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ugm_gavi.py
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# -*- coding: UTF-8 -*-
"""
Gradient Ascent Variational Inference process to approximate an
univariate gaussian
"""
from __future__ import absolute_import
import argparse
import math
from time import time
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt
import numpy as np
import tensorflow as tf
"""
Parameters:
* maxIter: Max number of iterations
* nElements: Number of data points to generate
* verbose: Printing time, intermediate variational parameters, plots, ...
Execution:
python ugm_gavi.py -nElements 1000 -verbose
"""
parser = argparse.ArgumentParser(description='GAVI in univariate gaussian')
parser.add_argument('-maxIter', metavar='maxIter', type=int, default=500)
parser.add_argument('-nElements', metavar='nElements', type=int, default=1000)
parser.add_argument('-verbose', dest='verbose', action='store_true')
parser.set_defaults(verbose=False)
args = parser.parse_args()
N = args.nElements
VERBOSE = args.verbose
DATA_MEAN = 7
LR = 100.
THRESHOLD = 1e-6
sess = tf.Session()
# Data generation
xn_np = np.random.normal(DATA_MEAN, 1, N)
xn = tf.convert_to_tensor(xn_np, dtype=tf.float64)
if VERBOSE: init_time = time()
# Model hyperparameters
m_o = tf.Variable(0., dtype=tf.float64)
beta_o = tf.Variable(0.0001, dtype=tf.float64)
a_o = tf.Variable(0.001, dtype=tf.float64)
b_o = tf.Variable(0.001, dtype=tf.float64)
# Needed for variational initilizations
a_ini = np.random.gamma(1, 1, 1)[0]
b_ini = np.random.gamma(1, 1, 1)[0]
# Variational parameters
a_var = tf.Variable(a_ini, dtype=tf.float64)
b_var = tf.Variable(b_ini, dtype=tf.float64)
lambda_m = tf.Variable(np.random.normal(0., (0.0001) ** (-1.), 1)[0],
dtype=tf.float64)
beta_var = tf.Variable(np.random.gamma(a_ini, b_ini, 1)[0], dtype=tf.float64)
# Maintain numerical stability
lambda_a = tf.nn.softplus(a_var)
lambda_b = tf.nn.softplus(b_var)
lambda_beta = tf.nn.softplus(beta_var)
# Lower Bound definition
LB = tf.multiply(tf.cast(1. / 2, tf.float64),
tf.log(tf.div(beta_o, lambda_beta)))
LB = tf.add(LB, tf.multiply(tf.multiply(tf.cast(1. / 2, tf.float64),
tf.add(tf.pow(lambda_m, 2),
tf.div(tf.cast(1., tf.float64),
lambda_beta))),
tf.subtract(lambda_beta, beta_o)))
LB = tf.subtract(LB, tf.multiply(lambda_m,
tf.subtract(tf.multiply(lambda_beta, lambda_m),
tf.multiply(beta_o, m_o))))
LB = tf.add(LB, tf.multiply(tf.cast(1. / 2, tf.float64),
tf.subtract(
tf.multiply(lambda_beta, tf.pow(lambda_m, 2)),
tf.multiply(beta_o, tf.pow(m_o, 2)))))
LB = tf.add(LB, tf.multiply(a_o, tf.log(b_o)))
LB = tf.subtract(LB, tf.multiply(lambda_a, tf.log(lambda_b)))
LB = tf.add(LB, tf.lgamma(lambda_a))
LB = tf.subtract(LB, tf.lgamma(a_o))
LB = tf.add(LB, tf.multiply(tf.subtract(tf.digamma(lambda_a), tf.log(lambda_b)),
tf.subtract(a_o, lambda_a)))
LB = tf.add(LB,
tf.multiply(tf.div(lambda_a, lambda_b), tf.subtract(lambda_b, b_o)))
LB = tf.add(LB,
tf.multiply(tf.div(tf.cast(N, tf.float64), tf.cast(2., tf.float64)),
tf.subtract(tf.digamma(lambda_a), tf.log(lambda_b))))
LB = tf.subtract(LB, tf.multiply(
tf.div(tf.cast(N, tf.float64), tf.cast(2., tf.float64)),
tf.log(tf.multiply(tf.cast(2., tf.float64), math.pi))))
LB = tf.subtract(LB, tf.multiply(tf.cast(1. / 2, tf.float64),
tf.multiply(tf.div(lambda_a, lambda_b),
tf.reduce_sum(tf.pow(xn, 2)))))
LB = tf.add(LB,
tf.multiply(tf.div(lambda_a, lambda_b),
tf.multiply(tf.reduce_sum(xn), lambda_m)))
LB = tf.subtract(LB, tf.multiply(
tf.div(tf.cast(N, tf.float64), tf.cast(2., tf.float64)),
tf.multiply(tf.div(lambda_a, lambda_b), tf.add(tf.pow(lambda_m, 2),
tf.div(
tf.cast(1.,
tf.float64),
lambda_beta)))))
# Optimizer definition
optimizer = tf.train.AdamOptimizer(learning_rate=LR)
grads_and_vars = optimizer.compute_gradients(-LB, var_list=[a_var, b_var,
lambda_m, beta_var])
train = optimizer.apply_gradients(grads_and_vars)
# Summaries definition
tf.summary.histogram('lambda_m', lambda_m)
tf.summary.histogram('lambda_beta', lambda_beta)
tf.summary.histogram('lambda_a', lambda_a)
tf.summary.histogram('lambda_a', lambda_b)
merged = tf.summary.merge_all()
file_writer = tf.summary.FileWriter('/tmp/tensorboard/', tf.get_default_graph())
def main():
if VERBOSE:
plt.plot(xn_np, 'ro', markersize=3)
plt.title('Simulated dataset')
plt.show()
# Inference
init = tf.global_variables_initializer()
sess.run(init)
lbs = []
n_iters = 0
for _ in range(args.maxIter):
# ELBO computation
_, mer, lb, m_out, beta_out, a_out, b_out = sess.run(
[train, merged, LB, lambda_m, lambda_beta, lambda_a, lambda_b])
lbs.append(lb)
if VERBOSE:
print('\n******* ITERATION {} *******'.format(n_iters))
print('lambda_m: {}'.format(m_out))
print('lambda_beta: {}'.format(beta_out))
print('lambda_a: {}'.format(a_out))
print('lambda_b: {}'.format(b_out))
print('ELBO: {}'.format(lb))
# Break condition
improve = lb - lbs[n_iters - 1]
if VERBOSE: print('Improve: {}'.format(improve))
if (n_iters == (args.maxIter - 1)) \
or (n_iters > 0 and 0 < improve < THRESHOLD):
break
n_iters += 1
file_writer.add_summary(mer, n_iters)
if VERBOSE:
plt.scatter(xn_np, mlab.normpdf(xn_np, m_out, a_out / b_out), s=5)
plt.title('Result')
plt.show()
final_time = time()
exec_time = final_time - init_time
print('Time: {} seconds'.format(exec_time))
print('Iterations: {}'.format(n_iters))
print('ELBOs: {}'.format(lbs))
if __name__ == '__main__': main()