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rnn.py
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""" Vanilla RNN
@author Graham Taylor
"""
import numpy as np
import theano
import theano.tensor as T
from sklearn.base import BaseEstimator
import logging
import time
import os
import datetime
import cPickle as pickle
logger = logging.getLogger(__name__)
import matplotlib.pyplot as plt
plt.ion()
mode = theano.Mode(linker='cvm')
#mode = 'DEBUG_MODE'
class RNN(object):
""" Recurrent neural network class
Supported output types:
real : linear output units, use mean-squared error
binary : binary output units, use cross-entropy error
softmax : single softmax out, use cross-entropy error
"""
def __init__(self, input, n_in, n_hidden, n_out, activation=T.tanh,
output_type='real', use_symbolic_softmax=False):
self.input = input
self.activation = activation
self.output_type = output_type
# when using HF, SoftmaxGrad.grad is not implemented
# use a symbolic softmax which is slightly slower than T.nnet.softmax
# See: http://groups.google.com/group/theano-dev/browse_thread/
# thread/3930bd5a6a67d27a
if use_symbolic_softmax:
def symbolic_softmax(x):
e = T.exp(x)
return e / T.sum(e, axis=1).dimshuffle(0, 'x')
self.softmax = symbolic_softmax
else:
self.softmax = T.nnet.softmax
# recurrent weights as a shared variable
W_init = np.asarray(np.random.uniform(size=(n_hidden, n_hidden),
low=-.01, high=.01),
dtype=theano.config.floatX)
self.W = theano.shared(value=W_init, name='W')
# input to hidden layer weights
W_in_init = np.asarray(np.random.uniform(size=(n_in, n_hidden),
low=-.01, high=.01),
dtype=theano.config.floatX)
self.W_in = theano.shared(value=W_in_init, name='W_in')
# hidden to output layer weights
W_out_init = np.asarray(np.random.uniform(size=(n_hidden, n_out),
low=-.01, high=.01),
dtype=theano.config.floatX)
self.W_out = theano.shared(value=W_out_init, name='W_out')
h0_init = np.zeros((n_hidden,), dtype=theano.config.floatX)
self.h0 = theano.shared(value=h0_init, name='h0')
bh_init = np.zeros((n_hidden,), dtype=theano.config.floatX)
self.bh = theano.shared(value=bh_init, name='bh')
by_init = np.zeros((n_out,), dtype=theano.config.floatX)
self.by = theano.shared(value=by_init, name='by')
self.params = [self.W, self.W_in, self.W_out, self.h0,
self.bh, self.by]
# for every parameter, we maintain it's last update
# the idea here is to use "momentum"
# keep moving mostly in the same direction
self.updates = {}
for param in self.params:
init = np.zeros(param.get_value(borrow=True).shape,
dtype=theano.config.floatX)
self.updates[param] = theano.shared(init)
# recurrent function (using tanh activation function) and linear output
# activation function
def step(x_t, h_tm1):
h_t = self.activation(T.dot(x_t, self.W_in) + \
T.dot(h_tm1, self.W) + self.bh)
y_t = T.dot(h_t, self.W_out) + self.by
return h_t, y_t
# the hidden state `h` for the entire sequence, and the output for the
# entire sequence `y` (first dimension is always time)
[self.h, self.y_pred], _ = theano.scan(step,
sequences=self.input,
outputs_info=[self.h0, None])
# L1 norm ; one regularization option is to enforce L1 norm to
# be small
self.L1 = 0
self.L1 += abs(self.W.sum())
self.L1 += abs(self.W_in.sum())
self.L1 += abs(self.W_out.sum())
# square of L2 norm ; one regularization option is to enforce
# square of L2 norm to be small
self.L2_sqr = 0
self.L2_sqr += (self.W ** 2).sum()
self.L2_sqr += (self.W_in ** 2).sum()
self.L2_sqr += (self.W_out ** 2).sum()
if self.output_type == 'real':
self.loss = lambda y: self.mse(y)
elif self.output_type == 'binary':
# push through sigmoid
self.p_y_given_x = T.nnet.sigmoid(self.y_pred) # apply sigmoid
self.y_out = T.round(self.p_y_given_x) # round to {0,1}
self.loss = lambda y: self.nll_binary(y)
elif self.output_type == 'softmax':
# push through softmax, computing vector of class-membership
# probabilities in symbolic form
self.p_y_given_x = self.softmax(self.y_pred)
# compute prediction as class whose probability is maximal
self.y_out = T.argmax(self.p_y_given_x, axis=-1)
self.loss = lambda y: self.nll_multiclass(y)
else:
raise NotImplementedError
def mse(self, y):
# error between output and target
return T.mean((self.y_pred - y) ** 2)
def nll_binary(self, y):
# negative log likelihood based on binary cross entropy error
return T.mean(T.nnet.binary_crossentropy(self.p_y_given_x, y))
def nll_multiclass(self, y):
# negative log likelihood based on multiclass cross entropy error
# y.shape[0] is (symbolically) the number of rows in y, i.e.,
# number of time steps (call it T) in the sequence
# T.arange(y.shape[0]) is a symbolic vector which will contain
# [0,1,2,... n-1] T.log(self.p_y_given_x) is a matrix of
# Log-Probabilities (call it LP) with one row per example and
# one column per class LP[T.arange(y.shape[0]),y] is a vector
# v containing [LP[0,y[0]], LP[1,y[1]], LP[2,y[2]], ...,
# LP[n-1,y[n-1]]] and T.mean(LP[T.arange(y.shape[0]),y]) is
# the mean (across minibatch examples) of the elements in v,
# i.e., the mean log-likelihood across the minibatch.
return -T.mean(T.log(self.p_y_given_x)[T.arange(y.shape[0]), y])
def errors(self, y):
"""Return a float representing the number of errors in the sequence
over the total number of examples in the sequence ; zero one
loss over the size of the sequence
:type y: theano.tensor.TensorType
:param y: corresponds to a vector that gives for each example the
correct label
"""
# check if y has same dimension of y_pred
if y.ndim != self.y_out.ndim:
raise TypeError('y should have the same shape as self.y_out',
('y', y.type, 'y_out', self.y_out.type))
if self.output_type in ('binary', 'softmax'):
# check if y is of the correct datatype
if y.dtype.startswith('int'):
# the T.neq operator returns a vector of 0s and 1s, where 1
# represents a mistake in prediction
return T.mean(T.neq(self.y_out, y))
else:
raise NotImplementedError()
class MetaRNN(BaseEstimator):
def __init__(self, n_in=5, n_hidden=50, n_out=5, learning_rate=0.01,
n_epochs=100, L1_reg=0.00, L2_reg=0.00, learning_rate_decay=1,
activation='tanh', output_type='real',
final_momentum=0.9, initial_momentum=0.5,
momentum_switchover=5,
use_symbolic_softmax=False):
self.n_in = int(n_in)
self.n_hidden = int(n_hidden)
self.n_out = int(n_out)
self.learning_rate = float(learning_rate)
self.learning_rate_decay = float(learning_rate_decay)
self.n_epochs = int(n_epochs)
self.L1_reg = float(L1_reg)
self.L2_reg = float(L2_reg)
self.activation = activation
self.output_type = output_type
self.initial_momentum = float(initial_momentum)
self.final_momentum = float(final_momentum)
self.momentum_switchover = int(momentum_switchover)
self.use_symbolic_softmax = use_symbolic_softmax
self.ready()
def ready(self):
# input (where first dimension is time)
self.x = T.matrix()
# target (where first dimension is time)
if self.output_type == 'real':
self.y = T.matrix(name='y', dtype=theano.config.floatX)
elif self.output_type == 'binary':
self.y = T.matrix(name='y', dtype='int32')
elif self.output_type == 'softmax': # only vector labels supported
self.y = T.vector(name='y', dtype='int32')
else:
raise NotImplementedError
# initial hidden state of the RNN
self.h0 = T.vector()
# learning rate
self.lr = T.scalar()
if self.activation == 'tanh':
activation = T.tanh
elif self.activation == 'sigmoid':
activation = T.nnet.sigmoid
elif self.activation == 'relu':
activation = lambda x: x * (x > 0)
elif self.activation == 'cappedrelu':
activation = lambda x: T.minimum(x * (x > 0), 6)
else:
raise NotImplementedError
self.rnn = RNN(input=self.x, n_in=self.n_in,
n_hidden=self.n_hidden, n_out=self.n_out,
activation=activation, output_type=self.output_type,
use_symbolic_softmax=self.use_symbolic_softmax)
if self.output_type == 'real':
self.predict = theano.function(inputs=[self.x, ],
outputs=self.rnn.y_pred,
mode=mode)
elif self.output_type == 'binary':
self.predict_proba = theano.function(inputs=[self.x, ],
outputs=self.rnn.p_y_given_x, mode=mode)
self.predict = theano.function(inputs=[self.x, ],
outputs=T.round(self.rnn.p_y_given_x),
mode=mode)
elif self.output_type == 'softmax':
self.predict_proba = theano.function(inputs=[self.x, ],
outputs=self.rnn.p_y_given_x, mode=mode)
self.predict = theano.function(inputs=[self.x, ],
outputs=self.rnn.y_out, mode=mode)
else:
raise NotImplementedError
def shared_dataset(self, data_xy):
""" Load the dataset into shared variables """
data_x, data_y = data_xy
shared_x = theano.shared(np.asarray(data_x,
dtype=theano.config.floatX))
shared_y = theano.shared(np.asarray(data_y,
dtype=theano.config.floatX))
if self.output_type in ('binary', 'softmax'):
return shared_x, T.cast(shared_y, 'int32')
else:
return shared_x, shared_y
def __getstate__(self):
""" Return state sequence."""
params = self._get_params() # parameters set in constructor
weights = [p.get_value() for p in self.rnn.params]
state = (params, weights)
return state
def _set_weights(self, weights):
""" Set fittable parameters from weights sequence.
Parameters must be in the order defined by self.params:
W, W_in, W_out, h0, bh, by
"""
i = iter(weights)
for param in self.rnn.params:
param.set_value(i.next())
def __setstate__(self, state):
""" Set parameters from state sequence.
Parameters must be in the order defined by self.params:
W, W_in, W_out, h0, bh, by
"""
params, weights = state
self.set_params(**params)
self.ready()
self._set_weights(weights)
def save(self, fpath='.', fname=None):
""" Save a pickled representation of Model state. """
fpathstart, fpathext = os.path.splitext(fpath)
if fpathext == '.pkl':
# User supplied an absolute path to a pickle file
fpath, fname = os.path.split(fpath)
elif fname is None:
# Generate filename based on date
date_obj = datetime.datetime.now()
date_str = date_obj.strftime('%Y-%m-%d-%H:%M:%S')
class_name = self.__class__.__name__
fname = '%s.%s.pkl' % (class_name, date_str)
fabspath = os.path.join(fpath, fname)
logger.info("Saving to %s ..." % fabspath)
file = open(fabspath, 'wb')
state = self.__getstate__()
pickle.dump(state, file, protocol=pickle.HIGHEST_PROTOCOL)
file.close()
def load(self, path):
""" Load model parameters from path. """
logger.info("Loading from %s ..." % path)
file = open(path, 'rb')
state = pickle.load(file)
self.__setstate__(state)
file.close()
def fit(self, X_train, Y_train, X_test=None, Y_test=None,
validation_frequency=100):
""" Fit model
Pass in X_test, Y_test to compute test error and report during
training.
X_train : ndarray (n_seq x n_steps x n_in)
Y_train : ndarray (n_seq x n_steps x n_out)
validation_frequency : int
in terms of number of sequences (or number of weight updates)
"""
if X_test is not None:
assert(Y_test is not None)
self.interactive = True
test_set_x, test_set_y = self.shared_dataset((X_test, Y_test))
else:
self.interactive = False
train_set_x, train_set_y = self.shared_dataset((X_train, Y_train))
n_train = train_set_x.get_value(borrow=True).shape[0]
if self.interactive:
n_test = test_set_x.get_value(borrow=True).shape[0]
######################
# BUILD ACTUAL MODEL #
######################
logger.info('... building the model')
index = T.lscalar('index') # index to a case
# learning rate (may change)
l_r = T.scalar('l_r', dtype=theano.config.floatX)
mom = T.scalar('mom', dtype=theano.config.floatX) # momentum
cost = self.rnn.loss(self.y) \
+ self.L1_reg * self.rnn.L1 \
+ self.L2_reg * self.rnn.L2_sqr
compute_train_error = theano.function(inputs=[index, ],
outputs=self.rnn.loss(self.y),
givens={
self.x: train_set_x[index],
self.y: train_set_y[index]},
mode=mode)
if self.interactive:
compute_test_error = theano.function(inputs=[index, ],
outputs=self.rnn.loss(self.y),
givens={
self.x: test_set_x[index],
self.y: test_set_y[index]},
mode=mode)
# compute the gradient of cost with respect to theta = (W, W_in, W_out)
# gradients on the weights using BPTT
gparams = []
for param in self.rnn.params:
gparam = T.grad(cost, param)
gparams.append(gparam)
updates = {}
for param, gparam in zip(self.rnn.params, gparams):
weight_update = self.rnn.updates[param]
upd = mom * weight_update - l_r * gparam
updates[weight_update] = upd
updates[param] = param + upd
# compiling a Theano function `train_model` that returns the
# cost, but in the same time updates the parameter of the
# model based on the rules defined in `updates`
train_model = theano.function(inputs=[index, l_r, mom],
outputs=cost,
updates=updates,
givens={
self.x: train_set_x[index],
self.y: train_set_y[index]},
mode=mode)
###############
# TRAIN MODEL #
###############
logger.info('... training')
epoch = 0
while (epoch < self.n_epochs):
epoch = epoch + 1
for idx in xrange(n_train):
effective_momentum = self.final_momentum \
if epoch > self.momentum_switchover \
else self.initial_momentum
example_cost = train_model(idx, self.learning_rate,
effective_momentum)
# iteration number (how many weight updates have we made?)
# epoch is 1-based, index is 0 based
iter = (epoch - 1) * n_train + idx + 1
if iter % validation_frequency == 0:
# compute loss on training set
train_losses = [compute_train_error(i)
for i in xrange(n_train)]
this_train_loss = np.mean(train_losses)
if self.interactive:
test_losses = [compute_test_error(i)
for i in xrange(n_test)]
this_test_loss = np.mean(test_losses)
logger.info('epoch %i, seq %i/%i, tr loss %f '
'te loss %f lr: %f' % \
(epoch, idx + 1, n_train,
this_train_loss, this_test_loss, self.learning_rate))
else:
logger.info('epoch %i, seq %i/%i, train loss %f '
'lr: %f' % \
(epoch, idx + 1, n_train, this_train_loss,
self.learning_rate))
self.learning_rate *= self.learning_rate_decay
def test_real():
""" Test RNN with real-valued outputs. """
n_hidden = 10
n_in = 5
n_out = 3
n_steps = 10
n_seq = 100
np.random.seed(0)
# simple lag test
seq = np.random.randn(n_seq, n_steps, n_in)
targets = np.zeros((n_seq, n_steps, n_out))
targets[:, 1:, 0] = seq[:, :-1, 3] # delayed 1
targets[:, 1:, 1] = seq[:, :-1, 2] # delayed 1
targets[:, 2:, 2] = seq[:, :-2, 0] # delayed 2
targets += 0.01 * np.random.standard_normal(targets.shape)
model = MetaRNN(n_in=n_in, n_hidden=n_hidden, n_out=n_out,
learning_rate=0.001, learning_rate_decay=0.999,
n_epochs=400, activation='tanh')
model.fit(seq, targets, validation_frequency=1000)
plt.close('all')
fig = plt.figure()
ax1 = plt.subplot(211)
plt.plot(seq[0])
ax1.set_title('input')
ax2 = plt.subplot(212)
true_targets = plt.plot(targets[0])
guess = model.predict(seq[0])
guessed_targets = plt.plot(guess, linestyle='--')
for i, x in enumerate(guessed_targets):
x.set_color(true_targets[i].get_color())
ax2.set_title('solid: true output, dashed: model output')
def test_binary(multiple_out=False, n_epochs=250):
""" Test RNN with binary outputs. """
n_hidden = 10
n_in = 5
if multiple_out:
n_out = 2
else:
n_out = 1
n_steps = 10
n_seq = 100
np.random.seed(0)
# simple lag test
seq = np.random.randn(n_seq, n_steps, n_in)
targets = np.zeros((n_seq, n_steps, n_out))
# whether lag 1 (dim 3) is greater than lag 2 (dim 0)
targets[:, 2:, 0] = np.cast[np.int](seq[:, 1:-1, 3] > seq[:, :-2, 0])
if multiple_out:
# whether product of lag 1 (dim 4) and lag 1 (dim 2)
# is less than lag 2 (dim 0)
targets[:, 2:, 1] = np.cast[np.int](
(seq[:, 1:-1, 4] * seq[:, 1:-1, 2]) > seq[:, :-2, 0])
model = MetaRNN(n_in=n_in, n_hidden=n_hidden, n_out=n_out,
learning_rate=0.001, learning_rate_decay=0.999,
n_epochs=n_epochs, activation='tanh', output_type='binary')
model.fit(seq, targets, validation_frequency=1000)
seqs = xrange(10)
plt.close('all')
for seq_num in seqs:
fig = plt.figure()
ax1 = plt.subplot(211)
plt.plot(seq[seq_num])
ax1.set_title('input')
ax2 = plt.subplot(212)
true_targets = plt.step(xrange(n_steps), targets[seq_num], marker='o')
guess = model.predict_proba(seq[seq_num])
guessed_targets = plt.step(xrange(n_steps), guess)
plt.setp(guessed_targets, linestyle='--', marker='d')
for i, x in enumerate(guessed_targets):
x.set_color(true_targets[i].get_color())
ax2.set_ylim((-0.1, 1.1))
ax2.set_title('solid: true output, dashed: model output (prob)')
def test_softmax(n_epochs=250):
""" Test RNN with softmax outputs. """
n_hidden = 10
n_in = 5
n_steps = 10
n_seq = 100
n_classes = 3
n_out = n_classes # restricted to single softmax per time step
np.random.seed(0)
# simple lag test
seq = np.random.randn(n_seq, n_steps, n_in)
targets = np.zeros((n_seq, n_steps), dtype=np.int)
thresh = 0.5
# if lag 1 (dim 3) is greater than lag 2 (dim 0) + thresh
# class 1
# if lag 1 (dim 3) is less than lag 2 (dim 0) - thresh
# class 2
# if lag 2(dim0) - thresh <= lag 1 (dim 3) <= lag2(dim0) + thresh
# class 0
targets[:, 2:][seq[:, 1:-1, 3] > seq[:, :-2, 0] + thresh] = 1
targets[:, 2:][seq[:, 1:-1, 3] < seq[:, :-2, 0] - thresh] = 2
#targets[:, 2:, 0] = np.cast[np.int](seq[:, 1:-1, 3] > seq[:, :-2, 0])
model = MetaRNN(n_in=n_in, n_hidden=n_hidden, n_out=n_out,
learning_rate=0.001, learning_rate_decay=0.999,
n_epochs=n_epochs, activation='tanh',
output_type='softmax', use_symbolic_softmax=False)
model.fit(seq, targets, validation_frequency=1000)
seqs = xrange(10)
plt.close('all')
for seq_num in seqs:
fig = plt.figure()
ax1 = plt.subplot(211)
plt.plot(seq[seq_num])
ax1.set_title('input')
ax2 = plt.subplot(212)
# blue line will represent true classes
true_targets = plt.step(xrange(n_steps), targets[seq_num], marker='o')
# show probabilities (in b/w) output by model
guess = model.predict_proba(seq[seq_num])
guessed_probs = plt.imshow(guess.T, interpolation='nearest',
cmap='gray')
ax2.set_title('blue: true class, grayscale: probs assigned by model')
if __name__ == "__main__":
logging.basicConfig(level=logging.INFO)
t0 = time.time()
test_real()
# problem takes more epochs to solve
#test_binary(multiple_out=True, n_epochs=2400)
#test_softmax(n_epochs=250)
print "Elapsed time: %f" % (time.time() - t0)