def main():
# Get arguments parsed
args = get_args()
# Setup for logging
output_dir = 'output/{}'.format(datetime.now(timezone('Canada/Central')).strftime('%Y-%m-%d_%H-%M-%S-%f')[:-3])
create_dir(output_dir)
LogHelper.setup(log_path='{}/training.log'.format(output_dir), level_str='INFO')
_logger = logging.getLogger(__name__)
# Save the configuration for logging purpose
save_yaml_config(args, path='{}/config.yaml'.format(output_dir))
# Reproducibility
set_seed(args.seed)
# Get dataset
dataset = SyntheticDataset(args.n, args.d, args.graph_type, args.degree, args.sem_type,
args.noise_scale, args.dataset_type)
_logger.info('Finished generating dataset')
model = NoTears(args.n, args.d, args.seed, args.l1_lambda, args.use_float64)
model.print_summary(print_func=model.logger.info)
trainer = ALTrainer(args.init_rho, args.rho_max, args.h_factor, args.rho_multiply,
args.init_iter, args.learning_rate, args.h_tol)
W_est = trainer.train(model, dataset.X, dataset.W, args.graph_thres,
args.max_iter, args.iter_step, output_dir)
_logger.info('Finished training model')
# Save raw estimated graph, ground truth and observational data after training
np.save('{}/true_graph.npy'.format(output_dir), dataset.W)
np.save('{}/X.npy'.format(output_dir), dataset.X)
np.save('{}/final_raw_estimated_graph.npy'.format(output_dir), W_est)
# Plot raw estimated graph
plot_estimated_graph(W_est, dataset.W,
save_name='{}/raw_estimated_graph.png'.format(output_dir))
_logger.info('Thresholding.')
# Plot thresholded estimated graph
W_est[np.abs(W_est) < args.graph_thres] = 0 # Thresholding
plot_estimated_graph(W_est, dataset.W,
save_name='{}/thresholded_estimated_graph.png'.format(output_dir))
results_thresholded = count_accuracy(dataset.W, W_est)
_logger.info('Results after thresholding by {}: {}'.format(args.graph_thres, results_thresholded))
def train_callback(self, epoch, loss, mse, h, W_true, W_est, graph_thres,
output_dir):
# Evaluate the learned W in each iteration after thresholding
W_thresholded = np.copy(W_est)
W_thresholded[np.abs(W_thresholded) < graph_thres] = 0
results_thresholded = count_accuracy(W_true, W_thresholded)
self._logger.info(
'[Iter {}] loss {:.3E}, mse {:.3E}, acyclic {:.3E}, shd {}, tpr {:.3f}, fdr {:.3f}, pred_size {}'
.format(epoch, loss, mse, h, results_thresholded['shd'],
results_thresholded['tpr'], results_thresholded['fdr'],
results_thresholded['pred_size']))
# Save the raw estimated graph in each iteration
create_dir('{}/raw_estimated_graph'.format(output_dir))
np.save(
'{}/raw_estimated_graph/graph_iteration_{}.npy'.format(
output_dir, epoch), W_est)
def log_and_save_intermediate_outputs(self, i, W_true, W_est, graph_thres,
loss, mse, h, output_dir):
# Evaluate the learned W in each iteration after thresholding
W_thresholded = np.copy(W_est)
W_thresholded = W_thresholded / np.max(np.abs(W_thresholded))
W_thresholded[np.abs(W_thresholded) < graph_thres] = 0
results = count_accuracy(W_true, W_thresholded)
# Logging
self._logger.info(
'[Iter {}] loss {:.3E}, mse {:.3E}, acyclic {:.3E}, shd {}, tpr {:.3f}, fdr {:.3f}, pred_size {}'
.format(i, loss, mse, h, results['shd'], results['tpr'],
results['fdr'], results['pred_size']))
# Save the raw recovered graph in each iteration
np.save(
'{}/raw_recovered_graph/graph_iteration_{}.npy'.format(
output_dir, i), W_est)
def main():
# Get arguments parsed
args = get_args()
# Setup for logging
output_dir = 'output/{}'.format(
datetime.now(
timezone('Asia/Hong_Kong')).strftime('%Y-%m-%d_%H-%M-%S-%f')[:-3])
create_dir(output_dir)
LogHelper.setup(log_path='{}/training.log'.format(output_dir),
level_str='INFO')
_logger = logging.getLogger(__name__)
# Save the configuration for logging purpose
save_yaml_config(args, path='{}/config.yaml'.format(output_dir))
# Reproducibility
set_seed(args.seed)
# Get dataset
dataset = SyntheticDataset(args.n, args.d, args.graph_type, args.degree,
args.sem_type, args.noise_scale,
args.dataset_type, args.x_dim)
_logger.info('Finished generating dataset')
model = GAE(args.n, args.d, args.x_dim, args.seed, args.num_encoder_layers,
args.num_decoder_layers, args.hidden_size, args.latent_dim,
args.l1_graph_penalty, args.use_float64)
model.print_summary(print_func=model.logger.info)
trainer = ALTrainer(args.init_rho, args.rho_thres, args.h_thres,
args.rho_multiply, args.init_iter, args.learning_rate,
args.h_tol, args.early_stopping,
args.early_stopping_thres)
W_est = trainer.train(model, dataset.X, dataset.W, args.graph_thres,
args.max_iter, args.iter_step, output_dir)
_logger.info('Finished training model')
# Save raw recovered graph, ground truth and observational data after training
np.save('{}/true_graph.npy'.format(output_dir), dataset.W)
np.save('{}/observational_data.npy'.format(output_dir), dataset.X)
np.save('{}/final_raw_recovered_graph.npy'.format(output_dir), W_est)
# Plot raw recovered graph
plot_recovered_graph(
W_est,
dataset.W,
save_name='{}/raw_recovered_graph.png'.format(output_dir))
_logger.info('Filter by constant threshold')
W_est = W_est / np.max(np.abs(W_est)) # Normalize
# Plot thresholded recovered graph
W_est[np.abs(W_est) < args.graph_thres] = 0 # Thresholding
plot_recovered_graph(
W_est,
dataset.W,
save_name='{}/thresholded_recovered_graph.png'.format(output_dir))
results_thresholded = count_accuracy(dataset.W, W_est)
_logger.info('Results after thresholding by {}: {}'.format(
args.graph_thres, results_thresholded))
def main():
# Setup for output directory and logging
output_dir = 'output/{}'.format(
datetime.now(
timezone('Asia/Hong_Kong')).strftime('%Y-%m-%d_%H-%M-%S-%f')[:-3])
create_dir(output_dir)
LogHelper.setup(log_path='{}/training.log'.format(output_dir),
level_str='INFO')
_logger = logging.getLogger(__name__)
_logger.info('Python version is {}'.format(platform.python_version()))
_logger.info('Current commit of code: ___')
# Get running configuration
config, _ = get_config()
config.save_model_path = '{}/model'.format(output_dir)
# config.restore_model_path = '{}/model'.format(output_dir)
config.summary_dir = '{}/summary'.format(output_dir)
config.plot_dir = '{}/plot'.format(output_dir)
config.graph_dir = '{}/graph'.format(output_dir)
# Create directory
create_dir(config.summary_dir)
create_dir(config.summary_dir)
create_dir(config.plot_dir)
create_dir(config.graph_dir)
# Reproducibility
set_seed(config.seed)
# Log the configuration parameters
_logger.info('Configuration parameters: {}'.format(
vars(config))) # Use vars to convert config to dict for logging
if config.read_data:
file_path = '{}/data.npy'.format(config.data_path)
solution_path = '{}/DAG.npy'.format(config.data_path)
training_set = DataGenerator_read_data(file_path, solution_path,
config.normalize,
config.transpose)
else:
raise ValueError("Only support importing data from existing files")
# set penalty weights
score_type = config.score_type
reg_type = config.reg_type
if config.lambda_flag_default:
sl, su, strue = BIC_lambdas(training_set.inputdata, None, None,
training_set.true_graph.T, reg_type,
score_type)
lambda1 = 0
lambda1_upper = 5
lambda1_update_add = 1
lambda2 = 1 / (10**(np.round(config.max_length / 3)))
lambda2_upper = 0.01
lambda2_update_mul = 10
lambda_iter_num = config.lambda_iter_num
# test initialized score
_logger.info('Original sl: {}, su: {}, strue: {}'.format(
sl, su, strue))
_logger.info('Transfomed sl: {}, su: {}, lambda2: {}, true: {}'.format(
sl, su, lambda2, (strue - sl) / (su - sl) * lambda1_upper))
else:
# test choices for the case with manually provided bounds
# not fully tested
sl = config.score_lower
su = config.score_upper
if config.score_bd_tight:
lambda1 = 2
lambda1_upper = 2
else:
lambda1 = 0
lambda1_upper = 5
lambda1_update_add = 1
lambda2 = 1 / (10**(np.round(config.max_length / 3)))
lambda2_upper = 0.01
lambda2_update_mul = config.lambda2_update
lambda_iter_num = config.lambda_iter_num
# actor
actor = Actor(config)
callreward = get_Reward(actor.batch_size, config.max_length,
actor.input_dimension, training_set.inputdata, sl,
su, lambda1_upper, score_type, reg_type,
config.l1_graph_reg, False)
_logger.info(
'Finished creating training dataset, actor model and reward class')
# Saver to save & restore all the variables.
variables_to_save = [
v for v in tf.global_variables() if 'Adam' not in v.name
]
saver = tf.train.Saver(var_list=variables_to_save,
keep_checkpoint_every_n_hours=1.0)
_logger.info('Starting session...')
sess_config = tf.ConfigProto(log_device_placement=False)
sess_config.gpu_options.allow_growth = True
with tf.Session(config=sess_config) as sess:
# Run initialize op
sess.run(tf.global_variables_initializer())
# Test tensor shape
_logger.info('Shape of actor.input: {}'.format(
sess.run(tf.shape(actor.input_))))
# _logger.info('training_set.true_graph: {}'.format(training_set.true_graph))
# _logger.info('training_set.b: {}'.format(training_set.b))
# Initialize useful variables
rewards_avg_baseline = []
rewards_batches = []
reward_max_per_batch = []
lambda1s = []
lambda2s = []
graphss = []
probsss = []
max_rewards = []
max_reward = float('-inf')
image_count = 0
accuracy_res = []
accuracy_res_pruned = []
max_reward_score_cyc = (lambda1_upper + 1, 0)
# Summary writer
writer = tf.summary.FileWriter(config.summary_dir, sess.graph)
_logger.info('Starting training.')
for i in (range(1, config.nb_epoch + 1)):
if config.verbose:
_logger.info('Start training for {}-th epoch'.format(i))
input_batch = training_set.train_batch(actor.batch_size,
actor.max_length,
actor.input_dimension)
graphs_feed = sess.run(actor.graphs,
feed_dict={actor.input_: input_batch})
reward_feed = callreward.cal_rewards(
graphs_feed, lambda1,
lambda2) #BTBT 得到生成的一个graph batch中每个graph的reward
# max reward, max reward per batch
max_reward = -callreward.update_scores(
[max_reward_score_cyc], lambda1, lambda2
)[0] #BTBT 每跑batch我们都会用更新后的lambda1/2对截至到目前找到的max_reward对应的max_reward_score_cyc再算一次rewaerd作为新的max_reward
max_reward_batch = float('inf')
max_reward_batch_score_cyc = (0, 0)
for reward_, score_, cyc_ in reward_feed:
if reward_ < max_reward_batch:
max_reward_batch = reward_
max_reward_batch_score_cyc = (score_, cyc_)
max_reward_batch = -max_reward_batch
if max_reward < max_reward_batch: #BTBT 若该batch的所有graph中有一个reward大于max_reward,该reward就作为max_reward
max_reward = max_reward_batch
max_reward_score_cyc = max_reward_batch_score_cyc
# for average reward per batch
reward_batch_score_cyc = np.mean(reward_feed[:, 1:], axis=0)
if config.verbose:
_logger.info(
'Finish calculating reward for current batch of graph')
# Get feed dict
feed = {
actor.input_: input_batch,
actor.reward_: -reward_feed[:, 0],
actor.graphs_: graphs_feed
}
summary, base_op, score_test, probs, graph_batch, \
reward_batch, reward_avg_baseline, train_step1, train_step2 = sess.run([
actor.merged,
actor.base_op,
actor.test_scores,
actor.log_softmax,
actor.graph_batch,
actor.reward_batch,
actor.avg_baseline,
actor.train_step1,
actor.train_step2], feed_dict=feed)
if config.verbose:
_logger.info(
'Finish updating actor and critic network using reward calculated'
)
lambda1s.append(lambda1)
lambda2s.append(lambda2)
rewards_avg_baseline.append(reward_avg_baseline)
rewards_batches.append(reward_batch_score_cyc)
reward_max_per_batch.append(max_reward_batch_score_cyc)
graphss.append(graph_batch)
probsss.append(probs)
max_rewards.append(max_reward_score_cyc)
# logging
if i == 1 or i % 500 == 0:
if i >= 500:
writer.add_summary(summary, i)
_logger.info(
'[iter {}] reward_batch: {}, max_reward: {}, max_reward_batch: {}'
.format(i, reward_batch, max_reward, max_reward_batch))
# other logger info; uncomment if you want to check
# _logger.info('graph_batch_avg: {}'.format(graph_batch))
# _logger.info('graph true: {}'.format(training_set.true_graph))
# _logger.info('graph weights true: {}'.format(training_set.b))
# _logger.info('=====================================')
plt.figure(1)
plt.plot(rewards_batches, label='reward per batch')
plt.plot(max_rewards, label='max reward')
plt.legend()
plt.savefig('{}/reward_batch_average.png'.format(
config.plot_dir))
plt.close()
image_count += 1
# this draw the average graph per batch.
# can be modified to draw the graph (with or w/o pruning) that has the best reward
fig = plt.figure(2)
fig.suptitle('Iteration: {}'.format(i))
ax = fig.add_subplot(1, 2, 1)
ax.set_title('recovered_graph')
ax.imshow(np.around(graph_batch.T).astype(int),
cmap=plt.cm.gray)
ax = fig.add_subplot(1, 2, 2)
ax.set_title('ground truth')
ax.imshow(training_set.true_graph, cmap=plt.cm.gray)
plt.savefig('{}/recovered_graph_iteration_{}.png'.format(
config.plot_dir, image_count))
plt.close()
# update lambda1, lamda2
if (i + 1) % lambda_iter_num == 0:
ls_kv = callreward.update_all_scores(lambda1, lambda2)
# np.save('{}/solvd_dict_epoch_{}.npy'.format(config.graph_dir, i), np.array(ls_kv))
max_rewards_re = callreward.update_scores(
max_rewards, lambda1, lambda2)
rewards_batches_re = callreward.update_scores(
rewards_batches, lambda1, lambda2)
reward_max_per_batch_re = callreward.update_scores(
reward_max_per_batch, lambda1, lambda2)
# saved somewhat more detailed logging info
np.save('{}/solvd_dict.npy'.format(config.graph_dir),
np.array(ls_kv))
pd.DataFrame(np.array(max_rewards_re)).to_csv(
'{}/max_rewards.csv'.format(output_dir))
pd.DataFrame(rewards_batches_re).to_csv(
'{}/rewards_batch.csv'.format(output_dir))
pd.DataFrame(reward_max_per_batch_re).to_csv(
'{}/reward_max_batch.csv'.format(output_dir))
pd.DataFrame(lambda1s).to_csv(
'{}/lambda1s.csv'.format(output_dir))
pd.DataFrame(lambda2s).to_csv(
'{}/lambda2s.csv'.format(output_dir))
graph_int, score_min, cyc_min = np.int32(
ls_kv[0][0]), ls_kv[0][1][1], ls_kv[0][1][-1]
if cyc_min < 1e-5:
lambda1_upper = score_min
lambda1 = min(lambda1 + lambda1_update_add, lambda1_upper)
lambda2 = min(lambda2 * lambda2_update_mul, lambda2_upper)
_logger.info(
'[iter {}] lambda1 {}, upper {}, lambda2 {}, upper {}, score_min {}, cyc_min {}'
.format(i + 1, lambda1, lambda1_upper, lambda2,
lambda2_upper, score_min, cyc_min))
graph_batch = convert_graph_int_to_adj_mat(graph_int)
#BTBT ??? graph prune 怎么做?
if reg_type == 'LR':
graph_batch_pruned = np.array(
graph_prunned_by_coef(graph_batch,
training_set.inputdata))
elif reg_type == 'QR':
graph_batch_pruned = np.array(
graph_prunned_by_coef_2nd(graph_batch,
training_set.inputdata))
elif reg_type == 'GPR':
# The R codes of CAM pruning operates the graph form that (i,j)=1 indicates i-th node-> j-th node
# so we need to do a tranpose on the input graph and another tranpose on the output graph
graph_batch_pruned = np.transpose(
pruning_cam(training_set.inputdata,
np.array(graph_batch).T))
# estimate accuracy
acc_est = count_accuracy(training_set.true_graph,
graph_batch.T)
acc_est2 = count_accuracy(training_set.true_graph,
graph_batch_pruned.T)
fdr, tpr, fpr, shd, nnz = acc_est['fdr'], acc_est['tpr'], acc_est['fpr'], acc_est['shd'], \
acc_est['pred_size']
fdr2, tpr2, fpr2, shd2, nnz2 = acc_est2['fdr'], acc_est2['tpr'], acc_est2['fpr'], acc_est2['shd'], \
acc_est2['pred_size']
accuracy_res.append((fdr, tpr, fpr, shd, nnz))
accuracy_res_pruned.append((fdr2, tpr2, fpr2, shd2, nnz2))
np.save('{}/accuracy_res.npy'.format(output_dir),
np.array(accuracy_res))
np.save('{}/accuracy_res2.npy'.format(output_dir),
np.array(accuracy_res_pruned))
_logger.info(
'before pruning: fdr {}, tpr {}, fpr {}, shd {}, nnz {}'.
format(fdr, tpr, fpr, shd, nnz))
_logger.info(
'after pruning: fdr {}, tpr {}, fpr {}, shd {}, nnz {}'.
format(fdr2, tpr2, fpr2, shd2, nnz2))
# Save the variables to disk
if i % max(1, int(config.nb_epoch / 5)) == 0 and i != 0:
curr_model_path = saver.save(sess,
'{}/tmp.ckpt'.format(
config.save_model_path),
global_step=i)
_logger.info('Model saved in file: {}'.format(curr_model_path))
_logger.info('Training COMPLETED !')
saver.save(sess, '{}/actor.ckpt'.format(config.save_model_path))
def rlbic(d, npx, npy, lambda_iter_num=1000, nb_epoch=20000):
# reset graph
tf.reset_default_graph()
# FIXME set the mx_length at the beginning. This might be used even in RLBIC
#
# but I'm not sure if the RLBIC code is already initialized with above settings
config.max_length = d
config.lambda_iter_num = lambda_iter_num
config.nb_epoch = nb_epoch
training_set = DataGenerator(npx, npy, False, True)
score_type = 'BIC'
# FIXME what is this?
reg_type = 'LR'
sl, su, strue = BIC_lambdas(training_set.inputdata, None, None,
training_set.true_graph.T, reg_type,
score_type)
lambda1 = 0
lambda1_upper = 5
lambda1_update_add = 1
lambda2 = 1 / (10**(np.round(config.max_length / 3)))
lambda2_upper = 0.01
lambda2_update_mul = 10
lambda_iter_num = config.lambda_iter_num
actor = Actor(config)
callreward = get_Reward(actor.batch_size, config.max_length,
actor.input_dimension, training_set.inputdata, sl,
su, lambda1_upper, score_type, reg_type,
config.l1_graph_reg, False)
sess_config = tf.ConfigProto(log_device_placement=False)
sess_config.gpu_options.allow_growth = True
with tf.Session(config=sess_config) as sess:
# Run initialize op
sess.run(tf.global_variables_initializer())
rewards_avg_baseline = []
rewards_batches = []
reward_max_per_batch = []
lambda1s = []
lambda2s = []
graphss = []
probsss = []
max_rewards = []
max_reward = float('-inf')
image_count = 0
accuracy_res = []
accuracy_res_pruned = []
max_reward_score_cyc = (lambda1_upper + 1, 0)
result = None
print('Starting training.')
for i in tqdm(range(1, config.nb_epoch + 1)):
# print('Start training for {}-th epoch'.format(i))
input_batch = training_set.train_batch(actor.batch_size,
actor.max_length,
actor.input_dimension)
graphs_feed = sess.run(actor.graphs,
feed_dict={actor.input_: input_batch})
reward_feed = callreward.cal_rewards(graphs_feed, lambda1, lambda2)
# max reward, max reward per batch
max_reward = -callreward.update_scores([max_reward_score_cyc],
lambda1, lambda2)[0]
max_reward_batch = float('inf')
max_reward_batch_score_cyc = (0, 0)
for reward_, score_, cyc_ in reward_feed:
if reward_ < max_reward_batch:
max_reward_batch = reward_
max_reward_batch_score_cyc = (score_, cyc_)
max_reward_batch = -max_reward_batch
if max_reward < max_reward_batch:
max_reward = max_reward_batch
max_reward_score_cyc = max_reward_batch_score_cyc
# for average reward per batch
reward_batch_score_cyc = np.mean(reward_feed[:, 1:], axis=0)
# print('Finish calculating reward for current batch of graph')
# Get feed dict
feed = {
actor.input_: input_batch,
actor.reward_: -reward_feed[:, 0],
actor.graphs_: graphs_feed
}
summary, base_op, score_test, probs, graph_batch, \
reward_batch, reward_avg_baseline, train_step1, train_step2 = sess.run([actor.merged, actor.base_op,
actor.test_scores, actor.log_softmax, actor.graph_batch, actor.reward_batch, actor.avg_baseline, actor.train_step1,
actor.train_step2], feed_dict=feed)
# print('Finish updating actor and critic network using reward calculated')
lambda1s.append(lambda1)
lambda2s.append(lambda2)
rewards_avg_baseline.append(reward_avg_baseline)
rewards_batches.append(reward_batch_score_cyc)
reward_max_per_batch.append(max_reward_batch_score_cyc)
graphss.append(graph_batch)
probsss.append(probs)
max_rewards.append(max_reward_score_cyc)
if i == 1 or i % 500 == 0:
print(
'[iter {}] reward_batch: {}, max_reward: {}, max_reward_batch: {}'
.format(i, reward_batch, max_reward, max_reward_batch))
# update lambda1, lamda2
if (i + 1) % lambda_iter_num == 0:
ls_kv = callreward.update_all_scores(lambda1, lambda2)
# np.save('{}/solvd_dict_epoch_{}.npy'.format(config.graph_dir, i), np.array(ls_kv))
max_rewards_re = callreward.update_scores(
max_rewards, lambda1, lambda2)
rewards_batches_re = callreward.update_scores(
rewards_batches, lambda1, lambda2)
reward_max_per_batch_re = callreward.update_scores(
reward_max_per_batch, lambda1, lambda2)
graph_int, score_min, cyc_min = np.int32(
ls_kv[0][0]), ls_kv[0][1][1], ls_kv[0][1][-1]
if cyc_min < 1e-5:
lambda1_upper = score_min
lambda1 = min(lambda1 + lambda1_update_add, lambda1_upper)
lambda2 = min(lambda2 * lambda2_update_mul, lambda2_upper)
graph_batch = convert_graph_int_to_adj_mat(graph_int)
if reg_type == 'LR':
graph_batch_pruned = np.array(
graph_prunned_by_coef(graph_batch,
training_set.inputdata))
elif reg_type == 'QR':
graph_batch_pruned = np.array(
graph_prunned_by_coef_2nd(graph_batch,
training_set.inputdata))
elif reg_type == 'GPR':
# The R codes of CAM pruning operates the graph form that (i,j)=1 indicates i-th node-> j-th node
# so we need to do a tranpose on the input graph and another tranpose on the output graph
graph_batch_pruned = np.transpose(
pruning_cam(training_set.inputdata,
np.array(graph_batch).T))
# estimate accuracy
# FIXME graph_batch or graph_batch_pruned
# FIXME .T should be adj mat?
acc_est = count_accuracy(training_set.true_graph,
graph_batch.T)
acc_est2 = count_accuracy(training_set.true_graph,
graph_batch_pruned.T)
# TODO return the adj matrix
fdr, tpr, fpr, shd, nnz = acc_est['fdr'], acc_est['tpr'], acc_est['fpr'], acc_est['shd'], \
acc_est['pred_size']
fdr2, tpr2, fpr2, shd2, nnz2 = acc_est2['fdr'], acc_est2['tpr'], acc_est2['fpr'], acc_est2['shd'], \
acc_est2['pred_size']
accuracy_res.append((fdr, tpr, fpr, shd, nnz))
accuracy_res_pruned.append((fdr2, tpr2, fpr2, shd2, nnz2))
print('fdr:', fdr, 'tpr:', tpr, 'fpr:', fpr, 'shd:', shd)
result = acc_est
return graph_batch.T