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updating week41

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mhjensen
2020-10-06 08:21:06 +02:00
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doc/src/week41/week41.do.txt
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@@ -7,7 +7,7 @@ DATE: today
===== Plan for week 40 =====
* Thursday: Building our own Feed-forward Neural Network
* Friday: Playing around with our own Feed-forward Neural Network and introduction to TensorFlow. Start convolutional Neural Networks.
* Friday: Playing around with our own Feed-forward Neural Network and introduction to TensorFlow. Start convolutional Neural Networks (CNN).
Reading suggestions for both days: "Aurelien Geron's chapters 10-11":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/T\
extbooks/TensorflowML.pdf" and Hastie et al chapter 11.
@@ -1385,7 +1385,6 @@ writer = tf.summary.FileWriter('logs/')
writer.add_graph(tf.get_default_graph())
!ec
!split
===== Using Keras =====
@@ -1400,23 +1399,26 @@ conda install keras
Alternatively, if you have Tensorflow or one of the other supported backends install you may use the pip package manager:
!bc pycod
pip3 install keras
pip install keras
!ec
or look up the "instructions here":"https://keras.io/".
!bc pycod
from keras.models import Sequential
from keras.layers import Dense
from keras.regularizers import l2
from keras.optimizers import SGD
import tensorflow as tf
from tensorflow.keras.layers import Input
from tensorflow.keras.models import Sequential #This allows appending layers to existing models
from tensorflow.keras.layers import Dense #This allows defining the characteristics of a particular layer
from tensorflow.keras import optimizers #This allows using whichever optimiser we want (sgd,adam,RMSprop)
from tensorflow.keras import regularizers #This allows using whichever regularizer we want (l1,l2,l1_l2)
from tensorflow.keras.utils import to_categorical #This allows using categorical cross entropy as the cost function
def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):
model = Sequential()
model.add(Dense(n_neurons_layer1, activation='sigmoid', kernel_regularizer=l2(lmbd)))
model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=l2(lmbd)))
model.add(Dense(n_neurons_layer1, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))
model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))
model.add(Dense(n_categories, activation='softmax'))
sgd = SGD(lr=eta)
sgd = optimizers.SGD(lr=eta)
model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
return model
@@ -1440,6 +1442,8 @@ for i, eta in enumerate(eta_vals):
print()
!ec
!bc pycod
# optional
# visual representation of grid search
@@ -1476,6 +1480,180 @@ plt.show()
!split
===== The Breast Cancer Data, now with Keras =====
!bc pycod
import tensorflow as tf
from tensorflow.keras.layers import Input
from tensorflow.keras.models import Sequential #This allows appending layers to existing models
from tensorflow.keras.layers import Dense #This allows defining the characteristics of a particular layer
from tensorflow.keras import optimizers #This allows using whichever optimiser we want (sgd,adam,RMSprop)
from tensorflow.keras import regularizers #This allows using whichever regularizer we want (l1,l2,l1_l2)
from tensorflow.keras.utils import to_categorical #This allows using categorical cross entropy as the cost function
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.model_selection import train_test_split as splitter
from sklearn.datasets import load_breast_cancer
import pickle
import os
"""Load breast cancer dataset"""
np.random.seed(0) #create same seed for random number every time
cancer=load_breast_cancer() #Download breast cancer dataset
inputs=cancer.data #Feature matrix of 569 rows (samples) and 30 columns (parameters)
outputs=cancer.target #Label array of 569 rows (0 for benign and 1 for malignant)
labels=cancer.feature_names[0:30]
print('The content of the breast cancer dataset is:') #Print information about the datasets
print(labels)
print('-------------------------')
print("inputs = " + str(inputs.shape))
print("outputs = " + str(outputs.shape))
print("labels = "+ str(labels.shape))
x=inputs #Reassign the Feature and Label matrices to other variables
y=outputs
#%%
# Visualisation of dataset (for correlation analysis)
plt.figure()
plt.scatter(x[:,0],x[:,2],s=40,c=y,cmap=plt.cm.Spectral)
plt.xlabel('Mean radius',fontweight='bold')
plt.ylabel('Mean perimeter',fontweight='bold')
plt.show()
plt.figure()
plt.scatter(x[:,5],x[:,6],s=40,c=y, cmap=plt.cm.Spectral)
plt.xlabel('Mean compactness',fontweight='bold')
plt.ylabel('Mean concavity',fontweight='bold')
plt.show()
plt.figure()
plt.scatter(x[:,0],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)
plt.xlabel('Mean radius',fontweight='bold')
plt.ylabel('Mean texture',fontweight='bold')
plt.show()
plt.figure()
plt.scatter(x[:,2],x[:,1],s=40,c=y,cmap=plt.cm.Spectral)
plt.xlabel('Mean perimeter',fontweight='bold')
plt.ylabel('Mean compactness',fontweight='bold')
plt.show()
# Generate training and testing datasets
#Select features relevant to classification (texture,perimeter,compactness and symmetery)
#and add to input matrix
temp1=np.reshape(x[:,1],(len(x[:,1]),1))
temp2=np.reshape(x[:,2],(len(x[:,2]),1))
X=np.hstack((temp1,temp2))
temp=np.reshape(x[:,5],(len(x[:,5]),1))
X=np.hstack((X,temp))
temp=np.reshape(x[:,8],(len(x[:,8]),1))
X=np.hstack((X,temp))
X_train,X_test,y_train,y_test=splitter(X,y,test_size=0.1) #Split datasets into training and testing
y_train=to_categorical(y_train) #Convert labels to categorical when using categorical cross entropy
y_test=to_categorical(y_test)
del temp1,temp2,temp
# %%
# Define tunable parameters"
eta=np.logspace(-3,-1,3) #Define vector of learning rates (parameter to SGD optimiser)
lamda=0.01 #Define hyperparameter
n_layers=2 #Define number of hidden layers in the model
n_neuron=np.logspace(0,3,4,dtype=int) #Define number of neurons per layer
epochs=100 #Number of reiterations over the input data
batch_size=100 #Number of samples per gradient update
# %%
"""Define function to return Deep Neural Network model"""
def NN_model(inputsize,n_layers,n_neuron,eta,lamda):
model=Sequential()
for i in range(n_layers): #Run loop to add hidden layers to the model
if (i==0): #First layer requires input dimensions
model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda),input_dim=inputsize))
else: #Subsequent layers are capable of automatic shape inferencing
model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda)))
model.add(Dense(2,activation='softmax')) #2 outputs - ordered and disordered (softmax for prob)
sgd=optimizers.SGD(lr=eta)
model.compile(loss='categorical_crossentropy',optimizer=sgd,metrics=['accuracy'])
return model
Train_accuracy=np.zeros((len(n_neuron),len(eta))) #Define matrices to store accuracy scores as a function
Test_accuracy=np.zeros((len(n_neuron),len(eta))) #of learning rate and number of hidden neurons for
for i in range(len(n_neuron)): #run loops over hidden neurons and learning rates to calculate
for j in range(len(eta)): #accuracy scores
DNN_model=NN_model(X_train.shape[1],n_layers,n_neuron[i],eta[j],lamda)
DNN_model.fit(X_train,y_train,epochs=epochs,batch_size=batch_size,verbose=1)
Train_accuracy[i,j]=DNN_model.evaluate(X_train,y_train)[1]
Test_accuracy[i,j]=DNN_model.evaluate(X_test,y_test)[1]
def plot_data(x,y,data,title=None):
# plot results
fontsize=16
fig = plt.figure()
ax = fig.add_subplot(111)
cax = ax.matshow(data, interpolation='nearest', vmin=0, vmax=1)
cbar=fig.colorbar(cax)
cbar.ax.set_ylabel('accuracy (%)',rotation=90,fontsize=fontsize)
cbar.set_ticks([0,.2,.4,0.6,0.8,1.0])
cbar.set_ticklabels(['0%','20%','40%','60%','80%','100%'])
# put text on matrix elements
for i, x_val in enumerate(np.arange(len(x))):
for j, y_val in enumerate(np.arange(len(y))):
c = "${0:.1f}\\%$".format( 100*data[j,i])
ax.text(x_val, y_val, c, va='center', ha='center')
# convert axis vaues to to string labels
x=[str(i) for i in x]
y=[str(i) for i in y]
ax.set_xticklabels(['']+x)
ax.set_yticklabels(['']+y)
ax.set_xlabel('$\\mathrm{learning\\ rate}$',fontsize=fontsize)
ax.set_ylabel('$\\mathrm{hidden\\ neurons}$',fontsize=fontsize)
if title is not None:
ax.set_title(title)
plt.tight_layout()
plt.show()
plot_data(eta,n_neuron,Train_accuracy, 'training')
plot_data(eta,n_neuron,Test_accuracy, 'testing')
!ec
!split
===== Which activation function should I use? =====
@@ -1678,7 +1856,7 @@ Some of these remarks are particular to DNNs, others are shared by all supervise
Convolutional neural networks (CNNs) were developed during the last
decade of the previous century, with a focus on character recognition
tasks. Nowadays, CNNs are a central element in the spectacular success
of dee learning methods. The success in for example image
of deep learning methods. The success in for example image
classifications have made them a central tool for most machine
learning practitioners.
@@ -1807,470 +1985,3 @@ the course
and the slides of "CS231":"http://cs231n.github.io/convolutional-networks/" which is taught at Stanford University (consistently ranked as one of the top computer science programs in the world). "Michael Nielsen's book is a must read, in particular chapter 6 which deals with CNNs":"http://neuralnetworksanddeeplearning.com/chap6.html".
!split
===== CNNs in more detail, building convolutional neural networks in Tensorflow and Keras =====
As discussed above, CNNs are neural networks built from the assumption that the inputs
to the network are 2D images. This is important because the number of features or pixels in images
grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network.
As before, we still have our input, a hidden layer and an output. What's novel about convolutional networks
are the _convolutional_ and _pooling_ layers stacked in pairs between the input and the hidden layer.
In addition, the data is no longer represented as a 2D feature matrix, instead each input is a number of 2D
matrices, typically 1 for each color dimension (Red, Green, Blue).
!split
===== Setting it up =====
It means that to represent the entire
dataset of images, we require a 4D matrix or _tensor_. This tensor has the dimensions:
!bt
\[
(n_{inputs},\, n_{pixels, width},\, n_{pixels, height},\, depth) .
\]
!et
!split
===== The MNIST dataset again =====
The MNIST dataset consists of grayscale images with a pixel size of
$28\times 28$, meaning we require $28 \times 28 = 724$ weights to each
neuron in the first hidden layer.
If we were to analyze images of size $128\times 128$ we would require
$128 \times 128 = 16384$ weights to each neuron. Even worse if we were
dealing with color images, as most images are, we have an image matrix
of size $128\times 128$ for each color dimension (Red, Green, Blue),
meaning 3 times the number of weights $= 49152$ are required for every
single neuron in the first hidden layer.
!split
===== Strong correlations =====
Images typically have strong local correlations, meaning that a small
part of the image varies little from its neighboring regions. If for
example we have an image of a blue car, we can roughly assume that a
small blue part of the image is surrounded by other blue regions.
Therefore, instead of connecting every single pixel to a neuron in the
first hidden layer, as we have previously done with deep neural
networks, we can instead connect each neuron to a small part of the
image (in all 3 RGB depth dimensions). The size of each small area is
fixed, and known as a "receptive":"https://en.wikipedia.org/wiki/Receptive_field".
!split
===== Layers of a CNN =====
The layers of a convolutional neural network arrange neurons in 3D: width, height and depth.
The input image is typically a square matrix of depth 3.
A _convolution_ is performed on the image which outputs
a 3D volume of neurons. The weights to the input are arranged in a number of 2D matrices, known as _filters_.
Each filter slides along the input image, taking the dot product
between each small part of the image and the filter, in all depth
dimensions. This is then passed through a non-linear function,
typically the _Rectified Linear (ReLu)_ function, which serves as the
activation of the neurons in the first convolutional layer. This is
further passed through a _pooling layer_, which reduces the size of the
convolutional layer, e.g. by taking the maximum or average across some
small regions, and this serves as input to the next convolutional
layer.
!split
===== Systematic reduction =====
By systematically reducing the size of the input volume, through
convolution and pooling, the network should create representations of
small parts of the input, and then from them assemble representations
of larger areas. The final pooling layer is flattened to serve as
input to a hidden layer, such that each neuron in the final pooling
layer is connected to every single neuron in the hidden layer. This
then serves as input to the output layer, e.g. a softmax output for
classification.
!split
===== Prerequisites: Collect and pre-process data =====
!bc pycod
# import necessary packages
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
# ensure the same random numbers appear every time
np.random.seed(0)
# display images in notebook
%matplotlib inline
plt.rcParams['figure.figsize'] = (12,12)
# download MNIST dataset
digits = datasets.load_digits()
# define inputs and labels
inputs = digits.images
labels = digits.target
# RGB images have a depth of 3
# our images are grayscale so they should have a depth of 1
inputs = inputs[:,:,:,np.newaxis]
print("inputs = (n_inputs, pixel_width, pixel_height, depth) = " + str(inputs.shape))
print("labels = (n_inputs) = " + str(labels.shape))
# choose some random images to display
n_inputs = len(inputs)
indices = np.arange(n_inputs)
random_indices = np.random.choice(indices, size=5)
for i, image in enumerate(digits.images[random_indices]):
plt.subplot(1, 5, i+1)
plt.axis('off')
plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
plt.title("Label: %d" % digits.target[random_indices[i]])
plt.show()
!ec
!split
===== Importing Keras and Tensorflow =====
!bc pycod
from keras.utils import to_categorical
from sklearn.model_selection import train_test_split
# representation of labels
labels = to_categorical(labels)
# split into train and test data
# one-liner from scikit-learn library
train_size = 0.8
test_size = 1 - train_size
X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
test_size=test_size)
!ec
!split
===== Using TensorFlow backend =====
We need to define model and architecture and choose cost function and optmizer.
!bc pycid
import tensorflow as tf
class ConvolutionalNeuralNetworkTensorflow:
def __init__(
self,
X_train,
Y_train,
X_test,
Y_test,
n_filters=10,
n_neurons_connected=50,
n_categories=10,
receptive_field=3,
stride=1,
padding=1,
epochs=10,
batch_size=100,
eta=0.1,
lmbd=0.0):
self.global_step = tf.Variable(0, dtype=tf.int32, trainable=False, name='global_step')
self.X_train = X_train
self.Y_train = Y_train
self.X_test = X_test
self.Y_test = Y_test
self.n_inputs, self.input_width, self.input_height, self.depth = X_train.shape
self.n_filters = n_filters
self.n_downsampled = int(self.input_width*self.input_height*n_filters / 4)
self.n_neurons_connected = n_neurons_connected
self.n_categories = n_categories
self.receptive_field = receptive_field
self.stride = stride
self.strides = [stride, stride, stride, stride]
self.padding = padding
self.epochs = epochs
self.batch_size = batch_size
self.iterations = self.n_inputs // self.batch_size
self.eta = eta
self.lmbd = lmbd
self.create_placeholders()
self.create_CNN()
self.create_loss()
self.create_optimiser()
self.create_accuracy()
def create_placeholders(self):
with tf.name_scope('data'):
self.X = tf.placeholder(tf.float32, shape=(None, self.input_width, self.input_height, self.depth), name='X_data')
self.Y = tf.placeholder(tf.float32, shape=(None, self.n_categories), name='Y_data')
def create_CNN(self):
with tf.name_scope('CNN'):
# Convolutional layer
self.W_conv = self.weight_variable([self.receptive_field, self.receptive_field, self.depth, self.n_filters], name='conv', dtype=tf.float32)
b_conv = self.weight_variable([self.n_filters], name='conv', dtype=tf.float32)
z_conv = tf.nn.conv2d(self.X, self.W_conv, self.strides, padding='SAME', name='conv') + b_conv
a_conv = tf.nn.relu(z_conv)
# 2x2 max pooling
a_pool = tf.nn.max_pool(a_conv, [1, 2, 2, 1], [1, 2, 2, 1], padding='SAME', name='pool')
# Fully connected layer
a_pool_flat = tf.reshape(a_pool, [-1, self.n_downsampled])
self.W_fc = self.weight_variable([self.n_downsampled, self.n_neurons_connected], name='fc', dtype=tf.float32)
b_fc = self.bias_variable([self.n_neurons_connected], name='fc', dtype=tf.float32)
a_fc = tf.nn.relu(tf.matmul(a_pool_flat, self.W_fc) + b_fc)
# Output layer
self.W_out = self.weight_variable([self.n_neurons_connected, self.n_categories], name='out', dtype=tf.float32)
b_out = self.bias_variable([self.n_categories], name='out', dtype=tf.float32)
self.z_out = tf.matmul(a_fc, self.W_out) + b_out
def create_loss(self):
with tf.name_scope('loss'):
softmax_loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits_v2(labels=self.Y, logits=self.z_out))
regularizer_loss_conv = tf.nn.l2_loss(self.W_conv)
regularizer_loss_fc = tf.nn.l2_loss(self.W_fc)
regularizer_loss_out = tf.nn.l2_loss(self.W_out)
regularizer_loss = self.lmbd*(regularizer_loss_conv + regularizer_loss_fc + regularizer_loss_out)
self.loss = softmax_loss + regularizer_loss
def create_accuracy(self):
with tf.name_scope('accuracy'):
probabilities = tf.nn.softmax(self.z_out)
predictions = tf.argmax(probabilities, 1)
labels = tf.argmax(self.Y, 1)
correct_predictions = tf.equal(predictions, labels)
correct_predictions = tf.cast(correct_predictions, tf.float32)
self.accuracy = tf.reduce_mean(correct_predictions)
def create_optimiser(self):
with tf.name_scope('optimizer'):
self.optimizer = tf.train.GradientDescentOptimizer(learning_rate=self.eta).minimize(self.loss, global_step=self.global_step)
def weight_variable(self, shape, name='', dtype=tf.float32):
initial = tf.truncated_normal(shape, stddev=0.1)
return tf.Variable(initial, name=name, dtype=dtype)
def bias_variable(self, shape, name='', dtype=tf.float32):
initial = tf.constant(0.1, shape=shape)
return tf.Variable(initial, name=name, dtype=dtype)
def fit(self):
data_indices = np.arange(self.n_inputs)
with tf.Session() as sess:
sess.run(tf.global_variables_initializer())
for i in range(self.epochs):
for j in range(self.iterations):
chosen_datapoints = np.random.choice(data_indices, size=self.batch_size, replace=False)
batch_X, batch_Y = self.X_train[chosen_datapoints], self.Y_train[chosen_datapoints]
sess.run([CNN.loss, CNN.optimizer],
feed_dict={CNN.X: batch_X,
CNN.Y: batch_Y})
accuracy = sess.run(CNN.accuracy,
feed_dict={CNN.X: batch_X,
CNN.Y: batch_Y})
step = sess.run(CNN.global_step)
self.train_loss, self.train_accuracy = sess.run([CNN.loss, CNN.accuracy],
feed_dict={CNN.X: self.X_train,
CNN.Y: self.Y_train})
self.test_loss, self.test_accuracy = sess.run([CNN.loss, CNN.accuracy],
feed_dict={CNN.X: self.X_test,
CNN.Y: self.Y_test})
!ec
!split
===== Train the model =====
We need now to train the model, evaluate it and test its performance on test data, and eventually include hyperparameters.
!bc pycod
epochs = 100
batch_size = 100
n_filters = 10
n_neurons_connected = 50
n_categories = 10
eta_vals = np.logspace(-5, 1, 7)
lmbd_vals = np.logspace(-5, 1, 7)
CNN_tf = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
for i, eta in enumerate(eta_vals):
for j, lmbd in enumerate(lmbd_vals):
CNN = ConvolutionalNeuralNetworkTensorflow(X_train, Y_train, X_test, Y_test,
n_filters=n_filters, n_neurons_connected=n_neurons_connected,
n_categories=n_categories, epochs=epochs, batch_size=batch_size,
eta=eta, lmbd=lmbd)
CNN.fit()
print("Learning rate = ", eta)
print("Lambda = ", lmbd)
print("Test accuracy: %.3f" % CNN.test_accuracy)
print()
CNN_tf[i][j] = CNN
!ec
!split
===== Visualizing the results =====
!bc pycod
# visual representation of grid search
# uses seaborn heatmap, could probably do this in matplotlib
import seaborn as sns
sns.set()
train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
for i in range(len(eta_vals)):
for j in range(len(lmbd_vals)):
CNN = CNN_tf[i][j]
train_accuracy[i][j] = CNN.train_accuracy
test_accuracy[i][j] = CNN.test_accuracy
fig, ax = plt.subplots(figsize = (10, 10))
sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
ax.set_title("Training Accuracy")
ax.set_ylabel("$\eta$")
ax.set_xlabel("$\lambda$")
plt.show()
fig, ax = plt.subplots(figsize = (10, 10))
sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
ax.set_title("Test Accuracy")
ax.set_ylabel("$\eta$")
ax.set_xlabel("$\lambda$")
plt.show()
!ec
!split
===== Running with Keras =====
!bc pycod
from keras.models import Sequential
from keras.layers.convolutional import Conv2D
from keras.layers.convolutional import MaxPooling2D
from keras.layers import Flatten
from keras.layers import Dense
from keras.regularizers import l2
from keras.optimizers import SGD
def create_convolutional_neural_network_keras(input_shape, receptive_field,
n_filters, n_neurons_connected, n_categories,
eta, lmbd):
model = Sequential()
model.add(Conv2D(n_filters, (receptive_field, receptive_field), input_shape=input_shape, padding='same',
activation='relu', kernel_regularizer=l2(lmbd)))
model.add(MaxPooling2D(pool_size=(2, 2)))
model.add(Flatten())
model.add(Dense(n_neurons_connected, activation='relu', kernel_regularizer=l2(lmbd)))
model.add(Dense(n_categories, activation='softmax', kernel_regularizer=l2(lmbd)))
sgd = SGD(lr=eta)
model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
return model
epochs = 100
batch_size = 100
input_shape = X_train.shape[1:4]
receptive_field = 3
n_filters = 10
n_neurons_connected = 50
n_categories = 10
eta_vals = np.logspace(-5, 1, 7)
lmbd_vals = np.logspace(-5, 1, 7)
!ec
!split
===== Final part =====
!bc pycod
CNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
for i, eta in enumerate(eta_vals):
for j, lmbd in enumerate(lmbd_vals):
CNN = create_convolutional_neural_network_keras(input_shape, receptive_field,
n_filters, n_neurons_connected, n_categories,
eta, lmbd)
CNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)
scores = CNN.evaluate(X_test, Y_test)
CNN_keras[i][j] = CNN
print("Learning rate = ", eta)
print("Lambda = ", lmbd)
print("Test accuracy: %.3f" % scores[1])
print()
!ec
!split
===== Final visualization =====
!bc
# visual representation of grid search
# uses seaborn heatmap, could probably do this in matplotlib
import seaborn as sns
sns.set()
train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
for i in range(len(eta_vals)):
for j in range(len(lmbd_vals)):
CNN = CNN_keras[i][j]
train_accuracy[i][j] = CNN.evaluate(X_train, Y_train)[1]
test_accuracy[i][j] = CNN.evaluate(X_test, Y_test)[1]
fig, ax = plt.subplots(figsize = (10, 10))
sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
ax.set_title("Training Accuracy")
ax.set_ylabel("$\eta$")
ax.set_xlabel("$\lambda$")
plt.show()
fig, ax = plt.subplots(figsize = (10, 10))
sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
ax.set_title("Test Accuracy")
ax.set_ylabel("$\eta$")
ax.set_xlabel("$\lambda$")
plt.show()
!ec
!split
===== Fun links =====
o "Self-Driving cars using a convolutional neural network":"https://arxiv.org/abs/1604.07316"
o "Abstract art using convolutional neural networks":"https://deepdreamgenerator.com/"