.3037 - val_loss: 10.1339 - val_mae: 2.1716 - val_mse: 10.1339
    Epoch 76/100
    354/354 [==============================] - 0s 158us/sample - loss: 6.0780 - mae: 1.6686 - mse: 6.0780 - val_loss: 11.9975 - val_mae: 2.3317 - val_mse: 11.9975
    Epoch 77/100
    354/354 [==============================] - 0s 165us/sample - loss: 6.3311 - mae: 1.7082 - mse: 6.3311 - val_loss: 11.6433 - val_mae: 2.2756 - val_mse: 11.6433
    Epoch 78/100
    354/354 [==============================] - 0s 155us/sample - loss: 6.0620 - mae: 1.6765 - mse: 6.0620 - val_loss: 13.0159 - val_mae: 2.5073 - val_mse: 13.0159
    Epoch 79/100
    354/354 [==============================] - 0s 167us/sample - loss: 6.1819 - mae: 1.7157 - mse: 6.1819 - val_loss: 10.1000 - val_mae: 2.1462 - val_mse: 10.1000
    Epoch 80/100
    354/354 [==============================] - 0s 158us/sample - loss: 5.9085 - mae: 1.6720 - mse: 5.9085 - val_loss: 11.7867 - val_mae: 2.5045 - val_mse: 11.7866
    Epoch 81/100
    354/354 [==============================] - 0s 168us/sample - loss: 6.0201 - mae: 1.6678 - mse: 6.0201 - val_loss: 10.8789 - val_mae: 2.3031 - val_mse: 10.8789
    Epoch 82/100
    354/354 [==============================] - 0s 159us/sample - loss: 6.1278 - mae: 1.6799 - mse: 6.1278 - val_loss: 9.8114 - val_mae: 2.1048 - val_mse: 9.8114
    Epoch 83/100
    354/354 [==============================] - 0s 150us/sample - loss: 5.6372 - mae: 1.6280 - mse: 5.6372 - val_loss: 10.0971 - val_mae: 2.1464 - val_mse: 10.0971
    Epoch 84/100
    354/354 [==============================] - 0s 153us/sample - loss: 5.9587 - mae: 1.6421 - mse: 5.9587 - val_loss: 9.4731 - val_mae: 2.1915 - val_mse: 9.4731
    Epoch 85/100
    354/354 [==============================] - 0s 158us/sample - loss: 5.6189 - mae: 1.6223 - mse: 5.6189 - val_loss: 9.9788 - val_mae: 2.3332 - val_mse: 9.9788
    Epoch 86/100
    354/354 [==============================] - 0s 158us/sample - loss: 5.8193 - mae: 1.6930 - mse: 5.8193 - val_loss: 10.4070 - val_mae: 2.1490 - val_mse: 10.4070
    Epoch 87/100
    354/354 [==============================] - 0s 155us/sample - loss: 5.5919 - mae: 1.6152 - mse: 5.5919 - val_loss: 9.9985 - val_mae: 2.2546 - val_mse: 9.9985
    Epoch 88/100
    354/354 [==============================] - 0s 160us/sample - loss: 5.6652 - mae: 1.6246 - mse: 5.6652 - val_loss: 9.1506 - val_mae: 2.0642 - val_mse: 9.1506
    Epoch 89/100
    354/354 [==============================] - 0s 157us/sample - loss: 5.6349 - mae: 1.6108 - mse: 5.6349 - val_loss: 9.8522 - val_mae: 2.0813 - val_mse: 9.8522
    Epoch 90/100
    354/354 [==============================] - 0s 159us/sample - loss: 5.6165 - mae: 1.6449 - mse: 5.6165 - val_loss: 9.1553 - val_mae: 2.0421 - val_mse: 9.1553
    Epoch 91/100
    354/354 [==============================] - 0s 161us/sample - loss: 5.5416 - mae: 1.6153 - mse: 5.5416 - val_loss: 10.4231 - val_mae: 2.2880 - val_mse: 10.4231
    Epoch 92/100
    354/354 [==============================] - 0s 158us/sample - loss: 5.3909 - mae: 1.5863 - mse: 5.3909 - val_loss: 8.8087 - val_mae: 2.1022 - val_mse: 8.8087
    Epoch 93/100
    354/354 [==============================] - 0s 155us/sample - loss: 5.3540 - mae: 1.5986 - mse: 5.3540 - val_loss: 9.6963 - val_mae: 2.1931 - val_mse: 9.6963
    Epoch 94/100
    354/354 [==============================] - 0s 161us/sample - loss: 5.3198 - mae: 1.6074 - mse: 5.3198 - val_loss: 9.1875 - val_mae: 2.1917 - val_mse: 9.1875
    Epoch 95/100
    354/354 [==============================] - 0s 165us/sample - loss: 5.2299 - mae: 1.5638 - mse: 5.2299 - val_loss: 8.8746 - val_mae: 2.1273 - val_mse: 8.8746
    Epoch 96/100
    354/354 [==============================] - 0s 163us/sample - loss: 5.2789 - mae: 1.5651 - mse: 5.2789 - val_loss: 9.7351 - val_mae: 2.2359 - val_mse: 9.7351
    Epoch 97/100
    354/354 [==============================] - 0s 153us/sample - loss: 5.3399 - mae: 1.6002 - mse: 5.3399 - val_loss: 9.7185 - val_mae: 2.1080 - val_mse: 9.7185
    Epoch 98/100
    354/354 [==============================] - 0s 159us/sample - loss: 5.0072 - mae: 1.5055 - mse: 5.0072 - val_loss: 8.3621 - val_mae: 2.0586 - val_mse: 8.3621
    Epoch 99/100
    354/354 [==============================] - 0s 156us/sample - loss: 5.2596 - mae: 1.5557 - mse: 5.2596 - val_loss: 8.6406 - val_mae: 2.0527 - val_mse: 8.6406
    Epoch 100/100
    354/354 [==============================] - 0s 159us/sample - loss: 5.0983 - mae: 1.5543 - mse: 5.0983 - val_loss: 8.4836 - val_mae: 2.0234 - val_mse: 8.4836
 %% Cell type:markdown id: tags:
 ## Step 6 - Evaluate
 ### 6.1 - Model evaluation
 MAE =  Mean Absolute Error (between the labels and predictions)
 A mae equal to 3 represents an average error in prediction of $3k.
 %% Cell type:code id: tags:
 ``` python
 score = model.evaluate(x_test, y_test, verbose=0)
 print('x_test / loss      : {:5.4f}'.format(score[0]))
 print('x_test / mae       : {:5.4f}'.format(score[1]))
 print('x_test / mse       : {:5.4f}'.format(score[2]))
 ```
 %% Output
    x_test / loss      : 8.4836
    x_test / mae       : 2.0234
    x_test / mse       : 8.4836
 %% Cell type:markdown id: tags:
 ### 6.2 - Training history
 What was the best result during our training ?
 %% Cell type:code id: tags:
 ``` python
 df=pd.DataFrame(data=history.history)
 df.describe()
 ```
 %% Output
                 loss         mae         mse    val_loss     val_mae     val_mse
    count  100.000000  100.000000  100.000000  100.000000  100.000000  100.000000
    mean    15.144930    2.312168   15.144930   17.019036    2.582618   17.019036
    std     43.707091    1.906713   43.707090   26.587745    1.288267   26.587746
    min      5.007155    1.505515    5.007155    8.362053    2.023406    8.362053
    25%      6.285225    1.716563    6.285225   10.419040    2.192718   10.419040
    50%      8.037316    1.922454    8.037317   12.488579    2.301342   12.488580
    75%     10.482029    2.189933   10.482029   14.470699    2.503943   14.470701
    max    414.560260   18.257650  414.560242  266.372801   13.991282  266.372803
 %% Cell type:code id: tags:
 ``` python
 print("min( val_mae ) : {:.4f}".format( min(history.history["val_mae"]) ) )
 ```
 %% Output
    min( val_mae ) : 2.0234
 %% Cell type:code id: tags:
 ``` python
 ooo.plot_history(history, plot={'MSE' :['mse', 'val_mse'],
                                'MAE' :['mae', 'val_mae'],
                                'LOSS':['loss','val_loss']})
 ```
 %% Output
 %% Cell type:markdown id: tags:
 ## Step 7 - Make a prediction
 %% Cell type:code id: tags:
 ``` python
 my_data = [ 1.26425925, -0.48522739,  1.0436489 , -0.23112788,  1.37120745,
       -2.14308942,  1.13489104, -1.06802005,  1.71189006,  1.57042287,
        0.77859951,  0.14769795,  2.7585581 ]
 real_price = 10.4
 my_data=np.array(my_data).reshape(1,13)
 ```
 %% Cell type:code id: tags:
 ``` python
 predictions = model.predict( my_data )
 print("Prédiction : {:.2f} K$".format(predictions[0][0]))
 print("Reality    : {:.2f} K$".format(real_price))
 ```
 %% Output
    Prédiction : 11.59 K$
    Reality    : 10.40 K$
 %% Cell type:markdown id: tags:
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