1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
|
################################################################################
# Copyright (C) 2015 Jaakko Luttinen
#
# This file is licensed under the MIT License.
################################################################################
"""
Demonstration of the pattern search method for PCA.
The pattern searches are compared to standard VB-EM algorithm in CPU
time. For more info on the pattern search method, see
:cite:`Honkela:2002`.
"""
import numpy as np
import scipy
import matplotlib.pyplot as plt
import bayespy.plot as myplt
from bayespy.utils import misc
from bayespy.utils import random
from bayespy import nodes
from bayespy.inference.vmp.vmp import VB
from bayespy.inference.vmp import transformations
import bayespy.plot as bpplt
from bayespy.demos import pca
def run(M=40, N=100, D_y=6, D=8, seed=42, rotate=False, maxiter=1000, debug=False, plot=True):
"""
Run pattern search demo for PCA.
"""
if seed is not None:
np.random.seed(seed)
# Generate data
w = np.random.normal(0, 1, size=(M,1,D_y))
x = np.random.normal(0, 1, size=(1,N,D_y))
f = misc.sum_product(w, x, axes_to_sum=[-1])
y = f + np.random.normal(0, 0.2, size=(M,N))
# Construct model
Q = pca.model(M, N, D)
# Data with missing values
mask = random.mask(M, N, p=0.5) # randomly missing
y[~mask] = np.nan
Q['Y'].observe(y, mask=mask)
# Initialize some nodes randomly
Q['X'].initialize_from_random()
Q['W'].initialize_from_random()
# Use a few VB-EM updates at the beginning
Q.update(repeat=10)
Q.save()
# Standard VB-EM as a baseline
Q.update(repeat=maxiter)
if plot:
bpplt.pyplot.plot(np.cumsum(Q.cputime), Q.L, 'k-')
# Restore initial state
Q.load()
# Pattern search method for comparison
for n in range(maxiter):
Q.pattern_search('W', 'tau', maxiter=3, collapsed=['X', 'alpha'])
Q.update(repeat=20)
if Q.has_converged():
break
if plot:
bpplt.pyplot.plot(np.cumsum(Q.cputime), Q.L, 'r:')
bpplt.pyplot.xlabel('CPU time (in seconds)')
bpplt.pyplot.ylabel('VB lower bound')
bpplt.pyplot.legend(['VB-EM', 'Pattern search'], loc='lower right')
if __name__ == '__main__':
import sys, getopt, os
try:
opts, args = getopt.getopt(sys.argv[1:],
"",
["m=",
"n=",
"d=",
"k=",
"seed=",
"maxiter=",
"debug"])
except getopt.GetoptError:
print('python demo_pca.py <options>')
print('--m=<INT> Dimensionality of data vectors')
print('--n=<INT> Number of data vectors')
print('--d=<INT> Dimensionality of the latent vectors in the model')
print('--k=<INT> Dimensionality of the true latent vectors')
print('--maxiter=<INT> Maximum number of VB iterations')
print('--seed=<INT> Seed (integer) for the random number generator')
print('--debug Check that the rotations are implemented correctly')
sys.exit(2)
kwargs = {}
for opt, arg in opts:
if opt == "--rotate":
kwargs["rotate"] = True
elif opt == "--maxiter":
kwargs["maxiter"] = int(arg)
elif opt == "--debug":
kwargs["debug"] = True
elif opt == "--seed":
kwargs["seed"] = int(arg)
elif opt in ("--m",):
kwargs["M"] = int(arg)
elif opt in ("--n",):
kwargs["N"] = int(arg)
elif opt in ("--d",):
kwargs["D"] = int(arg)
elif opt in ("--k",):
kwargs["D_y"] = int(arg)
run(**kwargs)
plt.show()
|
