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bucket_model.py
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# -*- coding: utf-8 -*-
import tensorflow as tf
from layers import EmbeddingLayer, BiLSTM, HiddenLayer, TimeDistributed, DropoutLayer, Convolution, Maxpooling, Forward
from time import time
import losses
import toolbox
import batch as Batch
import numpy as np
import random
import cPickle as pickle
import math
class Model(object):
def __init__(self, nums_chars, nums_tags, buckets_char, counts=None, pic_size=None, font=None, batch_size=10,
tag_scheme='BIES', word_vec=True, radical=False, graphic=False, crf=1, ngram=None, metric='F1-score',
mode='RNN'):
self.nums_chars = nums_chars
self.nums_tags = nums_tags
self.buckets_char = buckets_char
self.counts = counts
self.tag_scheme = tag_scheme
self.graphic = graphic
self.word_vec = word_vec
self.radical = radical
self.crf = crf
self.ngram = ngram
self.emb_layer = None
self.radical_layer = None
self.pos_emb_f, self.pos_emb_b = None, None
self.gram_layers = []
self.font = font
self.pic_size = pic_size
self.batch_size = batch_size
self.l_rate, self.decay = None, None
self.train_step = None
self.saver = None
self.decode_holders = None
self.scores = None
self.params = None
self.pixels = None
self.metric = metric
self.mode = mode
self.updates = []
self.bucket_dit = {}
self.input_v = []
self.input_w = []
self.input_p = None
self.output, self.output_, self.output_p, self.output_w, self.output_w_ = [], [], [], [], []
if self.crf > 0:
self.transition_char = []
for i in range(len(self.nums_tags)):
self.transition_char.append(tf.get_variable('transitions_char' + str(i), [self.nums_tags[i] + 1,
self.nums_tags[i] + 1]))
self.all_metrics = None
self.all_metrics = ['Precision', 'Recall', 'F1-score', 'True-Negative-Rate', 'Boundary-F1-score']
while len(self.buckets_char) > len(self.counts):
self.counts.append(1)
self.real_batches = toolbox.get_real_batch(self.counts, self.batch_size)
def main_graph(self, trained_model, scope, emb_dim, gru, rnn_dim, rnn_num, fnn_dim, window_size, drop_out=0.5,
rad_dim=30, emb=None, ng_embs=None, pixels=None, con_width=None, filters=None, pooling_size=None):
if trained_model is not None:
param_dic = {}
param_dic['nums_chars'] = self.nums_chars
param_dic['nums_tags'] = self.nums_tags
param_dic['tag_scheme'] = self.tag_scheme
param_dic['graphic'] = self.graphic
param_dic['pic_size'] = self.pic_size
param_dic['word_vec'] = self.word_vec
param_dic['radical'] = self.radical
param_dic['crf'] = self.crf
param_dic['emb_dim'] = emb_dim
param_dic['gru'] = gru
param_dic['rnn_dim'] = rnn_dim
param_dic['rnn_num'] = rnn_num
param_dic['fnn_dim'] = fnn_dim
param_dic['window_size'] = window_size
param_dic['drop_out'] = drop_out
param_dic['filter_size'] = con_width
param_dic['filters'] = filters
param_dic['pooling_size'] = pooling_size
param_dic['font'] = self.font
param_dic['buckets_char'] = self.buckets_char
param_dic['ngram'] = self.ngram
param_dic['mode'] = self.mode
#print param_dic
if self.metric == 'All':
pindex = trained_model.rindex('/') + 1
for m in self.all_metrics:
f_model = open(trained_model[:pindex] + m + '_' + trained_model[pindex:], 'w')
pickle.dump(param_dic, f_model)
f_model.close()
else:
f_model = open(trained_model, 'w')
pickle.dump(param_dic, f_model)
f_model.close()
# define shared weights and variables
dr = tf.placeholder(tf.float32, [], name='drop_out_holder')
self.drop_out = dr
self.drop_out_v = drop_out
#concat_emb_dim = emb_dim * 2
concat_emb_dim = 0
if self.word_vec:
self.emb_layer = EmbeddingLayer(self.nums_chars + 500, emb_dim, weights=emb, name='emb_layer')
concat_emb_dim += emb_dim
if self.radical:
self.radical_layer = EmbeddingLayer(216, rad_dim, name='radical_layer')
concat_emb_dim += rad_dim
if self.ngram is not None:
if ng_embs is not None:
assert len(ng_embs) == len(self.ngram)
else:
ng_embs = [None for _ in range(len(self.ngram))]
for i, n_gram in enumerate(self.ngram):
self.gram_layers.append(EmbeddingLayer(n_gram + 1000 * (i + 2), emb_dim, weights=ng_embs[i],
name= str(i + 2) + 'gram_layer'))
concat_emb_dim += emb_dim
wrapper_conv_1, wrapper_mp_1, wrapper_conv_2 = None, None, None
wrapper_mp_2, wrapper_dense, wrapper_dr = None, None, None
if self.graphic:
self.input_p = []
assert pixels is not None and filters is not None and pooling_size is not None and con_width is not None
self.pixels = pixels
pixel_dim = int(math.sqrt(len(pixels[0])))
wrapper_conv_1 = Convolution(con_width, 1, filters, name='conv_1')
wrapper_mp_1 = Maxpooling(pooling_size, pooling_size, name='pooling_1')
p_size_1 = toolbox.down_pool(pixel_dim, pooling_size)
wrapper_conv_2 = Convolution(con_width, filters, filters, name='conv_2')
wrapper_mp_2 = Maxpooling(pooling_size, pooling_size, name='pooling_2')
p_size_2 = toolbox.down_pool(p_size_1, pooling_size)
wrapper_dense = HiddenLayer(p_size_2 * p_size_2 * filters, 100, activation='tanh', name='conv_dense')
wrapper_dr = DropoutLayer(self.drop_out)
concat_emb_dim += 100
fw_rnn_cell, bw_rnn_cell = None, None
if self.mode == 'RNN':
with tf.variable_scope('BiRNN'):
if gru:
fw_rnn_cell = tf.nn.rnn_cell.GRUCell(rnn_dim)
bw_rnn_cell = tf.nn.rnn_cell.GRUCell(rnn_dim)
else:
fw_rnn_cell = tf.nn.rnn_cell.LSTMCell(rnn_dim, state_is_tuple=True)
bw_rnn_cell = tf.nn.rnn_cell.LSTMCell(rnn_dim, state_is_tuple=True)
if rnn_num > 1:
fw_rnn_cell = tf.nn.rnn_cell.MultiRNNCell([fw_rnn_cell]*rnn_num, state_is_tuple=True)
bw_rnn_cell = tf.nn.rnn_cell.MultiRNNCell([bw_rnn_cell]*rnn_num, state_is_tuple=True)
output_wrapper = HiddenLayer(rnn_dim * 2, self.nums_tags[0], activation='linear', name='out_wrapper')
fnn_weights, fnn_bias = None, None
else:
with tf.variable_scope('FNN'):
fnn_weights = tf.get_variable('conv_w', [2*window_size + 1, concat_emb_dim, 1, fnn_dim])
fnn_bias = tf.get_variable('conv_b', [fnn_dim], initializer=tf.constant_initializer(0.1))
output_wrapper = HiddenLayer(fnn_dim, self.nums_tags[0], activation='linear', name='out_wrapper')
#define model for each bucket
for idx, bucket in enumerate(self.buckets_char):
if idx == 1:
scope.reuse_variables()
t1 = time()
input_v = tf.placeholder(tf.int32, [None, bucket], name='input_' + str(bucket))
self.input_v.append([input_v])
emb_set = []
if self.word_vec:
word_out = self.emb_layer(input_v)
emb_set.append(word_out)
if self.radical:
input_r = tf.placeholder(tf.int32, [None, bucket], name='input_r' + str(bucket))
self.input_v[-1].append(input_r)
radical_out = self.radical_layer(input_r)
emb_set.append(radical_out)
if self.ngram is not None:
for i in range(len(self.ngram)):
input_g = tf.placeholder(tf.int32, [None, bucket], name='input_g' + str(i) + str(bucket))
self.input_v[-1].append(input_g)
gram_out = self.gram_layers[i](input_g)
emb_set.append(gram_out)
if self.graphic:
input_p = tf.placeholder(tf.float32, [None, bucket, pixel_dim*pixel_dim])
self.input_p.append(input_p)
pix_out = tf.reshape(input_p, [-1, pixel_dim, pixel_dim, 1])
conv_out_1 = wrapper_conv_1(pix_out)
pooling_out_1 = wrapper_mp_1(conv_out_1)
conv_out_2 = wrapper_conv_2(pooling_out_1)
pooling_out_2 = wrapper_mp_2(conv_out_2)
assert p_size_2 == pooling_out_2[0].get_shape().as_list()[1]
pooling_out = tf.reshape(pooling_out_2, [-1, bucket, p_size_2 * p_size_2 * filters])
graphic_out = wrapper_dense(pooling_out)
graphic_out = wrapper_dr(graphic_out)
emb_set.append(graphic_out)
if len(emb_set) > 1:
emb_out = tf.concat(axis=2, values=emb_set)
else:
emb_out = emb_set[0]
if self.mode == 'RNN':
rnn_out = BiLSTM(rnn_dim, fw_cell=fw_rnn_cell, bw_cell=bw_rnn_cell, p=dr, name='BiLSTM' + str(bucket),
scope='BiRNN')(emb_out, input_v)
output = output_wrapper(rnn_out)
else:
emb_out = tf.pad(emb_out, [[0, 0], [window_size, window_size], [0, 0]])
emb_out = tf.reshape(emb_out, [-1, bucket + 2 * window_size, concat_emb_dim, 1])
conv_out = tf.nn.conv2d(emb_out, fnn_weights, [1, 1, 1, 1], padding='VALID') + fnn_bias
fnn_out = tf.nn.tanh(conv_out)
fnn_out = tf.reshape(fnn_out, [-1, bucket, fnn_dim])
output = output_wrapper(fnn_out)
self.output.append([output])
self.output_.append([tf.placeholder(tf.int32, [None, bucket], name='tags' + str(bucket))])
self.bucket_dit[bucket] = idx
print 'Bucket %d, %f seconds' % (idx + 1, time() - t1)
assert len(self.input_v) == len(self.output) and len(self.output) == len(self.output_) \
and len(self.output) == len(self.counts)
self.params = tf.trainable_variables()
self.saver = tf.train.Saver()
def config(self, optimizer, decay, lr_v=None, momentum=None, clipping=False, max_gradient_norm=5.0):
self.decay = decay
print 'Training preparation...'
print 'Defining loss...'
loss = []
if self.crf > 0:
loss_function = losses.crf_loss
for i in range(len(self.input_v)):
bucket_loss = losses.loss_wrapper(self.output[i], self.output_[i], loss_function,
transitions=self.transition_char, nums_tags=self.nums_tags,
batch_size=self.real_batches[i])
loss.append(bucket_loss)
else:
loss_function = losses.sparse_cross_entropy
for output, output_ in zip(self.output, self.output_):
bucket_loss = losses.loss_wrapper(output, output_, loss_function)
loss.append(bucket_loss)
l_rate = tf.placeholder(tf.float32, [], name='learning_rate_holder')
self.l_rate = l_rate
if optimizer == 'sgd':
if momentum is None:
optimizer = tf.train.GradientDescentOptimizer(learning_rate=l_rate)
else:
optimizer = tf.train.MomentumOptimizer(learning_rate=l_rate, momentum=momentum)
elif optimizer == 'adagrad':
assert lr_v is not None
optimizer = tf.train.AdagradOptimizer(learning_rate=l_rate)
elif optimizer == 'adam':
optimizer = tf.train.AdamOptimizer(learning_rate=l_rate)
else:
raise Exception('optimiser error')
self.train_step = []
print 'Computing gradients...'
for idx, l in enumerate(loss):
t2 = time()
if clipping:
gradients = tf.gradients(l, self.params)
clipped_gradients, norm = tf.clip_by_global_norm(gradients, max_gradient_norm)
train_step = optimizer.apply_gradients(zip(clipped_gradients, self.params))
else:
train_step = optimizer.minimize(l)
print 'Bucket %d, %f seconds' % (idx + 1, time() - t2)
self.train_step.append(train_step)
def decode_graph(self):
self.decode_holders = []
self.scores = []
for bucket in self.buckets_char:
decode_holders = []
scores = []
for nt in self.nums_tags:
ob = tf.placeholder(tf.float32, [None, bucket, nt])
trans = tf.placeholder(tf.float32, [nt + 1, nt + 1])
nums_steps = ob.get_shape().as_list()[1]
length = tf.placeholder(tf.int32, [None])
b_size = tf.placeholder(tf.int32, [])
small = -1000
class_pad = tf.stack(small * tf.ones([b_size, nums_steps, 1]))
observations = tf.concat(axis=2, values=[ob, class_pad])
b_vec = tf.tile(([small] * nt + [0]), [b_size])
b_vec = tf.cast(b_vec, tf.float32)
b_vec = tf.reshape(b_vec, [b_size, 1, -1])
e_vec = tf.tile(([0] + [small] * nt), [b_size])
e_vec = tf.cast(e_vec, tf.float32)
e_vec = tf.reshape(e_vec, [b_size, 1, -1])
observations = tf.concat(axis=1, values=[b_vec, observations, e_vec])
transitions = tf.reshape(tf.tile(trans, [b_size, 1]), [b_size, nt + 1, nt + 1])
observations = tf.reshape(observations, [-1, nums_steps + 2, nt + 1, 1])
observations = tf.transpose(observations, [1, 0, 2, 3])
previous = observations[0, :, :, :]
max_scores = []
max_scores_pre = []
alphas = [previous]
for t in xrange(1, nums_steps + 2):
previous = tf.reshape(previous, [-1, nt + 1, 1])
current = tf.reshape(observations[t, :, :, :], [-1, 1, nt + 1])
alpha_t = previous + current + transitions
max_scores.append(tf.reduce_max(alpha_t, axis=1))
max_scores_pre.append(tf.argmax(alpha_t, axis=1))
alpha_t = tf.reshape(Forward.log_sum_exp(alpha_t, axis=1), [-1, nt + 1, 1])
alphas.append(alpha_t)
previous = alpha_t
max_scores = tf.stack(max_scores, axis=1)
max_scores_pre = tf.stack(max_scores_pre, axis=1)
decode_holders.append([ob, trans, length, b_size])
scores.append((max_scores, max_scores_pre))
self.decode_holders.append(decode_holders)
self.scores.append(scores)
def train(self, t_x, t_y, v_x, v_y, idx2tag, idx2char, sess, epochs, trained_model, lr=0.05, decay=0.05,
decay_step=1, tag_num=1):
lr_r = lr
best_epoch, best_score, best_seg, best_pos, c_tag, c_seg, c_score = {}, {}, {}, {}, {}, {}, {}
pindex = 0
metric = self.metric
for m in self.all_metrics:
best_epoch[m] = 0
best_score[m] = 0
best_seg[m] = 0
best_pos[m] = 0
c_tag[m] = 0
c_seg[m] = 0
c_score[m] = 0
v_y = toolbox.merge_bucket(v_y)
v_y = toolbox.unpad_zeros(v_y)
gold = toolbox.decode_tags(v_y, idx2tag, self.tag_scheme)
input_chars = toolbox.merge_bucket([v_x[0]])
chars = toolbox.decode_chars(input_chars[0], idx2char)
gold_out = toolbox.generate_output(chars, gold, self.tag_scheme)
for epoch in range(epochs):
print 'epoch: %d' % (epoch + 1)
t = time()
if epoch % decay_step == 0 and decay > 0:
lr_r = lr/(1 + decay*(epoch/decay_step))
data_list = t_x + t_y
samples = zip(*data_list)
random.shuffle(samples)
for sample in samples:
c_len = len(sample[0][0])
idx = self.bucket_dit[c_len]
real_batch_size = self.real_batches[idx]
model = self.input_v[idx] + self.output_[idx]
pt_holder = None
if self.graphic:
pt_holder = self.input_p[idx]
Batch.train(sess=sess[0], model=model, batch_size=real_batch_size, config=self.train_step[idx],
lr=self.l_rate, lrv=lr_r, dr=self.drop_out, drv=self.drop_out_v, data=list(sample),
pt_h=pt_holder, pixels=self.pixels, verbose=False)
predictions = []
for v_b_x in zip(*v_x):
c_len = len(v_b_x[0][0])
idx = self.bucket_dit[c_len]
pt_holder = None
if self.graphic:
pt_holder = self.input_p[idx]
b_prediction = self.predict(data=v_b_x, sess=sess, model=self.input_v[idx] + self.output[idx],
index=idx, pt_h=pt_holder, pt=self.pixels, batch_size=200)
b_prediction = toolbox.decode_tags(b_prediction, idx2tag, self.tag_scheme)
predictions.append(b_prediction)
predictions = zip(*predictions)
predictions = toolbox.merge_bucket(predictions)
prediction_out = toolbox.generate_output(chars, predictions, self.tag_scheme)
scores = toolbox.evaluator(prediction_out, gold_out, metric=metric, verbose=True, tag_num=tag_num)
scores = np.asarray(scores)
#Score_seg * Score_seg&tag
c_seg['Precision'] = scores[0]
c_seg['Recall'] = scores[1]
c_seg['F1-score'] = scores[2]
c_seg['True-Negative-Rate'] = scores[6]
c_seg['Boundary-F1-score'] = scores[10]
if self.tag_scheme != 'seg':
c_tag['Precision'] = scores[3]
c_tag['Recall'] = scores[4]
c_tag['F1-score'] = scores[5]
c_tag['True-Negative-Rate'] = scores[7]
c_tag['Boundary-F1-score'] = scores[13]
else:
c_tag['Precision'] = 1
c_tag['Recall'] = 1
c_tag['F1-score'] = 1
c_tag['True-Negative-Rate'] = 1
c_tag['Boundary-F1-score'] = 1
if metric == 'All':
for m in self.all_metrics:
print 'Segmentation ' + m + ': %f' % c_seg[m]
print 'POS Tagging ' + m + ': %f\n' % c_tag[m]
pindex = trained_model.rindex('/') + 1
else:
print 'Segmentation ' + metric + ': %f' % c_seg[metric]
if self.tag_scheme != 'seg':
print 'POS Tagging ' + metric + ': %f\n' % c_tag[metric]
for m in self.all_metrics:
c_score[m] = c_seg[m] * c_tag[m]
if metric == 'All':
for m in self.all_metrics:
if c_score[m] > best_score[m] and epoch > 4:
best_epoch[m] = epoch + 1
best_score[m] = c_score[m]
best_seg[m] = c_seg[m]
best_pos[m] = c_tag[m]
self.saver.save(sess[0], trained_model[:pindex] + m + '_' + trained_model[pindex:],
write_meta_graph=False)
elif c_score[metric] > best_score[metric] and epoch > 4:
best_epoch[metric] = epoch + 1
best_score[metric] = c_score[metric]
best_seg[metric] = c_seg[metric]
best_pos[metric] = c_tag[metric]
self.saver.save(sess[0], trained_model, write_meta_graph=False)
print 'Time consumed: %d seconds' % int(time() - t)
print 'Training is finished!'
if metric == 'All':
for m in self.all_metrics:
print 'Best segmentation ' + m + ': %f' % best_seg[m]
print 'Best POS Tagging ' + m + ': %f' % best_pos[m]
print 'Best epoch: %d\n' % best_epoch[m]
else:
print 'Best segmentation ' + metric + ': %f' % best_seg[metric]
print 'Best POS Tagging ' + metric + ': %f' % best_pos[metric]
print 'Best epoch: %d\n' % best_epoch[metric]
def define_updates(self, new_chars, emb_path, char2idx, new_grams=None, ng_emb_path=None, gram2idx=None):
self.nums_chars += len(new_chars)
if self.word_vec and emb_path is not None:
old_emb_weights = self.emb_layer.embeddings
emb_dim = old_emb_weights.get_shape().as_list()[1]
emb_len = old_emb_weights.get_shape().as_list()[0]
new_emb = toolbox.get_new_embeddings(new_chars, emb_dim, emb_path)
n_emb_sh = new_emb.get_shape().as_list()
if len(n_emb_sh) > 1:
new_emb_weights = tf.concat(axis=0, values=[old_emb_weights[:len(char2idx) - len(new_chars)], new_emb,
old_emb_weights[len(char2idx):]])
if new_emb_weights.get_shape().as_list()[0] > emb_len:
new_emb_weights = new_emb_weights[:emb_len]
assign_op = old_emb_weights.assign(new_emb_weights)
self.updates.append(assign_op)
if self.ngram is not None and ng_emb_path is not None:
old_gram_weights = [ng_layer.embeddings for ng_layer in self.gram_layers]
ng_emb_dim = old_gram_weights[0].get_shape().as_list()[1]
new_ng_emb = toolbox.get_new_ng_embeddings(new_grams, ng_emb_dim, ng_emb_path)
for i in range(len(old_gram_weights)):
new_ng_weight = tf.concat(axis=0, values=[old_gram_weights[i][:len(gram2idx[i]) - len(new_grams[i])],
new_ng_emb[i], old_gram_weights[i][len(gram2idx[i]):]])
assign_op = old_gram_weights[i].assign(new_ng_weight)
self.updates.append(assign_op)
def run_updates(self, sess, weight_path):
self.saver.restore(sess, weight_path)
for op in self.updates:
sess.run(op)
print 'Loaded.'
def test(self, sess, t_x, t_y, idx2tag, idx2char, outpath=None, ensemble=None, batch_size=200, tag_num=1):
t_y = toolbox.unpad_zeros(t_y)
gold = toolbox.decode_tags(t_y, idx2tag, self.tag_scheme)
chars = toolbox.decode_chars(t_x[0], idx2char)
gold_out = toolbox.generate_output(chars, gold, self.tag_scheme)
pt_holder = None
if self.graphic:
pt_holder = self.input_p[0]
prediction = self.predict(data=t_x, sess=sess, model=self.input_v[0] + self.output[0], index=0, pt_h=pt_holder,
pt=self.pixels, ensemble=ensemble, batch_size=batch_size)
prediction = toolbox.decode_tags(prediction, idx2tag, self.tag_scheme)
prediction_out = toolbox.generate_output(chars, prediction, self.tag_scheme)
scores = toolbox.evaluator(prediction_out, gold_out, metric='All', verbose=True, tag_num=tag_num)
print 'Best scores: '
print 'Segmentation F1-score: %f' % scores[2]
print 'Segmentation Precision: %f' % scores[0]
print 'Segmentation Recall: %f' % scores[1]
print 'Segmentation True Negative Rate: %f' % scores[6]
print 'Segmentation Boundary-F1-score: %f\n' % scores[10]
print 'Joint POS tagging F-score: %f' % scores[5]
print 'Joint POS tagging Precision: %f' % scores[3]
print 'Joint POS tagging Recall: %f' % scores[4]
print 'Joint POS True Negative Rate: %f' % scores[7]
print 'Joint POS tagging Boundary-F1-score: %f\n' % scores[13]
if outpath is not None:
final_out = prediction_out[0]
toolbox.printer(final_out, outpath)
def tag(self, sess, r_x, idx2tag, idx2char, char2idx, outpath='out.txt', ensemble=None, batch_size=200,
large_file=False):
chars = toolbox.decode_chars(r_x[0], idx2char)
char_num = len(set(char2idx.values()))
r_x = np.asarray(r_x)
r_x[0][r_x[0] > char_num - 1] = char2idx['<UNK>']
pt_holder = None
if self.graphic:
pt_holder = self.input_p[0]
c_len = len(r_x[0][0])
idx = self.bucket_dit[c_len]
real_batch = batch_size * 300 / c_len
prediction = self.predict(data=r_x, sess=sess, model=self.input_v[idx] + self.output[idx], index=idx,
pt_h=pt_holder, pt=self.pixels, ensemble=ensemble, batch_size=real_batch)
prediction = toolbox.decode_tags(prediction, idx2tag, self.tag_scheme)
prediction_out = toolbox.generate_output(chars, prediction, self.tag_scheme)
final_out = prediction_out[0]
if large_file:
return final_out
else:
toolbox.printer(final_out, outpath)
def predict(self, data, sess, model, index=None, argmax=True, batch_size=100, pt_h=None, pt=None, ensemble=None,
verbose=False):
if self.crf:
assert index is not None
predictions = Batch.predict(sess=sess[0], decode_sess=sess[1], model=model,
transitions=self.transition_char, crf=self.crf, scores=self.scores[index],
decode_holders=self.decode_holders[index], argmax=argmax, batch_size=batch_size,
data=data, dr=self.drop_out, pixels=pt, pt_h=pt_h, ensemble=ensemble,
verbose=verbose)
else:
predictions = Batch.predict(sess=sess[0], model=model, crf=self.crf, argmax=argmax, batch_size=batch_size,
data=data, dr=self.drop_out, pixels=pt, pt_h=pt_h, ensemble=ensemble,
verbose=verbose)
return predictions