def linear_regression(a=1.0, b=0.0):
X = np.linspace(-100, 100, 200)
X = X.reshape((-1, 1))
[train_x, test_x] = split_data(X, ratio=0.8, random=True)
train_y = a * train_x + b
test_y = a * test_x + b
i = Input(1)
x = Dense(1)(i)
# define trainer
trainer = Trainer(loss='mse',
optimizer=Adam(learning_rate=0.2),
batch_size=50,
epochs=50)
# create model
model = Sequential(i, x, trainer)
model.summary()
# training process
model.fit(train_x, train_y)
# predict
y_hat = model.predict(test_x)
plt.plot(test_x, test_y, 'b')
plt.plot(test_x, y_hat, 'r')
plt.show()
def linear_classification(a=1.0, b=0.0, graph=False):
# prepare data
x = np.linspace(-100, 100, 200)
y = a * x + b
X = np.array(list(zip(x, y))) + np.random.randn(200, 2) * 100
Y = to_one_hot(np.where(a * X[:, 0] + b > X[:, 1], 1, 0))
(train_x, train_y), (test_x, test_y) = split_data(X,
Y,
ratio=0.8,
random=True)
# build simple FNN
i = Input(2)
x = Dense(2, activation='softmax')(i)
# define trainer
trainer = Trainer(loss='cross_entropy',
optimizer=Adam(learning_rate=0.05),
batch_size=50,
epochs=50,
metrics=['accuracy'])
# create model
model = Sequential(i, x, trainer)
model.summary()
# training process
model.fit(train_x, train_y)
print(model.evaluate(test_x, test_y))
if graph:
plt.plot(model.history['loss'])
plt.show()
# predict
y_hat = model.predict(test_x)
y_hat = np.argmax(y_hat, axis=1)
simple_plot(test_x, y_hat, a, b)
def binary_classification():
def separate_label(data):
X = normalize(data[:, :2].astype('float32'))
Y = np.where(data[:, 2] == b'black', 0, 1)
return X, Y
# prepare train data
data_dir = "data/examples/binary_classification"
train_data_path = os.path.join(data_dir, 'training.arff')
train_data = load_arff(train_data_path)
train_x, train_y = separate_label(train_data)
train_y = to_one_hot(train_y)
# build simple FNN
i = Input(2)
x = Dense(30, activation='relu')(i)
x = Dense(30, activation='relu')(x)
x = Dense(2, activation='softmax')(x)
# define trainer
trainer = Trainer(loss='cross_entropy', optimizer=Adam(clipvalue=1.0), batch_size=256, epochs=500, metrics=['accuracy'])
# create model
model = Sequential(i, x, trainer)
model.summary()
# training process
model.fit(train_x, train_y)
plt.plot(range(len(model.history['loss'])), model.history['loss'])
plt.show()
# predict
test_data_path = os.path.join(data_dir, 'test.arff')
test_data = load_arff(test_data_path)
test_x, _ = separate_label(test_data)
y_hat = model.predict(test_x)
simple_plot(test_x, y_hat)
def universal_approximation(f, x):
[train_x, test_x] = split_data(x, ratio=0.8, random=True)
train_y = f(train_x)
test_x = np.sort(test_x, axis=0)
test_y = f(test_x)
# build simple FNN
i = Input(1)
x = Dense(50, activation='relu')(i)
x = Dense(1)(x)
# define trainer
schedule = ExponentialDecay(initial_learning_rate=0.01, decay_rate=0.75)
trainer = Trainer(loss='mse',
optimizer=Adam(learning_rate=schedule),
batch_size=50,
epochs=750)
# create model
model = Sequential(i, x, trainer)
model.summary()
# training process
start = time.time()
model.fit(train_x, train_y)
print(time.time() - start)
plt.plot(range(len(model.history['loss'])), model.history['loss'])
plt.show()
# predict
y_hat = model.predict(test_x)
plt.plot(test_x, test_y, 'b-', label='original')
plt.plot(test_x, y_hat, 'r-', label='predicted')
plt.legend()
plt.show()