def test_neuralNetwork_adam():
from sklearn.neural_network._stochastic_optimizers import AdamOptimizer
np.random.seed(2019)
X = np.random.normal(size=(1, 500))
target = 3.9285985 * X
nn = NeuralNetwork(inputs=1,
neurons=3,
outputs=1,
activations='sigmoid',
silent=True)
nn.addLayer()
nn.addLayer()
nn.addOutputLayer(activations='identity')
learning_rate = 0.001
yhat = nn.forward_pass(X)
nn.backpropagation(yhat.T, target.T)
nn.learning_rate = learning_rate
nn.initializeAdam()
nn.adam()
skl_adam = AdamOptimizer(params=nn.param, learning_rate_init=learning_rate)
upd = skl_adam._get_updates(nn.grad)
for update_nn, update_skl in zip(nn.change, upd):
assert update_nn == pytest.approx(update_skl)
def test_neuralNetwork_sgd():
from sklearn.neural_network._stochastic_optimizers import SGDOptimizer
np.random.seed(2019)
X = np.random.normal(size=(1, 500))
target = 3.9285985 * X
nn = NeuralNetwork(inputs=1,
neurons=3,
outputs=1,
activations='sigmoid',
silent=True)
nn.addLayer()
nn.addLayer()
nn.addOutputLayer(activations='identity')
learning_rate = 0.001
yhat = nn.forward_pass(X)
nn.backpropagation(yhat.T, target.T)
nn.learning_rate = learning_rate
initial_params = copy.deepcopy(nn.weights + nn.biases)
nn.sgd()
grad = nn.d_weights + nn.d_biases
params = nn.weights + nn.biases
change = [p - i_p for p, i_p in zip(params, initial_params)]
skl_sgd = SGDOptimizer(params=initial_params,
learning_rate_init=learning_rate,
nesterov=False,
momentum=1.0)
upd = skl_sgd._get_updates(grad)
for update_nn, update_skl in zip(change, upd):
assert update_nn == pytest.approx(update_skl)
def test_neuralNetwork_network(silent=False):
# Lets set up a sci-kit learn neural network and copy over the weights
# and biases to our network, verify that the two give the exact same
# result.
from sklearn.neural_network import MLPRegressor
X = [[0.0], [1.0], [2.0], [3.0], [4.0], [5.0]]
y = [0, 2, 4, 6, 8, 10]
mlp = MLPRegressor(solver='sgd',
alpha=0.0,
hidden_layer_sizes=(3, 3),
random_state=1,
activation='relu')
mlp.fit(X, y)
W_skl = mlp.coefs_
b_skl = mlp.intercepts_
nn = NeuralNetwork(inputs=1,
outputs=1,
layers=3,
neurons=3,
activations='relu',
silent=silent)
nn.addLayer()
nn.addLayer()
nn.addOutputLayer(activations='identity')
W_nn = nn.weights
b_nn = nn.biases
for i in range(len(W_nn)):
W_nn[i] = W_skl[i]
for i in range(len(b_nn)):
b_nn[i] = np.expand_dims(b_skl[i], axis=1)
X_test = np.array([[1.2857], [9.2508255], [-5.25255], [3.251095]])
output_skl = mlp.predict(X_test)
output_nn = np.squeeze(nn(X_test.T))
if not silent:
print("%20.15f %20.15f %20.15f %20.15f" % (*output_skl, ))
print("%20.15f %20.15f %20.15f %20.15f" % (*output_nn, ))
assert output_nn == pytest.approx(output_skl)
return nn, mlp
def test_neuralNetwork_fit_adam():
np.random.seed(2019)
X = np.random.normal(size=(1, 500))
target = 3.9285985 * X
nn = NeuralNetwork(inputs=1,
neurons=3,
outputs=1,
activations='tanh',
silent=True)
nn.addLayer()
nn.addLayer()
nn.addOutputLayer(activations='identity')
nn.fit(X,
target,
shuffle=True,
batch_size=100,
validation_fraction=0.2,
learning_rate=0.05,
verbose=True,
silent=False,
epochs=100,
optimizer='adam')
loss = nn.loss
nn.fit(X,
target,
shuffle=True,
batch_size=100,
validation_fraction=0.2,
learning_rate=0.05,
verbose=True,
silent=False,
epochs=100,
optimizer='adam')
assert loss > nn.loss
def test_neuralNetwork_fit_sgd():
np.random.seed(2019)
X = np.random.normal(size=(1, 500))
target = 3.9285985 * X
nn = NeuralNetwork(inputs=1,
neurons=3,
outputs=1,
activations='sigmoid',
silent=True)
nn.addLayer()
nn.addLayer()
nn.addOutputLayer(activations='identity')
nn.fit(X,
target,
shuffle=True,
batch_size=100,
validation_fraction=0.2,
learning_rate=0.05,
verbose=False,
silent=True,
epochs=100)
loss_after_100 = nn.loss
nn.fit(X,
target,
shuffle=True,
batch_size=100,
validation_fraction=0.2,
learning_rate=0.05,
verbose=False,
silent=True,
epochs=100)
loss_after_200 = nn.loss
assert loss_after_200 < loss_after_100
def test_neuralNetwork_backpropagation_multiple_outputs():
# Similar to the test_neuralNetwork_backpropagation() test, but with
# multiple samples and features, X having dimensions
# (n_samples, n_features) = (3,2), as well as the target having dimensions
# (n_outputs) = (2)
from sklearn.neural_network import MLPRegressor
X = np.array([[0, 1], [1, 2], [2, 3]])
y = np.array([[0, 1], [2, 3], [3, 4]])
mlp = MLPRegressor(solver='sgd',
alpha=0.0,
learning_rate='constant',
learning_rate_init=1e-20,
max_iter=1,
hidden_layer_sizes=(3, 3),
random_state=1,
activation='logistic')
# Force sklearn to set up all the matrices by fitting a data set.
with warnings.catch_warnings():
warnings.simplefilter("ignore")
mlp.fit(X, y)
W_skl = mlp.coefs_
b_skl = mlp.intercepts_
nn = NeuralNetwork(inputs=2,
outputs=2,
layers=3,
neurons=3,
activations='sigmoid',
silent=True)
nn.addLayer()
nn.addLayer()
nn.addOutputLayer(activations='identity')
for i, w in enumerate(W_skl):
nn.weights[i] = w
for i, b in enumerate(b_skl):
nn.biases[i] = np.expand_dims(b, axis=1)
# ========================================================================
n_samples, n_features = X.shape
batch_size = n_samples
hidden_layer_sizes = mlp.hidden_layer_sizes
if not hasattr(hidden_layer_sizes, "__iter__"):
hidden_layer_sizes = [hidden_layer_sizes]
hidden_layer_sizes = list(hidden_layer_sizes)
layer_units = ([n_features] + hidden_layer_sizes + [mlp.n_outputs_])
activations = [X]
activations.extend(
np.empty((batch_size, n_fan_out)) for n_fan_out in layer_units[1:])
deltas = [np.empty_like(a_layer) for a_layer in activations]
coef_grads = [
np.empty((n_fan_in_, n_fan_out_))
for n_fan_in_, n_fan_out_ in zip(layer_units[:-1], layer_units[1:])
]
intercept_grads = [np.empty(n_fan_out_) for n_fan_out_ in layer_units[1:]]
# ========================================================================
activations = mlp._forward_pass(activations)
if y.ndim == 1:
y = y.reshape((-1, 1))
loss, coef_grads, intercept_grads = mlp._backprop(X, y, activations,
deltas, coef_grads,
intercept_grads)
yhat = nn.forward_pass(X.T)
nn.backpropagation(yhat.T, y)
for i, d_bias in enumerate(nn.d_biases):
assert np.squeeze(d_bias) == pytest.approx(
np.squeeze(intercept_grads[i]))
for i, d_weight in enumerate(nn.d_weights):
assert np.squeeze(d_weight) == pytest.approx(np.squeeze(coef_grads[i]))
def test_neuralNetwork_backpropagation():
# We re-use the test_neuralNetwork_network networks and this time check
# that the computed backpropagation derivatives are equal.
from sklearn.neural_network import MLPRegressor
X = [[0.0], [1.0], [2.0], [3.0], [4.0], [5.0]]
y = [0, 2, 4, 6, 8, 10]
mlp = MLPRegressor(solver='sgd',
alpha=0.0,
hidden_layer_sizes=(3, 3),
random_state=1,
activation='logistic')
# Force sklearn to set up all the matrices by fitting a data set.
with warnings.catch_warnings():
warnings.simplefilter("ignore")
mlp.fit(X, y)
# Throw away all the fitted values, randomize W and b matrices.
np.random.seed(18)
for i, coeff in enumerate(mlp.coefs_):
mlp.coefs_[i] = np.random.normal(size=coeff.shape)
for i, bias in enumerate(mlp.intercepts_):
mlp.intercepts_[i] = np.random.normal(size=bias.shape)
W_skl = mlp.coefs_
b_skl = mlp.intercepts_
nn = NeuralNetwork(inputs=1,
outputs=1,
layers=3,
neurons=3,
activations='sigmoid',
silent=False)
nn.addLayer()
nn.addLayer()
nn.addOutputLayer(activations='identity')
nn.weights = W_skl
for i, b in enumerate(b_skl):
nn.biases[i] = np.expand_dims(b, axis=1)
# From the sklearn source, we need to set up some lists to use the _backprop
# function in MLPRegressor, see:
#
# https://github.com/scikit-learn/scikit-learn/blob/bac89c2/sklearn/neural_network/multilayer_perceptron.py#L355
#
# ========================================================================
# Initialize lists
X = np.array([[1.125982598]])
y = np.array([8.29289285])
mlp.predict(X)
n_samples, n_features = X.shape
batch_size = n_samples
hidden_layer_sizes = mlp.hidden_layer_sizes
# Make sure self.hidden_layer_sizes is a list
if not hasattr(hidden_layer_sizes, "__iter__"):
hidden_layer_sizes = [hidden_layer_sizes]
hidden_layer_sizes = list(hidden_layer_sizes)
layer_units = ([n_features] + hidden_layer_sizes + [mlp.n_outputs_])
activations = [X]
activations.extend(
np.empty((batch_size, n_fan_out)) for n_fan_out in layer_units[1:])
deltas = [np.empty_like(a_layer) for a_layer in activations]
coef_grads = [
np.empty((n_fan_in_, n_fan_out_))
for n_fan_in_, n_fan_out_ in zip(layer_units[:-1], layer_units[1:])
]
intercept_grads = [np.empty(n_fan_out_) for n_fan_out_ in layer_units[1:]]
# ========================================================================
activations = mlp._forward_pass(activations)
loss, coef_grads, intercept_grads = mlp._backprop(X, y, activations,
deltas, coef_grads,
intercept_grads)
yhat = nn(X)
nn.backpropagation(yhat, y)
for i, d_bias in enumerate(nn.d_biases):
assert np.squeeze(d_bias) == pytest.approx(
np.squeeze(intercept_grads[i]))
for i, d_weight in enumerate(nn.d_weights):
assert np.squeeze(d_weight) == pytest.approx(np.squeeze(coef_grads[i]))
def train_net_predict_energy(L=10, N=5000):
ising = Ising(L, N)
X, y = ising.generateTrainingData1D()
y /= L
n_samples, n_features = X.shape
nn = NeuralNetwork(inputs=L,
neurons=L * L,
outputs=1,
activations='sigmoid',
cost='mse',
silent=False)
nn.addLayer(neurons=L * L)
nn.addLayer(neurons=L * L)
nn.addOutputLayer(activations='identity')
validation_skip = 10
epochs = 1000
nn.fit(X.T,
y,
shuffle=True,
batch_size=1000,
validation_fraction=0.2,
learning_rate=0.001,
verbose=False,
silent=False,
epochs=epochs,
validation_skip=validation_skip,
optimizer='adam')
# Use the net to predict the energies for the validation set.
x_validation = nn.x_validation
y_validation = nn.predict(x_validation)
target_validation = nn.target_validation
# Sort the targets for better visualization of the network output.
ind = np.argsort(target_validation)
y_validation = np.squeeze(y_validation.T[ind])
target_validation = np.squeeze(target_validation.T[ind])
# We dont want to plot the discontinuities in the target.
target_validation[np.where(
np.abs(np.diff(target_validation)) > 1e-5)] = np.nan
plt.rc('text', usetex=True)
plt.figure()
plt.plot(target_validation, 'k--', label=r'Target')
plt.plot(y_validation, 'r.', markersize=0.5, label=r'NN output')
plt.legend(fontsize=10)
plt.xlabel(r'Validation sample', fontsize=10)
plt.ylabel(r'$E / L$', fontsize=10)
#plt.savefig(os.path.join(os.path.dirname(__file__), 'figures', 'nn_1d_energy_predict' + str(L) + '.png'), transparent=True, bbox_inches='tight')
# Plot the training / validation loss during training.
training_loss = nn.training_loss
validation_loss = nn.validation_loss
# There are more training loss values than validation loss values, lets
# align them so the plot makes sense.
xaxis_validation_loss = np.zeros_like(validation_loss)
xaxis_validation_loss[0] = 0
xaxis_validation_loss[1:-1] = np.arange(validation_skip,
len(training_loss),
validation_skip)
xaxis_validation_loss[-1] = len(training_loss)
plt.figure()
plt.semilogy(training_loss, 'r-', label=r'Training loss')
plt.semilogy(xaxis_validation_loss,
validation_loss,
'k--',
label=r'Validation loss')
plt.legend(fontsize=10)
plt.xlabel(r'Epoch', fontsize=10)
plt.ylabel(r'Cost $C(\theta)$', fontsize=10)
#plt.savefig(os.path.join(os.path.dirname(__file__), 'figures', 'nn_1d_loss' + str(L) + '.png'), transparent=True, bbox_inches='tight')
plt.show()
def R2_versus_lasso():
L = 3
N = 10000
training_fraction = 0.4
ising = Ising(L, N)
D, ry = ising.generateDesignMatrix1D()
X, y = ising.generateTrainingData1D()
y /= L
D_train = D[int(training_fraction * N):, :]
ry_train = ry[int(training_fraction * N):]
D_validation = D[:int(training_fraction * N), :]
ry_validation = ry[:int(training_fraction * N)]
lasso = LeastSquares(method='lasso', backend='skl')
lasso.setLambda(1e-2)
lasso.fit(D_train, ry_train)
lasso.y = ry_validation
lasso_R2 = sklearn.metrics.mean_squared_error(
ry_validation / L,
lasso.predict(D_validation) / L)
n_samples, n_features = X.shape
nn = NeuralNetwork(inputs=L * L,
neurons=L,
outputs=1,
activations='identity',
cost='mse',
silent=False)
nn.addLayer(neurons=1)
nn.addOutputLayer(activations='identity')
validation_skip = 100
epochs = 50000
nn.fit(D.T,
ry,
shuffle=True,
batch_size=2000,
validation_fraction=1 - training_fraction,
learning_rate=0.0001,
verbose=False,
silent=False,
epochs=epochs,
validation_skip=validation_skip,
optimizer='adam')
plt.rc('text', usetex=True)
validation_loss = nn.validation_loss_improving
validation_ep = np.linspace(0, epochs, len(nn.validation_loss_improving))
plt.semilogy(validation_ep, validation_loss, 'r-', label=r'NN')
plt.semilogy([0, epochs],
np.array([lasso_R2, lasso_R2]),
'k--',
label=r'Lasso')
plt.xlabel(r'Epoch', fontsize=10)
plt.ylabel(r'Mean squared error', fontsize=10)
plt.legend(fontsize=10)
plt.xlim((0, epochs))
ax = plt.gca()
ymin, ymax = ax.get_ylim()
if ymin > pow(10, -5):
ymin = pow(10, -5)
#plt.ylim((ymin,ymax))
plt.savefig(os.path.join(os.path.dirname(__file__), 'figures',
'NN_compare_lasso.png'),
transparent=True,
bbox_inches='tight')
