forked from parismav87/air2014
-
Notifications
You must be signed in to change notification settings - Fork 0
/
acquisition_function.py
190 lines (141 loc) · 4.37 KB
/
acquisition_function.py
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
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
import numpy as np
import scipy.spatial.distance as sp
import math
# see REMBO paper page 5 definition 4
# l = length scale > 0
# defined at first run, should be tuned
l = 1
def get_beta(t,d):
delta = 0.01
#a and b: to find out! it is a constant, see therom 2 of
#gaussian process paper.
a = 1
b = 1
r = 1 #theorem 2, page 5, has something to do with D
t = t+1
beta = 2*np.log(t**2*r*math.pi**2/(3*delta)) + 2*d*np.log(t**2*d*b*r*math.sqrt(np.log(4*d*a/delta)))
return beta
# Function to select random point
def select_random_point(y):
test_set=[]
idx = np.random.randint(0, len(y))
test_set.append(y[idx])
return np.matrix(test_set)
# Function to select test set from bounded box
def select_sample_set(n_test, y):
test_set = []
for i in xrange(0, n_test):
idx = np.random.randint(0, len(y))
test_set.append(y[idx])
return np.matrix(test_set)
# Function to return noisy sample
# GP Paper page 3
def sample_training_output(xtrain):
return f_func(xtrain) + np.random.normal(0, 0.001)
def f_func(x):
return -(x.sum(1))**2
def get_Kinv(t,Y):
K = np.zeros([t,t])
for ind in range(t):
for jnd in range(t):
K[ind,jnd] = sqexp_kernel(Y[ind],Y[jnd])
Kinv = np.linalg.inv(K+0.01*np.eye(t))
return Kinv
#input: No. of samples output: vector fY
def calculate_fY(number_of_samples,A,Y,t):
fY = np.zeros([t,1])
for q in range(0,number_of_samples):
fY[q]= f_func(np.dot(A,(Y[q].T)).T)
return fY
def compute_kVector(t,Y,y_new):
#compute the k vector according to the third paper page 8.
k_vector = []
for j in range(0,t):
k_vector=np.append(k_vector,sqexp_kernel(Y[j],y_new))
return k_vector
# Function to calculate GP Posterior
# It returns predictive mean and variance
# REMBO paper page 3
def gp_posterior(data,Y, y, A, t, d, number_of_samples):
mu =[]
sigma=[]
candidates=[]
Kinv = get_Kinv(t,Y)
fY = np.array()
for q in range(0,number_of_samples):
fY[q]=f_func(Y[q])
for i in xrange(0, len(y)):
y_instance = Y[i]
y_projected = projection(data,A*y_projected)
x = np.dot(A,y)
x = x.T
#add new line and column to the COV matrix.
# temp_sigma = np.append(temp_sigma, np.matrix(k_vector), 1)
# temp = np.append(k_vector, [sqexp_kernel(x, x)], 0)
# temp_sigma = np.append(temp_sigma, np.matrix(temp), 0)
# temp = np.matrix(temp)
# temp = temp.T
# temp_sigma = np.append(temp_sigma, temp, 0)
# temp_sigma[:,t+1] = [k_vector[len(k_vector)-1].T]
#calculate mu and sigma according to the rembo paper.
# This code is still not working
temp_mu = k_vector.T * Kinv * fY
temp_sigma = sqexp_kernel(y_instance,y_instance) - k_vector.T * Kinv * k_vector
#call the aqcuisition function here, and find argmax.
#using temp_mu and temp_sigma
candidate = UCB(t, d, temp_mu, temp_sigma)
# print candidate
candidates.append(candidate)
mu.append(temp_mu)
sigma.append(temp_sigma)
# Find the best candidate
# print len(candidates)
# print len(Y)
best_index = np.argmax(candidates)
print best_index
ybest = y[best_index]
return ybest
#given a point y outside Y, find its projection in Y
def projection(Y,y):
dist = 10000
min_z = Y[1]
for i in range(0,len(Y)):
z = Y[i];
temp_dist = np.linalg.norm(y-z)
if temp_dist<dist:
dist=temp_dist
min_z=Y[i]
return min_z
# Function squared exponential kernel a.k.a radial basis function kernel
# REMBO paper page 5
def sqexp_kernel(y1, y2):
# length scale
# should be tuned
l = 1
# we are using squared euclidan distance
# http://mlg.eng.cam.ac.uk/duvenaud/cookbook/index.html
# http://en.wikipedia.org/wiki/Radial_basis_function_kernel
distance = sp.euclidean(y1, y2)
k = np.exp(-(distance/2*(l**2)))
# return np.matrix(k)
return k
# Acquisition Function
# GP-UCB Algorithm
# GP Paper page 4
def UCB(t, d, mu, sigma):
# ycandidates = []
# print "=========="
# print math.sqrt(get_beta(t,d))
# print "=========="
# print sigma
return mu + math.sqrt(get_beta(t, d)) * sigma
# temp_y = mu[i] + math.sqrt(get_beta(t, d)) * sigma[i]
# ycandidates.append(temp_y)
# best_index = np.argmax(ycandidates)
# return xtest[best_index]
def augment_data(xtrain, fY, xbest, A):
train = A * xbest.T
train = train.T
xtrain = np.concatenate((xtrain, train), 0)
fY = np.concatenate((fY, f_func(train)), 0)
return xtrain, fY