-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathhpf_model.py
250 lines (198 loc) · 11.4 KB
/
hpf_model.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
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
"""Methods calculating E[Y] and E[Y^2] (and therefore also Var[Y]) over prior predictive distribution for Hierarchical Poisson Matrix Factorization."""
import numpy as np
import tensorflow as tf
import tensorflow_probability as tfp
from tensorflow_probability import distributions as tfd
import warnings
def _ttf(v):
return tf.Variable(v, dtype=tf.float64) if type(v) is float else v
#a=0.3, ap=0.3, bp=1.0, c=0.3, cp=0.3, dp=1.0,
def empirical_Ey_and_Ey2_np_fast(a=3, ap=3, bp=1.0, c=3, cp=3, dp=1.0,
nsamples_latent=100, nsamples_latent1=1,
nsamples_output=10, K=25, N=1, M=1):
"""
Returns E_prior[Y] and E_prior[Y^2] for given set of hyperparameters.
Parametrization like in: http://jakehofman.com/inprint/poisson_recs.pdf
"""
if N!=1: warnings.warn("N!=1 will be ignored!")
if N!=1: warnings.warn("M!=1 will be ignored!")
N = nsamples_latent*nsamples_latent1*nsamples_output
ksi = np.random.gamma(ap, bp/ap, size=N)
theta = np.random.gamma(a, 1.0/ksi, size=(K, N))
eta = np.random.gamma(cp, dp/cp, size=N)
beta = np.random.gamma(c, 1.0/eta, size=(K, N))
latent = (theta*beta).sum(0)
ys = np.random.poisson(latent)
expectation = np.mean(ys)
expectation_squared = np.mean(np.array(ys)**2)
return expectation, expectation_squared
#a=0.3, ap=0.3, bp=1.0, c=0.3, cp=0.3, dp=1.0,
def empirical_Ey_and_Ey2_np(a=3, ap=3, bp=1.0, c=3, cp=3, dp=1.0,
nsamples_latent=100, nsamples_latent1=1,
nsamples_output=10, K=25, N=1, M=1):
"""
Returns E_prior[Y] and E_prior[Y^2] for given set of hyperparameters.
Parametrization like in: http://jakehofman.com/inprint/poisson_recs.pdf
Naive numpy implementation for testing purposes.
"""
if N!=1: warnings.warn("N!=1 will be ignored!")
if N!=1: warnings.warn("M!=1 will be ignored!")
ys = []
for _ in range(nsamples_latent*nsamples_latent1*nsamples_output):
ksi = np.random.gamma(ap, bp/ap)
theta = np.random.gamma(a, 1.0/ksi, size=K)
eta = np.random.gamma(cp, dp/cp)
beta = np.random.gamma(c, 1.0/eta, size=K)
latent = (theta*beta).sum()
if latent>1e16:
warnings.warn("Skipping too large latent value: %s" % latent)
continue
y = np.random.poisson(latent)
ys.append(y)
expectation = np.mean(ys)
expectation_squared = np.mean(np.array(ys)**2)
return expectation, expectation_squared
@tf.function
def empirical_Ey_and_Ey2_tf_logscore(a=3, ap=3, bp=1.0, c=3, cp=3, dp=1.0,
nsamples_latent=100, nsamples_latent1=1,
nsamples_output=10, K=25, N=1, M=1):
"""
Returns E_prior[Y] and E_prior[Y^2] for given set of hyperparameters.
Parametrization like in: http://jakehofman.com/inprint/poisson_recs.pdf
Gradients obtained with log-score derivative trick.
"""
if N!=1: warnings.warn("N!=1 will be ignored!")
if N!=1: warnings.warn("M!=1 will be ignored!")
ksi = tfd.Gamma(ap, ap/bp).sample(nsamples_latent) # NL0
theta = tfd.Gamma(a, ksi).sample((K,nsamples_latent1)) # K x NL1 x NL0
eta = tfd.Gamma(cp, cp/dp).sample(nsamples_latent)
beta = tfd.Gamma(c, eta).sample((K,nsamples_latent1))
latent = tf.reduce_sum(theta*beta, 0) # NL1 x NL0
latent = tf.reshape(latent, [-1]) # NL1*NL0
poisson = tfd.Poisson(rate=latent)
y_samples = poisson.sample([nsamples_output])
conditional_expectation = tfp.monte_carlo.expectation(
f=lambda x: x,
samples=y_samples,
log_prob=poisson.log_prob, use_reparameterization = False)
conditional_expectation_squared = tfp.monte_carlo.expectation(
f=lambda x: x*x,
samples=y_samples,
log_prob=poisson.log_prob, use_reparameterization = False)
expectation = tf.reduce_mean(conditional_expectation)
expectation_squared = tf.reduce_mean(conditional_expectation_squared)
return expectation, expectation_squared
@tf.function
def empirical_Ey_and_Ey2_tf(a=3, ap=3, bp=1.0, c=3, cp=3, dp=1.0,
nsamples_latent=100, nsamples_latent1=1,
nsamples_output=10, K=25, N=1, M=1):
"""
Returns E_prior[Y] and E_prior[Y^2] for given set of hyperparameters.
Parametrization like in: http://jakehofman.com/inprint/poisson_recs.pdf
"""
if N!=1: warnings.warn("N!=1 will be ignored!")
if N!=1: warnings.warn("M!=1 will be ignored!")
#a, ap, bp, c, cp, dp = _ttf(a), _ttf(ap), _ttf(bp), _ttf(c), _ttf(cp), _ttf(dp) # cast to tf
ksi = tfd.Gamma(ap, ap/bp).sample(nsamples_latent) # NL0
theta = tfd.Gamma(a, ksi).sample((K,nsamples_latent1)) # K x NL1 x NL0
eta = tfd.Gamma(cp, cp/dp).sample(nsamples_latent)
beta = tfd.Gamma(c, eta).sample((K,nsamples_latent1))
latent = tf.reduce_sum(theta*beta, 0) # NL1 x NL0
latent = tf.reshape(latent, [-1]) # NL1*NL0
poisson = tfd.Poisson(rate=latent)
#y_samples = np.random.poisson(latent, size=[nsamples_output, nsamples_latent*nsamples_latent1]) # NO x NL1*NL0
y_samples = tf.stop_gradient( poisson.sample([nsamples_output]) )
y_probs = tf.exp( poisson.log_prob(y_samples) )
#y_probs1 = np.array([[tf.exp(tfd.Poisson(rate=latent[i]).log_prob(y_samples[j,i])).numpy()
# for j in range(nsamples_output)]
# for i in range(nsamples_latent * nsamples_latent1)]).T
#assert (y_probs - y_probs1).numpy().max()<1e-12
total_prob = tf.reduce_sum(y_probs, 0)
conditional_expectation = tf.reduce_sum(y_probs * y_samples, 0) / total_prob
conditional_expectation_squared = tf.reduce_sum(y_probs * (y_samples**2), 0) / total_prob
expectation = tf.reduce_mean(conditional_expectation)
expectation_squared = tf.reduce_mean(conditional_expectation_squared)
return expectation, expectation_squared
def create_moments_estimator(K=25, ESTIMATOR_NO=-1, N=1, M=1,
empirical_Ey_and_Ey2 = empirical_Ey_and_Ey2_tf_logscore):
def theoretical_moments(a=3, ap=3, bp=1.0, c=3, cp=3, dp=1.0, nsamples=1000000):
""" No theoretical derivation for HPF available;
using numpy approximation instead.
"""
ey,ey2 = empirical_Ey_and_Ey2_np_fast(a, ap, bp, c, cp, dp,
nsamples_latent=nsamples, nsamples_latent1=1, nsamples_output=1, K=K)
e, v = ey, ey2-(ey**2)
return e, v
def empirical_moments_EV(a, ap, bp, c, cp, dp,
nsamples_latent, nsamples_output,
N=N, M=M, K=K):
""" Returns empirical estimates of expectation & variance."""
expectation, expectation_squared = empirical_Ey_and_Ey2(a, ap, bp, c, cp, dp,
nsamples_latent=nsamples_latent,
nsamples_output=nsamples_output,
N=N, M=M, K=K)
variance = expectation_squared - expectation**2
expectation, variance = tf.reduce_mean(expectation), tf.reduce_mean(variance)
return expectation, variance
def empirical_moments_EV_decoupled(a, ap, bp, c, cp, dp,
nsamples_latent, nsamples_output,
N=N, M=M, K=K):
""" Returns empirical estimates of expectation & variance.
Decoupled E & V but E[y] and E[y^2] for V computed together.
"""
expectation, _ = empirical_moments_EV(a, ap, bp, c, cp, dp,
nsamples_latent=nsamples_latent,
nsamples_output=nsamples_output,
N=N, M=M, K=K)
_, variance = empirical_moments_EV(a, ap, bp, c, cp, dp,
nsamples_latent=nsamples_latent,
nsamples_output=nsamples_output,
N=N, M=M, K=K)
return expectation, variance
def empirical_moments_V_decoupled(a, ap, bp, c, cp, dp,
nsamples_latent, nsamples_output,
N=N, M=M, K=K):
""" Returns empirical estimates of expectation & variance.
Uses the same E[y] for both E and V; E[y^2] independent of E[y].
"""
expectation, _ = empirical_Ey_and_Ey2(a, ap, bp, c, cp, dp,
nsamples_latent=nsamples_latent,
nsamples_output=nsamples_output,
N=N, M=M, K=K)
_, expectation_squared = empirical_Ey_and_Ey2(a, ap, bp, c, cp, dp,
nsamples_latent=nsamples_latent,
nsamples_output=nsamples_output,
N=N, M=M, K=K)
variance = expectation_squared - expectation**2
expectation, variance = tf.reduce_mean(expectation), tf.reduce_mean(variance)
return expectation, variance
def empirical_moments_fully_decoupled(a, ap, bp, c, cp, dp,
nsamples_latent, nsamples_output,
N=N, M=M, K=K):
""" Returns empirical estimates of expectation & variance.
Computes E[y] for E independent of E[y] for V. E[y^2] independent of E[y].
"""
expectation, _ = empirical_Ey_and_Ey2(a, ap, bp, c, cp, dp,
nsamples_latent=nsamples_latent,
nsamples_output=nsamples_output,
N=N, M=M, K=K)
_, expectation_squared = empirical_Ey_and_Ey2(a, ap, bp, c, cp, dp,
nsamples_latent=nsamples_latent,
nsamples_output=nsamples_output,
N=N, M=M, K=K)
variance = expectation_squared - expectation**2
variance = tf.reduce_mean(variance) # empirical
expectation, _ = empirical_Ey_and_Ey2(a, ap, bp, c, cp, dp,
nsamples_latent=nsamples_latent,
nsamples_output=nsamples_output,
N=N, M=M, K=K)
expectation = tf.reduce_mean(expectation)
return expectation, variance
NO2ESTIMATOR = {-1: theoretical_moments,
0: empirical_moments_fully_decoupled,
1: empirical_moments_EV_decoupled,
2: empirical_moments_EV,
3: empirical_moments_V_decoupled}
if ESTIMATOR_NO not in NO2ESTIMATOR: raise Exception("Wrong estimator number! Try: %s" % NO2ESTIMATOR)
estimator = NO2ESTIMATOR[ESTIMATOR_NO]
return estimator