Experiments approximating the posterior with diagonal Gaussians using variational inference

We start by building the model and showing the basic inference procedure and calculation of the performance on the MNIST classification and the outlier detection task. Then perform multiple runs of the model with different number of samples in the ensemble to calculate performance statistics. This experiment uses the same base learning rate as the noisy-Adam example to produce comparable results.



In [1]:

    
# Let's first setup the libraries, session and experimental data
import experiment
import inferences
import edward as ed
import tensorflow as tf
import numpy as np
import os

s = experiment.setup()
mnist, notmnist = experiment.get_data()









    



Extracting MNIST_data/train-images-idx3-ubyte.gz
Extracting MNIST_data/train-labels-idx1-ubyte.gz
Extracting MNIST_data/t10k-images-idx3-ubyte.gz
Extracting MNIST_data/t10k-labels-idx1-ubyte.gz
Extracting notMNIST_data/train-images-idx3-ubyte.gz
Extracting notMNIST_data/train-labels-idx1-ubyte.gz
Extracting notMNIST_data/t10k-images-idx3-ubyte.gz
Extracting notMNIST_data/t10k-labels-idx1-ubyte.gz



In [2]:

    
# Builds the model and approximation variables used for the model
y_, model_variables = experiment.get_model_3layer()
approx_variables = experiment.get_vi_approximation_variables_3layer()



In [3]:

    
# Performs inference with edward's KLpq class
optimizer = tf.train.AdamOptimizer(0.005)
inference_dict = {model_variables[key]: val for key, val in approx_variables.iteritems()}
inference = ed.KLpq(inference_dict, data={y_: model_variables['y']})
n_iter=1000
inference.initialize(n_iter=n_iter, optimizer=optimizer, n_samples=50)

tf.global_variables_initializer().run()
for i in range(n_iter):
    batch = mnist.train.next_batch(100)
    info_dict = inference.update({model_variables['x']: batch[0],
                                  model_variables['y']: batch[1]})
    inference.print_progress(info_dict)

inference.finalize()









    



1000/1000 [100%] ██████████████████████████████ Elapsed: 278s | Loss: -3587.841



In [4]:

    
# Computes the accuracy of our model
accuracy, disagreement = experiment.get_metrics(model_variables, approx_variables, num_samples=10)
print(accuracy.eval({model_variables['x']: mnist.test.images, model_variables['y']: mnist.test.labels}))
print(disagreement.eval({model_variables['x']: mnist.test.images, model_variables['y']: mnist.test.labels}))









    



0.1365
[ 18.86696625  16.95742416  18.86696625 ...,  16.43417549  18.86696053
  16.95742416]



In [5]:

    
# Computes some statistics for the proposed outlier detection
outlier_stats = experiment.get_outlier_stats(model_variables, disagreement, mnist, notmnist)
print(outlier_stats)
print('TP/(FN+TP): {}'.format(float(outlier_stats['TP']) / (outlier_stats['TP'] + outlier_stats['FN'])))
print('FP/(FP+TN): {}'.format(float(outlier_stats['FP']) / (outlier_stats['FP'] + outlier_stats['TN'])))









    



{'FP': 0, 'TN': 10000, 'FN': 10000, 'TP': 0}
TP/(FN+TP): 0.0
FP/(FP+TN): 0.0

The following cell performs multiple runs of this model with different number of samples within the ensemble to capture performance statistics. Results are saved in VI_KLpq_Adam.csv.



In [6]:

    
import pandas as pd

results = pd.DataFrame(columns=('run', 'samples', 'acc', 'TP', 'FN', 'TN', 'FP'))

for run in range(5):
    lr = tf.placeholder(tf.float32, shape=[])
    optimizer = tf.train.GradientDescentOptimizer(lr)
    inference_dict = {model_variables[key]: val for key, val in approx_variables.iteritems()}
    inference = ed.KLpq(inference_dict, data={y_: model_variables['y']})
    n_iter=1000
    inference.initialize(n_iter=n_iter, optimizer=optimizer, n_samples=10)

    tf.global_variables_initializer().run()
    for i in range(n_iter):
        batch = mnist.train.next_batch(100)
        info_dict = inference.update({model_variables['x']: batch[0],
                                      model_variables['y']: batch[1],
                                      lr:0.005/(i+1.)})
        inference.print_progress(info_dict)

    inference.finalize()
    
    for num_samples in range(15):
        accuracy, disagreement = experiment.get_metrics(model_variables, approx_variables,
                                                        num_samples=num_samples + 1)
        acc = accuracy.eval({model_variables['x']: mnist.test.images, model_variables['y']: mnist.test.labels})
        outlier_stats = experiment.get_outlier_stats(model_variables, disagreement, mnist, notmnist)
        results.loc[len(results)] = [run, num_samples + 1, acc,
                                     outlier_stats['TP'], outlier_stats['FN'],
                                     outlier_stats['TN'], outlier_stats['FP']]
results.to_csv('VI_KLpq_Adam.csv', index=False)









    



1000/1000 [100%] ██████████████████████████████ Elapsed: 62s | Loss: -25353.051
1000/1000 [100%] ██████████████████████████████ Elapsed: 62s | Loss: -26564.094
1000/1000 [100%] ██████████████████████████████ Elapsed: 62s | Loss: -23792.889
1000/1000 [100%] ██████████████████████████████ Elapsed: 63s | Loss: -25506.625
1000/1000 [100%] ██████████████████████████████ Elapsed: 64s | Loss: -25013.225