Diabetes-Vorhersage

Wir importieren zunächst Keras und Numpy und laden den Datensatz.

In [1]:
import keras

C:\Users\Sebastian\Anaconda3\lib\site-packages\h5py\__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.
  from ._conv import register_converters as _register_converters
Using Theano backend.
In [2]:
import numpy as np
In [6]:
data = np.loadtxt('diabetes.csv', delimiter=',')

Die Daten bestehen aus 8 features mit Diabetes-Indikatoren sowie einem binären Ausgabewert, welcher angibt ob der Patient fünf Jahre später Diabetes entwickelt hat.

In [7]:
data
Out[7]:
array([[  6.   , 148.   ,  72.   , ...,   0.627,  50.   ,   1.   ],
       [  1.   ,  85.   ,  66.   , ...,   0.351,  31.   ,   0.   ],
       [  8.   , 183.   ,  64.   , ...,   0.672,  32.   ,   1.   ],
       ...,
       [  5.   , 121.   ,  72.   , ...,   0.245,  30.   ,   0.   ],
       [  1.   , 126.   ,  60.   , ...,   0.349,  47.   ,   1.   ],
       [  1.   ,  93.   ,  70.   , ...,   0.315,  23.   ,   0.   ]])
In [8]:
data.shape
Out[8]:
(768, 9)

Wir trennen die Daten in Trainings- und Testdaten auf.

In [9]:
X = data[:,:8]
In [10]:
y = data[:, 8]

Wir verwenden ein sequentielles Netzwerk, d.h. eines bei welchem Informationen lediglich von einer Lage zur nächsten weiter gegeben werden.

In [11]:
from keras.models import Sequential

Wir bauen nun zunächst das Netzwerk Lage für Lage auf, und müssen dazu zunächst eine Instanz eines sequentiellen Netzwerken initialisieren.

In [12]:
model = Sequential()

Unser Netzwerk besteht lediglich aus dichten Lagen.

In [13]:
from keras.layers import Dense

Der ersten Lage muss die Input-Dimension, d.h. die Anzahl features vorgegeben werden. Jede Lage benötigt darüber hinaus eine Initialisation der Gewichte sowie eine nichtlineare Aktivierungsfunktion.

In [16]:
model.add(Dense(12, input_dim=8, kernel_initializer='uniform', activation='relu'))
In [18]:
model.add(Dense(8, kernel_initializer='uniform', activation='relu'))

Die Ausgabelage muss der Problemstellung entsprechen. Hier handelt es sich lediglich um eine Ja/Nein-Entscheidung, d.h. eine binäre Klassifikation, es wird daher lediglich ein Knoten verwendet welcher die Wahrscheinlichkeit ausgibt.

In [19]:
model.add(Dense(1, kernel_initializer='uniform', activation='relu'))

Unser Netzwerk ist vollständig aufgebaut und kann nun kompiliert werden, d.h. wir versehen es mit einer loss-Funktion, einer Optimierungsmethode und einer Auswertungsmetrik.

In [20]:
model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy'])

Nun kann das Netzwerk mit den oben bereit gestellten Daten trainiert werden.

In [21]:
model.fit(X, y, epochs=150, batch_size=10, verbose=2)

Epoch 1/150
 - 0s - loss: 1.1076 - acc: 0.6576
Epoch 2/150
 - 0s - loss: 0.6063 - acc: 0.6771
Epoch 3/150
 - 0s - loss: 0.5989 - acc: 0.6758
Epoch 4/150
 - 0s - loss: 0.5932 - acc: 0.6810
Epoch 5/150
 - 0s - loss: 0.5918 - acc: 0.6901
Epoch 6/150
 - 0s - loss: 0.5845 - acc: 0.6797
Epoch 7/150
 - 0s - loss: 0.5824 - acc: 0.6901
Epoch 8/150
 - 0s - loss: 0.5732 - acc: 0.6953
Epoch 9/150
 - 0s - loss: 0.5675 - acc: 0.7266
Epoch 10/150
 - 0s - loss: 0.5627 - acc: 0.7240
Epoch 11/150
 - 0s - loss: 0.5531 - acc: 0.7057
Epoch 12/150
 - 0s - loss: 0.5474 - acc: 0.7266
Epoch 13/150
 - 0s - loss: 0.5503 - acc: 0.7292
Epoch 14/150
 - 0s - loss: 0.5411 - acc: 0.7435
Epoch 15/150
 - 0s - loss: 0.5561 - acc: 0.7357
Epoch 16/150
 - 0s - loss: 0.5641 - acc: 0.7227
Epoch 17/150
 - 0s - loss: 0.5453 - acc: 0.7214
Epoch 18/150
 - 0s - loss: 0.5411 - acc: 0.7370
Epoch 19/150
 - 0s - loss: 0.5620 - acc: 0.7253
Epoch 20/150
 - 0s - loss: 0.5409 - acc: 0.7266
Epoch 21/150
 - 0s - loss: 0.5335 - acc: 0.7292
Epoch 22/150
 - 0s - loss: 0.5317 - acc: 0.7461
Epoch 23/150
 - 0s - loss: 0.5339 - acc: 0.7331
Epoch 24/150
 - 0s - loss: 0.5358 - acc: 0.7370
Epoch 25/150
 - 0s - loss: 0.5321 - acc: 0.7370
Epoch 26/150
 - 0s - loss: 0.5298 - acc: 0.7422
Epoch 27/150
 - 0s - loss: 0.5277 - acc: 0.7318
Epoch 28/150
 - 0s - loss: 0.5301 - acc: 0.7292
Epoch 29/150
 - 0s - loss: 0.5262 - acc: 0.7383
Epoch 30/150
 - 0s - loss: 0.5460 - acc: 0.7292
Epoch 31/150
 - 0s - loss: 0.5225 - acc: 0.7461
Epoch 32/150
 - 0s - loss: 0.5283 - acc: 0.7435
Epoch 33/150
 - 0s - loss: 0.5231 - acc: 0.7474
Epoch 34/150
 - 0s - loss: 0.5388 - acc: 0.7487
Epoch 35/150
 - 0s - loss: 0.5168 - acc: 0.7409
Epoch 36/150
 - 0s - loss: 0.5177 - acc: 0.7435
Epoch 37/150
 - 0s - loss: 0.5196 - acc: 0.7526
Epoch 38/150
 - 0s - loss: 0.5183 - acc: 0.7370
Epoch 39/150
 - 0s - loss: 0.5329 - acc: 0.7474
Epoch 40/150
 - 0s - loss: 0.5127 - acc: 0.7461
Epoch 41/150
 - 0s - loss: 0.5379 - acc: 0.7435
Epoch 42/150
 - 0s - loss: 0.5071 - acc: 0.7383
Epoch 43/150
 - 0s - loss: 0.5339 - acc: 0.7474
Epoch 44/150
 - 0s - loss: 0.5018 - acc: 0.7565
Epoch 45/150
 - 0s - loss: 0.5181 - acc: 0.7448
Epoch 46/150
 - 0s - loss: 0.5055 - acc: 0.7526
Epoch 47/150
 - 0s - loss: 0.5143 - acc: 0.7682
Epoch 48/150
 - 0s - loss: 0.5654 - acc: 0.7370
Epoch 49/150
 - 0s - loss: 0.5193 - acc: 0.7435
Epoch 50/150
 - 0s - loss: 0.5085 - acc: 0.7682
Epoch 51/150
 - 0s - loss: 0.5063 - acc: 0.7578
Epoch 52/150
 - 0s - loss: 0.5018 - acc: 0.7630
Epoch 53/150
 - 0s - loss: 0.5215 - acc: 0.7552
Epoch 54/150
 - 0s - loss: 0.5123 - acc: 0.7578
Epoch 55/150
 - 0s - loss: 0.5136 - acc: 0.7513
Epoch 56/150
 - 0s - loss: 0.5254 - acc: 0.7565
Epoch 57/150
 - 0s - loss: 0.4955 - acc: 0.7812
Epoch 58/150
 - 0s - loss: 0.4899 - acc: 0.7604
Epoch 59/150
 - 0s - loss: 0.4963 - acc: 0.7513
Epoch 60/150
 - 0s - loss: 0.4897 - acc: 0.7552
Epoch 61/150
 - 0s - loss: 0.4996 - acc: 0.7695
Epoch 62/150
 - 0s - loss: 0.5099 - acc: 0.7617
Epoch 63/150
 - 0s - loss: 0.6380 - acc: 0.7344
Epoch 64/150
 - 0s - loss: 0.5120 - acc: 0.7552
Epoch 65/150
 - 0s - loss: 0.4980 - acc: 0.7682
Epoch 66/150
 - 0s - loss: 0.4921 - acc: 0.7695
Epoch 67/150
 - 0s - loss: 0.4878 - acc: 0.7617
Epoch 68/150
 - 0s - loss: 0.4963 - acc: 0.7591
Epoch 69/150
 - 0s - loss: 0.4850 - acc: 0.7526
Epoch 70/150
 - 0s - loss: 0.4962 - acc: 0.7552
Epoch 71/150
 - 0s - loss: 0.4777 - acc: 0.7708
Epoch 72/150
 - 0s - loss: 0.4813 - acc: 0.7760
Epoch 73/150
 - 0s - loss: 0.4852 - acc: 0.7617
Epoch 74/150
 - 0s - loss: 0.4802 - acc: 0.7695
Epoch 75/150
 - 0s - loss: 0.4844 - acc: 0.7591
Epoch 76/150
 - 0s - loss: 0.4811 - acc: 0.7552
Epoch 77/150
 - 0s - loss: 0.4810 - acc: 0.7695
Epoch 78/150
 - 0s - loss: 0.5463 - acc: 0.7461
Epoch 79/150
 - 0s - loss: 0.5016 - acc: 0.7552
Epoch 80/150
 - 0s - loss: 0.4898 - acc: 0.7669
Epoch 81/150
 - 0s - loss: 0.4793 - acc: 0.7669
Epoch 82/150
 - 0s - loss: 0.4812 - acc: 0.7578
Epoch 83/150
 - 0s - loss: 0.4734 - acc: 0.7656
Epoch 84/150
 - 0s - loss: 0.4716 - acc: 0.7578
Epoch 85/150
 - 0s - loss: 0.8901 - acc: 0.7383
Epoch 86/150
 - 0s - loss: 0.5346 - acc: 0.7357
Epoch 87/150
 - 0s - loss: 0.5222 - acc: 0.7526
Epoch 88/150
 - 0s - loss: 0.5037 - acc: 0.7552
Epoch 89/150
 - 0s - loss: 0.4978 - acc: 0.7656
Epoch 90/150
 - 0s - loss: 0.4903 - acc: 0.7695
Epoch 91/150
 - 0s - loss: 0.4834 - acc: 0.7695
Epoch 92/150
 - 0s - loss: 0.4807 - acc: 0.7578
Epoch 93/150
 - 0s - loss: 0.4812 - acc: 0.7747
Epoch 94/150
 - 0s - loss: 0.4770 - acc: 0.7695
Epoch 95/150
 - 0s - loss: 0.4799 - acc: 0.7630
Epoch 96/150
 - 0s - loss: 0.4750 - acc: 0.7591
Epoch 97/150
 - 0s - loss: 0.4988 - acc: 0.7604
Epoch 98/150
 - 0s - loss: 0.4777 - acc: 0.7565
Epoch 99/150
 - 0s - loss: 0.4767 - acc: 0.7617
Epoch 100/150
 - 0s - loss: 0.4938 - acc: 0.7669
Epoch 101/150
 - 0s - loss: 0.4905 - acc: 0.7591
Epoch 102/150
 - 0s - loss: 0.4863 - acc: 0.7565
Epoch 103/150
 - 0s - loss: 0.4753 - acc: 0.7630
Epoch 104/150
 - 0s - loss: 0.4833 - acc: 0.7643
Epoch 105/150
 - 0s - loss: 0.4756 - acc: 0.7695
Epoch 106/150
 - 0s - loss: 0.4840 - acc: 0.7656
Epoch 107/150
 - 0s - loss: 0.4739 - acc: 0.7695
Epoch 108/150
 - 0s - loss: 0.4737 - acc: 0.7669
Epoch 109/150
 - 0s - loss: 0.7047 - acc: 0.7578
Epoch 110/150
 - 0s - loss: 0.6306 - acc: 0.7305
Epoch 111/150
 - 0s - loss: 0.5035 - acc: 0.7604
Epoch 112/150
 - 0s - loss: 0.5001 - acc: 0.7578
Epoch 113/150
 - 0s - loss: 0.4978 - acc: 0.7682
Epoch 114/150
 - 0s - loss: 0.4953 - acc: 0.7773
Epoch 115/150
 - 0s - loss: 0.4938 - acc: 0.7734
Epoch 116/150
 - 0s - loss: 0.4921 - acc: 0.7773
Epoch 117/150
 - 0s - loss: 0.4922 - acc: 0.7747
Epoch 118/150
 - 0s - loss: 0.4911 - acc: 0.7695
Epoch 119/150
 - 0s - loss: 0.4890 - acc: 0.7669
Epoch 120/150
 - 0s - loss: 0.4885 - acc: 0.7695
Epoch 121/150
 - 0s - loss: 0.4897 - acc: 0.7812
Epoch 122/150
 - 0s - loss: 0.4896 - acc: 0.7669
Epoch 123/150
 - 0s - loss: 0.4845 - acc: 0.7708
Epoch 124/150
 - 0s - loss: 0.4839 - acc: 0.7656
Epoch 125/150
 - 0s - loss: 0.4834 - acc: 0.7721
Epoch 126/150
 - 0s - loss: 0.4836 - acc: 0.7773
Epoch 127/150
 - 0s - loss: 0.4842 - acc: 0.7773
Epoch 128/150
 - 0s - loss: 0.4813 - acc: 0.7721
Epoch 129/150
 - 0s - loss: 0.4805 - acc: 0.7708
Epoch 130/150
 - 0s - loss: 0.4790 - acc: 0.7734
Epoch 131/150
 - 0s - loss: 0.4795 - acc: 0.7708
Epoch 132/150
 - 0s - loss: 0.4968 - acc: 0.7669
Epoch 133/150
 - 0s - loss: 0.4793 - acc: 0.7708
Epoch 134/150
 - 0s - loss: 0.4781 - acc: 0.7760
Epoch 135/150
 - 0s - loss: 0.4780 - acc: 0.7682
Epoch 136/150
 - 0s - loss: 0.4759 - acc: 0.7682
Epoch 137/150
 - 0s - loss: 0.4764 - acc: 0.7604
Epoch 138/150
 - 0s - loss: 0.4924 - acc: 0.7747
Epoch 139/150
 - 0s - loss: 0.4948 - acc: 0.7500
Epoch 140/150
 - 0s - loss: 0.4757 - acc: 0.7799
Epoch 141/150
 - 0s - loss: 0.4797 - acc: 0.7708
Epoch 142/150
 - 0s - loss: 0.4735 - acc: 0.7656
Epoch 143/150
 - 0s - loss: 0.5145 - acc: 0.7565
Epoch 144/150
 - 0s - loss: 0.4779 - acc: 0.7721
Epoch 145/150
 - 0s - loss: 0.4784 - acc: 0.7734
Epoch 146/150
 - 0s - loss: 0.4920 - acc: 0.7682
Epoch 147/150
 - 0s - loss: 0.4758 - acc: 0.7656
Epoch 148/150
 - 0s - loss: 0.4723 - acc: 0.7708
Epoch 149/150
 - 0s - loss: 0.4915 - acc: 0.7721
Epoch 150/150
 - 0s - loss: 0.4737 - acc: 0.7734
Out[21]:
<keras.callbacks.History at 0x275da361f60>

Zu guter Letzt machen wir Vorhersagen über die Trainingsdatenpunkte (in der Realität würden wir Vorhersagen für neue Patienten treffen wollen).

In [22]:
predictions = model.predict(X)
In [23]:
predictions
Out[23]:
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Wir wandeln noch die Wahrscheinlichkeiten in eine Ja/Nein-Vorhersage um.

In [24]:
rounded = [round(x[0]) for x in predictions]
In [25]:
print(rounded)

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MNIST: Vorhersage handschriftlicher Ziffern

In [30]:
from keras.datasets import mnist
In [ ]:
data = mnist.load_data()
In [26]:
data = np.load('mnist.npz')
In [27]:
data.keys()
Out[27]:
['x_test', 'x_train', 'y_train', 'y_test']
In [36]:
X_train = data['x_train']
X_test = data['x_test']
y_train = data['y_train']
y_test = data['y_test']
In [66]:
X_test_plot = data['x_test']
In [31]:
print(X_train.shape)

(60000, 28, 28)
In [32]:
import matplotlib.pyplot as plt
In [33]:
plt.imshow(X_train[0])
Out[33]:
<matplotlib.image.AxesImage at 0x275da6d1240>
In [37]:
X_train = X_train.reshape(X_train.shape[0], 28, 28, 1)
X_test = X_test.reshape(X_test.shape[0], 28, 28, 1)
In [38]:
print(X_train.shape)

(60000, 28, 28, 1)
In [40]:
X_train = X_train.astype('float32')
In [41]:
X_test = X_test.astype('float32')
In [42]:
X_train /= 255
In [43]:
X_test /= 255
In [44]:
y_train.shape
Out[44]:
(60000,)
In [45]:
y_train[:10]
Out[45]:
array([5, 0, 4, 1, 9, 2, 1, 3, 1, 4], dtype=uint8)
In [46]:
from keras.utils import np_utils
In [47]:
Y_train = np_utils.to_categorical(y_train, 10)
Y_test = np_utils.to_categorical(y_test, 10)
In [48]:
Y_train[:10]
Out[48]:
array([[0., 0., 0., 0., 0., 1., 0., 0., 0., 0.],
       [1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],
       [0., 1., 0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0., 0., 1.],
       [0., 0., 1., 0., 0., 0., 0., 0., 0., 0.],
       [0., 1., 0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 1., 0., 0., 0., 0., 0., 0.],
       [0., 1., 0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 1., 0., 0., 0., 0., 0.]], dtype=float32)
In [49]:
model = Sequential()
In [50]:
from keras.layers import Dense, Dropout, Activation, Flatten
from keras.layers import Convolution2D, MaxPooling2D
In [51]:
model.add(Convolution2D(32, (3,3), activation='relu', input_shape=(28,28,1)))
In [52]:
model.add(Convolution2D(32, (3,3), activation='relu'))
In [53]:
model.add(MaxPooling2D(pool_size=(2,2)))
In [54]:
model.add(Dropout(0.25))
In [55]:
model.add(Flatten())
In [56]:
model.add(Dense(128, activation='relu'))
In [57]:
model.add(Dropout(0.25))
In [58]:
model.add(Dense(10, activation='softmax'))
In [59]:
model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])
In [61]:
model.fit(X_train, Y_train, batch_size=32, nb_epoch=10)

C:\Users\Sebastian\Anaconda3\lib\site-packages\ipykernel_launcher.py:1: UserWarning: The `nb_epoch` argument in `fit` has been renamed `epochs`.
  """Entry point for launching an IPython kernel.

Epoch 1/10
60000/60000 [==============================] - 157s 3ms/step - loss: 0.1530 - acc: 0.9533
Epoch 2/10
60000/60000 [==============================] - 167s 3ms/step - loss: 0.0582 - acc: 0.9825
Epoch 3/10
60000/60000 [==============================] - 168s 3ms/step - loss: 0.0435 - acc: 0.9866
Epoch 4/10
60000/60000 [==============================] - 166s 3ms/step - loss: 0.0345 - acc: 0.9890
Epoch 5/10
60000/60000 [==============================] - 168s 3ms/step - loss: 0.0302 - acc: 0.9905
Epoch 6/10
60000/60000 [==============================] - 165s 3ms/step - loss: 0.0239 - acc: 0.9921
Epoch 7/10
60000/60000 [==============================] - 163s 3ms/step - loss: 0.0205 - acc: 0.9931
Epoch 8/10
60000/60000 [==============================] - 161s 3ms/step - loss: 0.0171 - acc: 0.9945
Epoch 9/10
60000/60000 [==============================] - 167s 3ms/step - loss: 0.0155 - acc: 0.9949
Epoch 10/10
60000/60000 [==============================] - 160s 3ms/step - loss: 0.0152 - acc: 0.9949
Out[61]:
<keras.callbacks.History at 0x275db588cf8>
In [62]:
score = model.evaluate(X_test, Y_test, verbose=0)
In [63]:
score
Out[63]:
[0.03348006168393522, 0.9925]
In [67]:
plt.imshow(X_test_plot[0])
Out[67]:
<matplotlib.image.AxesImage at 0x275de47afd0>
In [69]:
model.predict(X_test)[0]
Out[69]:
array([4.04813854e-17, 4.27083976e-12, 3.23459569e-16, 8.13762252e-12,
       7.12233578e-19, 1.30600265e-16, 6.17592616e-24, 1.00000000e+00,
       1.02562075e-17, 1.10087122e-11], dtype=float32)
In [70]:
predictions = model.predict(X_test)
In [77]:
maximum = predictions.max(axis=1)
In [96]:
worst = [pos for pos in range(len(maximum)) if maximum[pos] < 0.5]
In [97]:
worst
Out[97]:
[659, 2109, 3225, 3558, 3778]
In [95]:
maximum[maximum < 0.5]
Out[95]:
array([0.4468845 , 0.49009094, 0.4399654 , 0.45273992, 0.48349267],
      dtype=float32)
In [101]:
print(predictions[worst[0]])
plt.imshow(X_test_plot[worst[0]])

[1.8582364e-08 4.4688451e-01 4.4022337e-01 1.0641524e-04 2.0676863e-07
 2.8719619e-08 4.8901544e-08 1.1275269e-01 1.0769197e-05 2.1960152e-05]
Out[101]:
<matplotlib.image.AxesImage at 0x275df5c2828>
In [106]:
y_test[worst[0]]
Out[106]:
2
In [102]:
print(predictions[worst[1]])
plt.imshow(X_test_plot[worst[1]])

[1.11594955e-08 3.62636627e-07 4.90090936e-01 7.70639032e-02
 4.63825527e-05 1.42198387e-05 9.87513715e-09 3.44737507e-02
 2.82777622e-02 3.70032668e-01]
Out[102]:
<matplotlib.image.AxesImage at 0x275df61c0b8>
In [107]:
y_test[worst[1]]
Out[107]:
3
In [103]:
print(predictions[worst[2]])
plt.imshow(X_test_plot[worst[2]])

[2.9086951e-07 2.9520717e-01 2.5429060e-06 1.8368043e-08 7.7149051e-04
 1.6801668e-08 3.4765837e-09 2.6258096e-01 1.4720911e-03 4.3996540e-01]
Out[103]:
<matplotlib.image.AxesImage at 0x275df66a9e8>
In [108]:
y_test[worst[2]]
Out[108]:
7
In [104]:
print(predictions[worst[3]])
plt.imshow(X_test_plot[worst[3]])

[4.5273992e-01 1.6775812e-04 1.7671537e-04 3.9434606e-01 5.1602549e-03
 1.3727109e-01 2.6351993e-03 5.2576601e-03 9.3135604e-05 2.1522050e-03]
Out[104]:
<matplotlib.image.AxesImage at 0x275df6c7278>
In [109]:
y_test[worst[3]]
Out[109]:
5
In [105]:
print(predictions[worst[4]])
plt.imshow(X_test_plot[worst[4]])

[1.35544411e-04 7.51636890e-07 1.00647576e-01 6.27233589e-04
 2.79875144e-06 4.83492672e-01 9.12043499e-04 1.12293565e-04
 3.85679334e-01 2.83897724e-02]
Out[105]:
<matplotlib.image.AxesImage at 0x275df716ba8>
In [110]:
y_test[worst[4]]
Out[110]:
5