-
Notifications
You must be signed in to change notification settings - Fork 3
/
Copy pathppgen.py
188 lines (150 loc) · 7 KB
/
ppgen.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
#!/usr/bin/env python
# -*- coding: utf-8 -*-
import abc
import scipy.stats
import numpy as np
class Intensity(object):
__metaclass__ = abc.ABCMeta
class IntensityHomogenuosPoisson(Intensity):
def __init__(self, lam):
self.lam = lam
def get_value(self, t=None, past_ts=None):
return self.lam
def get_upper_bound(self, past_ts=None, t=None, to_t=None):
return self.lam
class IntensityGaussianMixture(Intensity):
def __init__(self, k=2, centers=[2, 4], stds=[1, 1], coefs= [1, 1]):
self.k = k
self.centers = centers
self.stds = stds
self.coefs = coefs
def get_value(self, t=None, past_ts=None):
return self._get_gaussianmixture_value(t)
def get_upper_bound(self, past_ts=None, t=None, to_t=None):
max_val = sum([ self._get_gaussianmixture_value(center) for center in self.centers ])
return max_val
def _get_gaussianmixture_value(self, t):
inten = 0
for i in range(self.k):
inten += self.coefs[i] * scipy.stats.norm.pdf(t, self.centers[i], self.stds[i])
return inten
def get_integral(self, t, past_ts=None):
return sum([ coef * (scipy.stats.norm.cdf(t, center, std) - \
scipy.stats.norm.cdf(0, center, std))
for coef, center, std in zip(self.coefs, self.centers, self.stds) ])
class IntensityHawkes(Intensity):
def __init__(self, mu=1, alpha=0.3, beta=1):
self.mu = mu
self.alpha = alpha
self.beta = beta
def get_value(self, t=None, past_ts=None):
inten = self.mu + np.sum(self.alpha * self.beta * np.exp(-self.beta * np.subtract(t, past_ts)))
return inten
def get_upper_bound(self, past_ts=None, t=None, to_t=None):
max_val = self.mu + np.sum(self.alpha * self.beta * np.exp(-self.beta * np.subtract(t, past_ts)))
return max_val
def get_integral(self, t, past_ts):
return self.mu * t + \
self.alpha * np.sum(1 - np.exp(-self.beta * (t - np.array(past_ts))))
class IntensityPoly(Intensity):
def __init__(self, segs=[0, 1, 2, 3], b=0, A=[1, 2, -3]):
self.segs = segs
self.b = b
self.A = A
if len(A) != len(segs) - 1:
raise Exception("Inequality lies in the numbers of segs and A.")
def get_value(self, t=None, past_ts=None):
return self._get_poly_value(t)
def get_upper_bound(self, past_ts=None, t=None, to_t=None):
max_val = 0
segs_within_range = [ s for s in self.segs if s > t and s < to_t ]
if len(segs_within_range) > 0:
max_val = max([ self._get_poly_value(t) for s in segs_within_range ])
max_val = max([ self._get_poly_value(t), self._get_poly_value(to_t), max_val ])
return max_val
def _get_poly_value(self, t):
if t > self.segs[-1]:
raise Exception("t is out of range.")
segs_before_t = [ s for s in self.segs if s < t ]
b = self.b
for seg_ind in range(len(segs_before_t)-1):
b = b + self.A[seg_ind] * (segs_before_t[seg_ind+1] - segs_before_t[seg_ind])
if len(segs_before_t) >= 1:
value = b + self.A[len(segs_before_t)-1] * (t - segs_before_t[len(segs_before_t)-1])
else:
value = b
return value
def get_integral(self, t, past_ts=None):
if t > self.segs[-1]:
raise Exception("t is out of range.")
segs_before_t = [ s for s in self.segs if s < t ]
# get starting intercepts (bs) for each of segments (size = len(segs_before_t) + 1)
bs = [self.b]
for seg_ind in range(len(segs_before_t)-1):
b = bs[seg_ind] + self.A[seg_ind] * \
(segs_before_t[seg_ind+1] - segs_before_t[seg_ind])
bs.append(b)
bs.append(self._get_poly_value(t)) # last intercept
# get length of each of segments (size = len(segs_before_t))
lens = []
for seg_ind in range(len(segs_before_t)-1):
lens.append(segs_before_t[seg_ind+1] - segs_before_t[seg_ind])
last_seg = segs_before_t[-1] if len(segs_before_t) > 0 else 0
lens.append(t - last_seg) # lengths of last segments
# get integrals (area) for each of segments
integrals = [ (width1 + width2) * height / 2.
for width1, width2, height in zip(bs[:-1], bs[1:], lens) ]
return sum(integrals)
class IntensityHawkesPlusPoly(IntensityHawkes, IntensityPoly):
def __init__(self, mu=1, alpha=0.3, beta=1,
segs=[0, 1, 2, 3], b=0, A=[1, 2, -3]):
IntensityPoly.__init__(self, segs=segs, b=b, A=A)
IntensityHawkes.__init__(self, mu=mu, alpha=alpha, beta=beta)
def get_value(self, t=None, past_ts=None):
return IntensityHawkes.get_value(self, t=t, past_ts=past_ts) + \
IntensityPoly.get_value(self, t=t)
def get_upper_bound(self, past_ts=None, t=None, to_t=None):
return IntensityPoly.get_upper_bound(self, t=t, to_t=to_t) + \
IntensityHawkes.get_upper_bound(self, past_ts=past_ts, t=t)
def get_integral(self, t, past_ts):
return IntensityPoly.get_integral(self, t=t) + \
IntensityHawkes.get_integral(self, t=t, past_ts=past_ts)
class IntensityHawkesPlusGaussianMixture(IntensityHawkes, IntensityGaussianMixture):
def __init__(self, mu=1, alpha=0.3, beta=1,
k=2, centers=[2, 4], stds=[1, 1], coefs=[1, 1]):
IntensityHawkes.__init__(self, mu=mu, alpha=alpha, beta=beta)
IntensityGaussianMixture.__init__(self, k=k, centers=centers, stds=stds, coefs=coefs)
def get_value(self, t=None, past_ts=None):
return IntensityHawkes.get_value(self, t=t, past_ts=past_ts) + \
IntensityGaussianMixture.get_value(self, t=t)
def get_upper_bound(self, past_ts=None, t=None, to_t=None):
return IntensityGaussianMixture.get_upper_bound(self, t=t, to_t=to_t) + \
IntensityHawkes.get_upper_bound(self, past_ts=past_ts, t=t)
def get_integral(self, t, past_ts):
return IntensityGaussianMixture.get_integral(self, t=t) + \
IntensityHawkes.get_integral(self, t=t, past_ts=past_ts)
def generate_sample(intensity, T, n):
seqs = []
i = 0
while True:
past_ts = []
cur_t = 0
while True:
intens1 = intensity.get_upper_bound(past_ts=past_ts, t=cur_t, to_t=T)
intens1 = intens1 if intens1 != 0 else 1e-4
t_delta = np.random.exponential(1.0/float(intens1))
next_t = cur_t + t_delta
# print "cur_t:%f, next_t:%f, delta_t:%f" % (cur_t, next_t, t_delta)
if next_t > T:
break
intens2 = intensity.get_value(t=next_t, past_ts=past_ts)
u = np.random.uniform()
if float(intens2)/float(intens1) >= u:
past_ts.append(next_t)
cur_t = next_t
if len(past_ts) > 1:
seqs.append(past_ts)
i += 1
if i == n:
break
return seqs