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tf_sparse_fit.py
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tf_sparse_fit.py
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## This module implements a sparse fit mechanism using Tensorflow.
import tensorflow as tf
import numpy as np
from scipy.stats import zscore
import time
def get_training_batches(X_tr, Y_tr, batch_size=200, delay=0, verbose=True):
"""
Given an object of training data return a generator that gives training
data batches.
"""
idx = 0
num_pts = np.shape(X_tr)[0] - delay
Y_tr = np.concatenate((Y_tr[delay:, :], Y_tr[:delay, :]), axis=0)
if verbose:
print "Shape of training set: " + str(np.shape(X_tr))
print "Shape of test set: " + str(np.shape(Y_tr))
assert np.shape(X_tr)[0] == np.shape(Y_tr)[0]
i = 0
while True:
if i + batch_size >= num_pts:
remaining_pts = num_pts - i
num_remove = batch_size - remaining_pts
X_batch = np.concatenate((X_tr[-remaining_pts:, :],
X_tr[:num_remove, :]), axis=0)
Y_batch = np.concatenate((Y_tr[-remaining_pts:, :],
Y_tr[:num_remove, :]), axis=0)
yield (X_batch, Y_batch)
i = num_remove
else:
yield (X_tr[i:i+batch_size, :],
Y_tr[i:i+batch_size, :])
i += batch_size
def pearson_correllations(y, y_pred):
"""Computes the pearson correllation of a set of predictions.
Parameters
----------
y:
Actual test set values. A numpy array of shape (npoints, nvariables)
y_pred:
The predicted values. A numpy array of shape (npoints, nvariables)
"""
return (zscore(y)*zscore(y_pred)).mean(axis=0)
def lsq_loss(y_predicted, y_actual, name='test_loss'):
"""Simple least-squares loss without regularization. Useful for evaluating
performance."""
with tf.name_scope(name):
loss = tf.reduce_sum(tf.square(tf.sub(y_actual, y_predicted)))
return loss
def l1_loss(lambda_l1, weights, name='l1_loss'):
"""Least squares loss along with L1 regularization."""
with tf.name_scope(name):
l1_penalty = tf.mul(lambda_l1, tf.reduce_mean(tf.abs(weights)))
return l1_penalty
def l1_group_loss(lambda_vec, weights, name='l1_loss'):
"""Least squares loss along with L1 regularization."""
with tf.name_scope(name):
l1_penalty = tf.reduce_mean(
tf.matmul(tf.diag(lambda_vec),
tf.abs(weights)))
return l1_penalty
def group_lasso_loss(lambda_vec, y_predicted, y_actual, weights):
"""Least squares with group LASSO"""
with tf.name_scope("group_lasso_loss"):
return tf.add(lsq_loss(y_predicted, y_actual),
l1_group_loss(lambda_vec, weights))
def threshold_by_percent_max(t, threshold, use_active_set=False):
"""Creates tensorflow ops to perform a thresholding of a tensor by a
percentage of the maximum value. To be used when thresholding gradients.
Optionally maintains an active set.
Parameters
----------
t: tensor
The tensor to threshold by percent max.
threshold: float
A number between 0 and 1 that specifies the threshold.
use_active_set: bool
Specifies whether or not to use an active set.
Returns
-------
A tensor of the same shape as t that has had all values under the threshold
set to 0.
"""
with tf.name_scope("threshold_by_percent_max"):
# t = tf.convert_to_tensor(t, name="t")
# shape = tf.shape(t)
abs_t = tf.abs(t)
thresh_percentile = tf.constant(threshold, dtype=tf.float32)
zeros = tf.zeros(shape=tf.shape(t), dtype=tf.float32)
maximum = tf.reduce_max(abs_t, reduction_indices=[0])
# A tensor, the same shape as t, that has the threshold values to be
# compared against every value.
thresh_one_voxel = tf.expand_dims(tf.mul(thresh_percentile,
maximum), 0)
thresh_tensor = tf.tile(thresh_one_voxel,
tf.pack([tf.shape(t)[0], 1]))
above_thresh_values = tf.greater_equal(abs_t, thresh_tensor)
if use_active_set:
active_set = tf.Variable(tf.equal(tf.ones(tf.shape(t)),
tf.zeros(tf.shape(t))),
name="active_set", dtype=tf.bool)
active_set_inc = tf.assign(active_set,
tf.logical_or(active_set,
above_thresh_values),
name="incremented_active_set")
active_set_size = tf.reduce_sum(tf.cast(active_set, tf.float32),
name="size_of_active_set")
return (tf.select(active_set_inc, t, zeros), active_set_size)
else:
return tf.select(above_thresh_values, t, zeros)
def group_lasso_fit(X_tr, Y_tr, X_test, Y_test, batch_size=100,
train_dir='.', max_iterations=350, learning_rate=0.0001,
l1_params=None, verbose=True):
"""Run group a LASSO fit using stochastic gradient descent on GPU.
Parameters
----------
X_tr:
The training set. A numpy array of shape (time_points, #features).
Y_tr:
The training labels. A numpy array of shape (time_points, #labels)
(The labels might be BOLD signal across different voxels,
for example.)
X_test:
The test set. A numpy array of shape (time_points, #features). The
number of time points may be different between the training and
test sets, but the number of features may not.
Y_test:
The test labels. A numpy array of shape (time_points, #labels)
batch_size: int, 100
The minibatch size for the stochastic gradient descent.
train_dir: str, '.'
The directory that model and log directories will be saved in.
This directory is important if you want to view the fit in
Tensorboard.
max_iterations: int, 350
Early stopping is not yet implemented. Right now, you simply set
a number of iterations.
learning_rate: float, 0.0001
The SGD learning rate.
l1_params:
A numpy array with length equal to the number of features, that
specifies L1 regularization constants for every feature.
Returns
-------
A dictionary containing both 'weights' and 'predictions', which are
numpy arrays containing the learned weights, and the pearson
correllation for each label, respectively.
"""
if len(np.shape(Y_tr)) <= 1:
num_predictors = 1
else:
num_predictors = np.shape(Y_tr)[1]
num_features = np.shape(X_test)[1]
if verbose:
print "Building computation graph..."
with tf.Graph().as_default():
with tf.name_scope('test_data'):
x_tst = tf.placeholder(tf.float32, shape=np.shape(X_test))
y_tst = tf.placeholder(tf.float32, shape=np.shape(Y_test))
with tf.name_scope('input_data'):
x_tr = tf.placeholder(tf.float32,
shape=(batch_size, num_features))
y_tr = tf.placeholder(tf.float32,
shape=(batch_size, num_predictors))
# Getting the Y predictions
W = tf.Variable(tf.zeros([num_features, num_predictors]),
name='weights')
y_pred = tf.matmul(x_tr, W)
# Loss function associated summaries.
if l1_params is None:
lambda_vec = tf.constant(tf.zeros([num_features],
dtype=tf.float32))
else:
assert len(l1_params) == num_features
lambda_vec = tf.constant(l1_params, dtype=tf.float32)
loss = group_lasso_loss(lambda_vec, y_pred, y_tr, W)
loss_summary = tf.scalar_summary("Test LASSO Loss", loss)
# Weight histogram summary.
W_hist_summary = tf.histogram_summary("Weight Distribution", W)
# Optimizer
global_step = tf.Variable(0, name='global_step', dtype=tf.int64)
optimizer = tf.train.GradientDescentOptimizer(learning_rate)
op = optimizer.minimize(loss)
train_summary = tf.merge_summary([W_hist_summary, loss_summary])
# Report the test set error (but don't optimize on it)
y_pred_test = tf.matmul(x_tst, W)
test_loss = lsq_loss(y_pred_test, y_tst, name='test_loss')
tst_loss_summary = tf.scalar_summary("Test LSQ Loss", test_loss)
# Tensorflow boilerplate
init = tf.initialize_all_variables()
saver = tf.train.Saver({'weights': W})
sess = tf.Session(config=tf.ConfigProto(log_device_placement=True))
summary_writer = tf.train.SummaryWriter(train_dir + '/log',
sess.graph)
if verbose:
print "initializing variables..."
sess.run(init)
batch_gen = get_training_batches(X_tr, Y_tr, batch_size=batch_size,
verbose=verbose)
# Run training.
start_time = time.time()
for step in xrange(max_iterations):
if verbose:
print('\n== Optimization Step %d of %d =='
% (step, max_iterations))
training_loss = 0.
if verbose:
print "...Generating batch"
X_batch, Y_batch = batch_gen.next()
if verbose:
print "...Calculating Gradients"
(_, loss_eval, train_summ_eval) = sess.run(
[op, loss, train_summary], feed_dict={x_tr: X_batch,
y_tr: Y_batch})
# Write out a bunch of summaries:
duration = time.time() - start_time
if verbose:
print('Step %d: loss=%.2f (%.3f sec)'
% (step, loss_eval, duration))
summary_writer.add_summary(train_summ_eval, step)
summary_writer.flush()
# We evaluate the test set every so often, just to visualize it
# in tensorboard.
if step > 0 and step % 10 == 0:
if verbose:
print "Shape of x_test: " + str(np.shape(X_test))
print "shape of y_test: " + str(np.shape(Y_test))
tst_summ, tst_loss = sess.run([tst_loss_summary, test_loss],
feed_dict={x_tst: X_test,
y_tst: Y_test})
if verbose:
print "test_loss: " + str(tst_loss)
print('Step %d: loss=%.2f test_loss=%.2f (%.3f sec)'
% (step, training_loss, tst_loss, duration))
summary_writer.add_summary(tst_summ, step)
summary_writer.flush()
fit = {}
y_pred_test_ev = sess.run([y_pred_test], feed_dict={x_tst: X_test,
y_tst: Y_test})[0]
final_W = sess.run([W])
fit['weights'] = final_W
# Evaluate Prediction Accuracy
fit['predictions'] = pearson_correllations(Y_test, y_pred_test_ev)
return fit
def threshold_gradient_descent_fit(X_tr, Y_tr, X_test, Y_test, batch_size=100,
train_dir='.', max_iterations=350, learning_rate=0.0001,
threshold_grad_desc = 0.5, use_active_set=True,
verbose=True):
"""Run Threshold gradient descent on GPU.
Parameters
----------
X_tr:
The training set. A numpy array of shape (time_points, #features).
Y_tr:
The training labels. A numpy array of shape (time_points, #labels)
(The labels might be BOLD signal across different voxels,
for example.)
X_test:
The test set. A numpy array of shape (time_points, #features). The
number of time points may be different between the training and test
sets, but the number of features may not.
Y_test:
The test labels. A numpy array of shape (time_points, #labels)
batch_size: int, 100
The minibatch size for the stochastic gradient descent.
train_dir: str, '.'
The directory that model and log directories will be saved in.
This directory is important if you want to view the fit in
Tensorboard.
max_iterations: int, 350
Early stopping is not yet implemented. Right now, you simply set
a number of iterations.
learning_rate: float, 0.0001
The SGD learning rate.
threshold_grad_desc: float, 0.5
A float between 0 and 1 specifying how to threshold the gradients.
A value of 0.dd will only allow gradients of magnitude that are
dd% of the maximum gradient's absolute value.
use_active_set: bool, True
Specifies whether or not to use an active set while fitting.
verbose: bool, True
Specifies whether or not to use
Returns
-------
A dictionary containing both 'weights' and 'predictions', which are
numpy arrays containing the learned weights, and the pearson
correllation for each label, respectively.
"""
if len(np.shape(Y_tr)) <= 1:
num_predictors = 1
else:
num_predictors = np.shape(Y_tr)[1]
num_features = np.shape(X_test)[1]
if verbose:
print "Building computation graph..."
with tf.Graph().as_default():
with tf.name_scope('test_data'):
x_tst = tf.placeholder(tf.float32, shape=np.shape(X_test))
y_tst = tf.placeholder(tf.float32, shape=np.shape(Y_test))
with tf.name_scope('input_data'):
x_tr = tf.placeholder(tf.float32,
shape=(batch_size, num_features))
y_tr = tf.placeholder(tf.float32,
shape=(batch_size, num_predictors))
# Getting the Y predictions
W = tf.Variable(tf.zeros([num_features, num_predictors]),
name='weights')
y_pred = tf.matmul(x_tr, W)
# Loss function associated summaries.
loss = lsq_loss(y_pred, y_tr, name='training_lsq_loss')
loss_summary = tf.scalar_summary("Training Loss", loss)
# Weight histogram summary.
W_hist_summary = tf.histogram_summary("Weight Distribution", W)
# Optimizer
global_step = tf.Variable(0, name='global_step', dtype=tf.int64)
optimizer = tf.train.GradientDescentOptimizer(learning_rate)
W_grad, W_var = optimizer.compute_gradients(loss, [W])[0]
# Normalize the gradient.
norm_grads = tf.nn.l2_normalize(W_grad, dim=0,
name="normalize_gradients")
# Apply threshold gradient descent.
thresholded_grads, active_set_count = threshold_by_percent_max(
norm_grads, threshold_grad_desc, use_active_set=True)
thresh_grad_hist_summary = tf.histogram_summary(
"Thresholded Gradients",
thresholded_grads)
# Keep track of the active set used for TGD.
active_set_count_summary = tf.scalar_summary(
"Number of Active Gradients",
active_set_count)
# Run this op to apply all the accumulated gradients.
op = optimizer.apply_gradients([(thresholded_grads, W_var)],
global_step=global_step,
name="apply_accumulated_grads")
train_summary = tf.merge_summary([thresh_grad_hist_summary,
active_set_count_summary,
W_hist_summary, loss_summary])
# Report the test set error (but don't optimize on it)
y_pred_test = tf.matmul(x_tst, W)
test_loss = lsq_loss(y_pred_test, y_tst, name='test_loss')
tst_loss_summary = tf.scalar_summary("Test LSQ Loss", test_loss)
# Tensorflow boilerplate
init = tf.initialize_all_variables()
saver = tf.train.Saver({'weights': W})
sess = tf.Session(config=tf.ConfigProto(
log_device_placement=verbose))
summary_writer = tf.train.SummaryWriter(train_dir + '/log',
sess.graph)
if verbose:
print "initializing variables..."
sess.run(init)
batch_gen = get_training_batches(X_tr, Y_tr, batch_size=batch_size,
verbose=verbose)
# Run training.
start_time = time.time()
for step in xrange(max_iterations):
if verbose:
print('\n== Optimization Step %d of %d =='
% (step, max_iterations))
training_loss = 0.
if verbose:
print "...Generating batch"
X_batch, Y_batch = batch_gen.next()
if verbose:
print "...Calculating Gradients"
(_, loss_eval, train_summ_eval) = sess.run(
[op, loss, train_summary], feed_dict={x_tr: X_batch,
y_tr: Y_batch})
# Write out a bunch of summaries:
duration = time.time() - start_time
if verbose:
print('Step %d: loss=%.2f (%.3f sec)'
% (step, loss_eval, duration))
summary_writer.add_summary(train_summ_eval, step)
summary_writer.flush()
# We evaluate the test set every so often, just to visualize it
# in tensorboard.
if step > 0 and step % 10 == 0:
if verbose:
print "Shape of x_test: " + str(np.shape(X_test))
print "shape of y_test: " + str(np.shape(Y_test))
tst_summ, tst_loss = sess.run([tst_loss_summary, test_loss],
feed_dict={x_tst: X_test,
y_tst: Y_test})
if verbose:
print "test_loss: " + str(tst_loss)
print('Step %d: loss=%.2f test_loss=%.2f (%.3f sec)'
% (step, training_loss, tst_loss, duration))
summary_writer.add_summary(tst_summ, step)
summary_writer.flush()
fit = {}
y_pred_test_ev = sess.run([y_pred_test], feed_dict={x_tst: X_test,
y_tst: Y_test})[0]
final_W = sess.run([W])
fit['weights'] = final_W
# Evaluate Prediction Accuracy
fit['predictions'] = pearson_correllations(Y_test, y_pred_test_ev)
return fit