def test_adadelta():
"""
Make sure that learning_rule.AdaDelta obtains the same parameter values as
with a hand-crafted AdaDelta implementation, given a dummy model and
learning rate scaler for each parameter.
Reference:
"AdaDelta: An Adaptive Learning Rate Method", Matthew D. Zeiler.
"""
# We include a cost other than SumOfParams so that data is actually
# queried from the training set, and the expected number of updates
# are applied.
cost = SumOfCosts([SumOfOneHalfParamsSquared(), (0., DummyCost())])
model = DummyModel(shapes, lr_scalers=scales)
dataset = ArangeDataset(1)
decay = 0.95
sgd = SGD(cost=cost,
learning_rate=learning_rate,
learning_rule=AdaDelta(decay),
batch_size=1)
sgd.setup(model=model, dataset=dataset)
state = {}
for param in model.get_params():
param_shape = param.get_value().shape
state[param] = {}
state[param]['g2'] = np.zeros(param_shape)
state[param]['dx2'] = np.zeros(param_shape)
def adadelta_manual(model, state):
inc = []
rval = []
for scale, param in izip(scales, model.get_params()):
pstate = state[param]
param_val = param.get_value()
# begin adadelta
pstate['g2'] = decay * pstate['g2'] + (1 - decay) * param_val**2
rms_g_t = np.sqrt(pstate['g2'] + scale * learning_rate)
rms_dx_tm1 = np.sqrt(pstate['dx2'] + scale * learning_rate)
dx_t = -rms_dx_tm1 / rms_g_t * param_val
pstate['dx2'] = decay * pstate['dx2'] + (1 - decay) * dx_t**2
rval += [param_val + dx_t]
return rval
manual = adadelta_manual(model, state)
sgd.train(dataset=dataset)
assert all(
np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param in izip(manual, model.get_params()))
manual = adadelta_manual(model, state)
sgd.train(dataset=dataset)
assert all(
np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param in izip(manual, model.get_params()))
def test_adadelta():
"""
Make sure that learning_rule.AdaDelta obtains the same parameter values as
with a hand-crafted AdaDelta implementation, given a dummy model and
learning rate scaler for each parameter.
Reference:
"AdaDelta: An Adaptive Learning Rate Method", Matthew D. Zeiler.
"""
# We include a cost other than SumOfParams so that data is actually
# queried from the training set, and the expected number of updates
# are applied.
cost = SumOfCosts([SumOfOneHalfParamsSquared(), (0., DummyCost())])
model = DummyModel(shapes, lr_scalers=scales)
dataset = ArangeDataset(1)
decay = 0.95
sgd = SGD(cost=cost,
learning_rate=learning_rate,
learning_rule=AdaDelta(decay),
batch_size=1)
sgd.setup(model=model, dataset=dataset)
state = {}
for param in model.get_params():
param_shape = param.get_value().shape
state[param] = {}
state[param]['g2'] = np.zeros(param_shape)
state[param]['dx2'] = np.zeros(param_shape)
def adadelta_manual(model, state):
inc = []
rval = []
for scale, param in izip(scales, model.get_params()):
pstate = state[param]
param_val = param.get_value()
# begin adadelta
pstate['g2'] = decay * pstate['g2'] + (1 - decay) * param_val ** 2
rms_g_t = np.sqrt(pstate['g2'] + scale * learning_rate)
rms_dx_tm1 = np.sqrt(pstate['dx2'] + scale * learning_rate)
dx_t = -rms_dx_tm1 / rms_g_t * param_val
pstate['dx2'] = decay * pstate['dx2'] + (1 - decay) * dx_t ** 2
rval += [param_val + dx_t]
return rval
manual = adadelta_manual(model, state)
sgd.train(dataset=dataset)
assert all(np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param
in izip(manual, model.get_params()))
manual = adadelta_manual(model, state)
sgd.train(dataset=dataset)
assert all(np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param in
izip(manual, model.get_params()))
def test_adagrad():
"""
Make sure that learning_rule.AdaGrad obtains the same parameter values as
with a hand-crafted AdaGrad implementation, given a dummy model and
learning rate scaler for each parameter.
Reference:
"Adaptive subgradient methods for online learning and
stochastic optimization", Duchi J, Hazan E, Singer Y.
"""
# We include a cost other than SumOfParams so that data is actually
# queried from the training set, and the expected number of updates
# are applied.
cost = SumOfCosts([SumOfOneHalfParamsSquared(), (0., DummyCost())])
model = DummyModel(shapes, lr_scalers=scales)
dataset = ArangeDataset(1)
sgd = SGD(cost=cost,
learning_rate=learning_rate,
learning_rule=AdaGrad(),
batch_size=1)
sgd.setup(model=model, dataset=dataset)
state = {}
for param in model.get_params():
param_shape = param.get_value().shape
state[param] = {}
state[param]['sg2'] = np.zeros(param_shape)
def adagrad_manual(model, state):
rval = []
for scale, param in izip(scales, model.get_params()):
pstate = state[param]
param_val = param.get_value()
# begin adadelta
pstate['sg2'] += param_val ** 2
dx_t = - (scale * learning_rate
/ np.sqrt(pstate['sg2'])
* param_val)
rval += [param_val + dx_t]
return rval
manual = adagrad_manual(model, state)
sgd.train(dataset=dataset)
assert all(np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param
in izip(manual, model.get_params()))
manual = adagrad_manual(model, state)
sgd.train(dataset=dataset)
assert all(np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param in
izip(manual, model.get_params()))
def test_adagrad():
"""
Make sure that learning_rule.AdaGrad obtains the same parameter values as
with a hand-crafted AdaGrad implementation, given a dummy model and
learning rate scaler for each parameter.
Reference:
"Adaptive subgradient methods for online learning and
stochastic optimization", Duchi J, Hazan E, Singer Y.
"""
# We include a cost other than SumOfParams so that data is actually
# queried from the training set, and the expected number of updates
# are applied.
cost = SumOfCosts([SumOfOneHalfParamsSquared(), (0., DummyCost())])
model = DummyModel(shapes, lr_scalers=scales)
dataset = ArangeDataset(1)
sgd = SGD(cost=cost,
learning_rate=learning_rate,
learning_rule=AdaGrad(),
batch_size=1)
sgd.setup(model=model, dataset=dataset)
state = {}
for param in model.get_params():
param_shape = param.get_value().shape
state[param] = {}
state[param]['sg2'] = np.zeros(param_shape)
def adagrad_manual(model, state):
rval = []
for scale, param in izip(scales, model.get_params()):
pstate = state[param]
param_val = param.get_value()
# begin adadelta
pstate['sg2'] += param_val**2
dx_t = -(scale * learning_rate / np.sqrt(pstate['sg2']) *
param_val)
rval += [param_val + dx_t]
return rval
manual = adagrad_manual(model, state)
sgd.train(dataset=dataset)
assert all(
np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param in izip(manual, model.get_params()))
manual = adagrad_manual(model, state)
sgd.train(dataset=dataset)
assert all(
np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param in izip(manual, model.get_params()))
def test_rmsprop():
"""
Make sure that learning_rule.RMSProp obtains the same parameter values as
with a hand-crafted RMSProp implementation, given a dummy model and
learning rate scaler for each parameter.
"""
# We include a cost other than SumOfParams so that data is actually
# queried from the training set, and the expected number of updates
# are applied.
cost = SumOfCosts([SumOfOneHalfParamsSquared(), (0., DummyCost())])
scales = [.01, .02, .05, 1., 5.]
shapes = [(1,), (9,), (8, 7), (6, 5, 4), (3, 2, 2, 2)]
model = DummyModel(shapes, lr_scalers=scales)
dataset = ArangeDataset(1)
learning_rate = .001
decay = 0.90
max_scaling = 1e5
sgd = SGD(cost=cost,
learning_rate=learning_rate,
learning_rule=RMSProp(decay),
batch_size=1)
sgd.setup(model=model, dataset=dataset)
state = {}
for param in model.get_params():
param_shape = param.get_value().shape
state[param] = {}
state[param]['g2'] = np.zeros(param_shape)
def rmsprop_manual(model, state):
inc = []
rval = []
epsilon = 1. / max_scaling
for scale, param in izip(scales, model.get_params()):
pstate = state[param]
param_val = param.get_value()
# begin rmsprop
pstate['g2'] = decay * pstate['g2'] + (1 - decay) * param_val ** 2
rms_g_t = np.maximum(np.sqrt(pstate['g2']), epsilon)
dx_t = - scale * learning_rate / rms_g_t * param_val
rval += [param_val + dx_t]
return rval
manual = rmsprop_manual(model, state)
sgd.train(dataset=dataset)
assert all(np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param
in izip(manual, model.get_params()))
def test_rmsprop():
"""
Make sure that learning_rule.RMSProp obtains the same parameter values as
with a hand-crafted RMSProp implementation, given a dummy model and
learning rate scaler for each parameter.
"""
# We include a cost other than SumOfParams so that data is actually
# queried from the training set, and the expected number of updates
# are applied.
cost = SumOfCosts([SumOfOneHalfParamsSquared(), (0., DummyCost())])
scales = [.01, .02, .05, 1., 5.]
shapes = [(1, ), (9, ), (8, 7), (6, 5, 4), (3, 2, 2, 2)]
model = DummyModel(shapes, lr_scalers=scales)
dataset = ArangeDataset(1)
learning_rate = .001
decay = 0.90
max_scaling = 1e5
sgd = SGD(cost=cost,
learning_rate=learning_rate,
learning_rule=RMSProp(decay),
batch_size=1)
sgd.setup(model=model, dataset=dataset)
state = {}
for param in model.get_params():
param_shape = param.get_value().shape
state[param] = {}
state[param]['g2'] = np.zeros(param_shape)
def rmsprop_manual(model, state):
inc = []
rval = []
epsilon = 1. / max_scaling
for scale, param in izip(scales, model.get_params()):
pstate = state[param]
param_val = param.get_value()
# begin rmsprop
pstate['g2'] = decay * pstate['g2'] + (1 - decay) * param_val**2
rms_g_t = np.maximum(np.sqrt(pstate['g2']), epsilon)
dx_t = -scale * learning_rate / rms_g_t * param_val
rval += [param_val + dx_t]
return rval
manual = rmsprop_manual(model, state)
sgd.train(dataset=dataset)
assert all(
np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param in izip(manual, model.get_params()))
def test_nesterov_momentum():
"""
Make sure that learning_rule.Momentum obtains the same parameter values as
with a hand-crafted sgd w/ momentum implementation, given a dummy model and
learning rate scaler for each parameter.
"""
# We include a cost other than SumOfParams so that data is actually
# queried from the training set, and the expected number of updates
# are applied.
cost = SumOfCosts([SumOfParams(), (0., DummyCost())])
model = DummyModel(shapes, lr_scalers=scales)
dataset = ArangeDataset(1)
momentum = 0.5
sgd = SGD(cost=cost,
learning_rate=learning_rate,
learning_rule=Momentum(momentum, nesterov_momentum=True),
batch_size=1)
sgd.setup(model=model, dataset=dataset)
manual = [param.get_value() for param in model.get_params()]
vel = [-learning_rate * scale for scale in scales]
updates = [
-learning_rate * scale + v * momentum
for scale, v in izip(scales, vel)
]
manual = [param + update for param, update in izip(manual, updates)]
sgd.train(dataset=dataset)
assert all(
np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param in izip(manual, model.get_params()))
vel = [
-learning_rate * scale + i * momentum
for scale, i in izip(scales, vel)
]
updates = [
-learning_rate * scale + v * momentum
for scale, v in izip(scales, vel)
]
manual = [param + update for param, update in izip(manual, updates)]
sgd.train(dataset=dataset)
assert all(
np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param in izip(manual, model.get_params()))
def test_momentum():
"""
Make sure that learning_rule.Momentum obtains the same parameter values as
with a hand-crafted sgd w/ momentum implementation, given a dummy model and
learning rate scaler for each parameter.
"""
# We include a cost other than SumOfParams so that data is actually
# queried from the training set, and the expected number of updates
# are applied.
cost = SumOfCosts([SumOfParams(), (0., DummyCost())])
scales = [.01, .02, .05, 1., 5.]
shapes = [(1, ), (9, ), (8, 7), (6, 5, 4), (3, 2, 2, 2)]
model = DummyModel(shapes, lr_scalers=scales)
dataset = ArangeDataset(1)
learning_rate = .001
momentum = 0.5
sgd = SGD(cost=cost,
learning_rate=learning_rate,
learning_rule=Momentum(momentum),
batch_size=1)
sgd.setup(model=model, dataset=dataset)
manual = [param.get_value() for param in model.get_params()]
inc = [-learning_rate * scale for param, scale in zip(manual, scales)]
manual = [param + i for param, i in zip(manual, inc)]
sgd.train(dataset=dataset)
assert all(
np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param in zip(manual, model.get_params()))
manual = [
param - learning_rate * scale + i * momentum
for param, scale, i in zip(manual, scales, inc)
]
sgd.train(dataset=dataset)
assert all(
np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param in zip(manual, model.get_params()))
def test_nesterov_momentum():
"""
Make sure that learning_rule.Momentum obtains the same parameter values as
with a hand-crafted sgd w/ momentum implementation, given a dummy model and
learning rate scaler for each parameter.
"""
# We include a cost other than SumOfParams so that data is actually
# queried from the training set, and the expected number of updates
# are applied.
cost = SumOfCosts([SumOfParams(), (0., DummyCost())])
model = DummyModel(shapes, lr_scalers=scales)
dataset = ArangeDataset(1)
momentum = 0.5
sgd = SGD(cost=cost,
learning_rate=learning_rate,
learning_rule=Momentum(momentum, nesterov_momentum=True),
batch_size=1)
sgd.setup(model=model, dataset=dataset)
manual = [param.get_value() for param in model.get_params()]
vel = [-learning_rate * scale for scale in scales]
updates = [-learning_rate * scale + v * momentum
for scale, v in izip(scales, vel)]
manual = [param + update for param, update in izip(manual, updates)]
sgd.train(dataset=dataset)
assert all(np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param
in izip(manual, model.get_params()))
vel = [-learning_rate * scale + i * momentum
for scale, i in izip(scales, vel)]
updates = [-learning_rate * scale + v * momentum
for scale, v in izip(scales, vel)]
manual = [param + update for param, update in izip(manual, updates)]
sgd.train(dataset=dataset)
assert all(np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param
in izip(manual, model.get_params()))
def test_momentum():
"""
Make sure that learning_rule.Momentum obtains the same parameter values as
with a hand-crafted sgd w/ momentum implementation, given a dummy model and
learning rate scaler for each parameter.
"""
# We include a cost other than SumOfParams so that data is actually
# queried from the training set, and the expected number of updates
# are applied.
cost = SumOfCosts([SumOfParams(), (0., DummyCost())])
scales = [.01, .02, .05, 1., 5.]
shapes = [(1,), (9,), (8, 7), (6, 5, 4), (3, 2, 2, 2)]
model = DummyModel(shapes, lr_scalers=scales)
dataset = ArangeDataset(1)
learning_rate = .001
momentum = 0.5
sgd = SGD(cost=cost,
learning_rate=learning_rate,
learning_rule=Momentum(momentum),
batch_size=1)
sgd.setup(model=model, dataset=dataset)
manual = [param.get_value() for param in model.get_params()]
inc = [-learning_rate * scale for scale in scales]
manual = [param + i for param, i in izip(manual, inc)]
sgd.train(dataset=dataset)
assert all(np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param in
izip(manual, model.get_params()))
manual = [param - learning_rate * scale + i * momentum
for param, scale, i in izip(manual, scales, inc)]
sgd.train(dataset=dataset)
assert all(np.allclose(manual_param, sgd_param.get_value())
for manual_param, sgd_param in
izip(manual, model.get_params()))
def prepare_adagrad_test(dataset_type='arange', model_type='random'):
"""
Factor out common code for AdaGrad tests.
Parameters
----------
dataset_type : string, optional
Can use either `arange` to use an ArangeDataset instance or
`zeros` to create an all-zeros DenseDesignMatrix.
model_type : string, optional
How to initialize the model; `random` will initialize parameters
to random values, `zeros` to zero.
"""
# We include a cost other than SumOfParams so that data is actually
# queried from the training set, and the expected number of updates
# are applied.
cost = SumOfCosts([SumOfOneHalfParamsSquared(), (0., DummyCost())])
model = DummyModel(shapes, lr_scalers=scales, init_type=model_type)
if dataset_type == 'arange':
dataset = ArangeDataset(1)
elif dataset_type == 'zeros':
X = np.zeros((1, 1))
X[:, 0] = np.arange(1)
dataset = DenseDesignMatrix(X)
else:
raise ValueError('Unknown value for dataset_type: %s',
dataset_type)
sgd = SGD(cost=cost,
learning_rate=learning_rate,
learning_rule=AdaGrad(),
batch_size=1)
sgd.setup(model=model, dataset=dataset)
state = {}
for param in model.get_params():
param_shape = param.get_value().shape
state[param] = {}
state[param]['sg2'] = np.zeros(param_shape)
return (cost, model, dataset, sgd, state)
def prepare_adagrad_test(dataset_type='arange', model_type='random'):
"""
Factor out common code for AdaGrad tests.
Parameters
----------
dataset_type : string, optional
Can use either `arange` to use an ArangeDataset instance or
`zeros` to create an all-zeros DenseDesignMatrix.
model_type : string, optional
How to initialize the model; `random` will initialize parameters
to random values, `zeros` to zero.
"""
# We include a cost other than SumOfParams so that data is actually
# queried from the training set, and the expected number of updates
# are applied.
cost = SumOfCosts([SumOfOneHalfParamsSquared(), (0., DummyCost())])
model = DummyModel(shapes, lr_scalers=scales, init_type=model_type)
if dataset_type == 'arange':
dataset = ArangeDataset(1)
elif dataset_type == 'zeros':
X = np.zeros((1, 1))
X[:, 0] = np.arange(1)
dataset = DenseDesignMatrix(X)
else:
raise ValueError('Unknown value for dataset_type: %s', dataset_type)
sgd = SGD(cost=cost,
learning_rate=learning_rate,
learning_rule=AdaGrad(),
batch_size=1)
sgd.setup(model=model, dataset=dataset)
state = {}
for param in model.get_params():
param_shape = param.get_value().shape
state[param] = {}
state[param]['sg2'] = np.zeros(param_shape)
return (cost, model, dataset, sgd, state)