Machine learning week 5(Andrew Ng)

Neural network training

1、Neural network training

• Binary cross entropy, which we’ve also referred to as logistic loss, is used for classifying between two classes (two categories).

2、Activation Functions

Some examples:

For the output layer:

For the hidden layer:
When the curve is too flat, the gradient descent is slow, so the relu is more commonly used by people

ReLU is a Non-Linear activation. When $z$ is equal to zero,$wx+b$ equals zero, so $x$ is not necessarily equal to zero.RELU

3、Multiclass classification

3.1、Softmax

3.2、Neural networks with softmax output

Change the output layer from 1 unit to 10 units.

3.3、Improved implementation of softmax

When we calculate 1 plus 1/10000 minus 1 minus 1/10000, it will be equal to 2/10000 after we simplify it. But the result in the jupyter notebook is 0.000199999999999978. There’s some round-off error. Because the computer has only a finite amount of memory to store each number, called a floating-point number in this case.

Tensorflow calculates Z as an intermediate value, but it can rearrange the items to make it more accurate.

The origin code

import numpy as np
import matplotlib.pyplot as plt
plt.style.use('./deeplearning.mplstyle')
import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense
from IPython.display import display, Markdown, Latex
from sklearn.datasets import make_blobs
%matplotlib widget
from matplotlib.widgets import Slider
from lab_utils_common import dlc
from lab_utils_softmax import plt_softmax
import logging
logging.getLogger("tensorflow").setLevel(logging.ERROR)
tf.autograph.set_verbosity(0)


# make  dataset for example
centers = [[-5, 2], [-2, -2], [1, 2], [5, -2]]
# use Scikit-Learn make_blobs function to make a training data set 
X_train, y_train = make_blobs(n_samples=2000, centers=centers, cluster_std=1.0,random_state=30)


model = Sequential(
    [ 
        Dense(25, activation = 'relu'),
        Dense(15, activation = 'relu'),
        Dense(4, activation = 'softmax')    # < softmax activation here
    ]
)
model.compile(
    loss=tf.keras.losses.SparseCategoricalCrossentropy(),
    optimizer=tf.keras.optimizers.Adam(0.001),
)

model.fit(
    X_train,y_train,
    epochs=10
)
# Because the softmax is integrated into the output layer, the output is a vector of probabilities.
p_nonpreferred = model.predict(X_train)
print(p_nonpreferred [:2])
print("largest value", np.max(p_nonpreferred), "smallest value", np.min(p_nonpreferred))

# result：[[5.48e-03 3.50e-03 9.81e-01 9.70e-03]
# [9.95e-01 4.42e-03 1.05e-04 7.80e-05]]
# largest value 0.9999962 smallest value 1.6942051e-08
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After improvement

preferred_model = Sequential(
    [ 
        Dense(25, activation = 'relu'),
        Dense(15, activation = 'relu'),
        Dense(4, activation = 'linear')   #<-- Note
    ]
)
preferred_model.compile(
    loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True),  #<-- Note
    optimizer=tf.keras.optimizers.Adam(0.001),
)

preferred_model.fit(
    X_train,y_train,
    epochs=10
)

p_preferred = preferred_model.predict(X_train)
print(f"two example output vectors:\n {p_preferred[:2]}")
print("largest value", np.max(p_preferred), "smallest value", np.min(p_preferred))

# result :
# two example output vectors:
# [[-0.74 -1.18  4.5   0.66]
#  [ 7.08  1.95 -0.59 -5.32]]
#largest value 14.613606 smallest value -9.5557785

# The output predictions are not probabilities!!!

sm_preferred = tf.nn.softmax(p_preferred).numpy()
print(f"two example output vectors:\n {sm_preferred[:2]}")
print("largest value", np.max(sm_preferred), "smallest value", np.min(sm_preferred))

# two example output vectors:
#  [[5.15e-03 3.33e-03 9.71e-01 2.10e-02]
# [9.94e-01 5.91e-03 4.66e-04 4.09e-06]]
# largest value 0.99999964 smallest value 3.1869094e-11


for i in range(5):
    print( f"{p_preferred[i]}, category: {np.argmax(p_preferred[i])}")

# [-0.74 -1.18  4.5   0.66], category: 2
# [ 7.08  1.95 -0.59 -5.32], category: 0
# [ 5.1   1.88 -0.5  -4.23], category: 0
# [-2.13  4.49 -1.03 -1.53], category: 1
# [ 1.56 -1.9   6.59 -1.74], ctegory: 2
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3.4、Adam algorithm

3.5、Convolutional layer

Each single neuron of the layer does not look at all the values of the input vector that is fed into that layer