/
model_simulation_epsilon.py
198 lines (168 loc) · 7.23 KB
/
model_simulation_epsilon.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
'''
No noise, ground and canopy model. Combined g and h dlm.
'''
from __future__ import division
import sys
import pdb
import pickle
from pylab import array, zeros, mean, ones, eye, sqrt
from pylab import isnan, logical_and, diag
from scipy import stats, ma, exp, log, nan, expand_dims
from scipy.stats import bernoulli
p = sys.path
sys.path.insert(0, '/home/bruce/Dropbox/thesis/code/pykalman')
from pykalman import KalmanFilter
sys.path = p
from gibbs import Model, GibbsStep
from misc import forward_filter_backward_sample
from stats_util import dirichlet, categorical, mvnorm, iid_dist
# Known values from simulation (can use to initialize sampler/skip burn-in)
p = pickle.load(open('../data/sims/simulation_delta_1.pkl', 'rb'))
g = p['g']
h = p['h']
T = p['T']
sigma_g = p['sigma_g']
sigma_h = p['sigma_h']
# Also needed for known parameters (so load the right pkl dummy!)
phi = p['phi']
mu_h = p['mu_h']
sigma_z_g = p['sigma_z_g']
sigma_z_h = p['sigma_z_h']
############################################################################################################
def define_model(data):
# Builds model object
n = len(data)
z = data.get('z')
variable_names = ['surfaces', 'T', 'p_type', 'sigma_g', 'sigma_h']
known_params = {'sigma_z_g': sigma_z_g,
'sigma_z_h': sigma_z_h,
'mu_h': mu_h,
'phi': phi}
hyper_params = {'alpha_type': array((1., 1., 1.)),
'prior_mu_g': -25.+zeros(n),
'prior_cov_g': 100.*eye(n),
'prior_mu_h': 30.+zeros(n),
'prior_cov_h': 100.*eye(n),
'a_g': 11,
'b_g': .1,
'a_h': 11,
'b_h': 40}
initials = {'surfaces': [-25, 30]*ones((n,2)),
'sigma_g': .1,
'sigma_h': 1,
'T': array([(0 if abs(z[i]+25)>1 else 1) for i in xrange(n)])}
#initials = {'sigma_g': sigma_g,
# 'sigma_h': sigma_h,
# 'T': T[:n],
# 'g': g[:n],
# 'h': h[:n]}
priors = {'p_type': dirichlet(hyper_params['alpha_type']),
'sigma_g': stats.invgamma(hyper_params['a_g'], scale=hyper_params['b_g']),
'sigma_h': stats.invgamma(hyper_params['a_h'], scale=hyper_params['b_h']),
'T': iid_dist(categorical(hyper_params['alpha_type']), n)}
FCP_samplers = {'p_type': p_type_step(),
'surfaces': surfaces_step(),
'sigma_g': sigma_ground_step(),
'sigma_h': sigma_height_step(),
'T': type_step()}
model = Model()
model.set_variable_names(variable_names)
model.set_known_params(known_params)
model.set_hyper_params(hyper_params)
model.set_priors(priors)
model.set_initials(initials)
model.set_FCP_samplers(FCP_samplers)
model.set_data(data)
return model
####################################################################################################
# Gibbs sampler parts - full conditional posterior/metropolis-hastings samplers
class surfaces_step(GibbsStep):
def __init__(self, *args, **kwargs):
super(surfaces_step, self).__init__(*args, **kwargs)
self._kalman = KalmanFilter()
def sample(self, model, evidence):
z = evidence['z']
T, surfaces, sigma_g, sigma_h = [evidence[var] for var in ['T', 'surfaces', 'sigma_g', 'sigma_h']]
mu_h, phi, sigma_z_g, sigma_z_h = [model.known_params[var] for var in ['mu_h', 'phi', 'sigma_z_g', 'sigma_z_h']]
prior_mu_g, prior_cov_g = [model.hyper_params[var] for var in ['prior_mu_g', 'prior_cov_g']]
prior_mu_h, prior_cov_h = [model.hyper_params[var] for var in ['prior_mu_h', 'prior_cov_h']]
n = len(g)
y = ma.asarray(ones((n, 2))*nan)
if sum(T==1) > 0:
y[T==1, 0] = z[T==1]
if sum(T==2) > 0:
y[T==2, 1] = z[T==2]
y[isnan(y)] = ma.masked
kalman = self._kalman
kalman.initial_state_mean=[prior_mu_g[0], prior_mu_h[0]]
kalman.initial_state_covariance=diag([prior_cov_g[0,0], prior_cov_h[0,0]])
kalman.transition_matrices=[[1, 0], [0, phi]]
kalman.transition_offsets =ones((n, 2))*[0, mu_h*(1-phi)]
kalman.transition_covariance=[[sigma_g**2, 0], [0, sigma_h**2]]
kalman.observation_matrices=[[1, 0], [1, 1]]
kalman.observation_covariance=[[sigma_z_g**2, 0], [0, sigma_z_h**2]]
sampled_surfaces = forward_filter_backward_sample(kalman, y)
return sampled_surfaces
class sigma_ground_step(GibbsStep):
def sample(self, model, evidence):
prior_mu_g, a_g, b_g = [model.hyper_params[var] for var in ['prior_mu_g', 'a_g', 'b_g']]
g = evidence['surfaces'][:,0]
n = len(g)
g_var_posterior = stats.invgamma(a_g + (n-1)/2., scale=b_g + sum((g[1:] - g[:-1])**2)/2.)
g_var = g_var_posterior.rvs()
return sqrt(g_var)
class sigma_height_step(GibbsStep):
def sample(self, model, evidence):
prior_mu_h, a_h, b_h = [model.hyper_params[var] for var in ['prior_mu_h', 'a_h', 'b_h']]
h = evidence['surfaces'][:,1]
n = len(h)
h_var_posterior = stats.invgamma(a_h + (n-1)/2., scale=b_h + sum((h[1:] - h[:-1])**2)/2.)
h_var = h_var_posterior.rvs()
return min(sqrt(h_var), 3)
class type_step(GibbsStep):
def sample(self, model, evidence):
surfaces, p_type, z, sigma_z_g, sigma_z_h = [evidence[var]
for var in ['surfaces', 'p_type', 'z', 'sigma_z_g', 'sigma_z_h']]
g, h = surfaces[:,0], surfaces[:,1]
N = len(z)
m = len(p_type)
T = zeros(N)
noise_rv = stats.uniform(z.min(), z.max() - z.min())
for i in xrange(N):
l = zeros(m)
l[0] = p_type[0]*noise_rv.pdf(z[i])
g_norm = stats.norm(g[i], sigma_z_g)
l[1] = p_type[1]*g_norm.pdf(z[i])
if z[i] > g[i]:
h_norm = stats.norm(h[i], sigma_z_h)
l[2] = p_type[2]*h_norm.pdf(z[i] - g[i])
p = l/sum(l)
T[i] = categorical(p).rvs()
if T[i] == 2 and z[i] < g[i]: pdb.set_trace()
return T
class p_type_step(GibbsStep):
def sample(self, model, evidence):
alpha_type = model.hyper_params['alpha_type']
T = evidence['T']
m = len(alpha_type)
return dirichlet(alpha_type + array([sum(T==i) for i in xrange(m)])).rvs()
def visualize_gibbs(sampler, evidence):
z, T, d, surfaces, sigma_g, sigma_h = [evidence[var] for var in ['z', 'T', 'd', 'surfaces', 'sigma_g', 'sigma_h']]
g, h = surfaces[:,0], surfaces[:,1]
g = g.reshape((len(g), ))
h = h.reshape((len(h), ))
print "sigma_g: %s" % sigma_g
print "sigma_h: %s" % sigma_h
print "T counts: %s" % [sum(T==i) for i in range(3)]
from matplotlib import pyplot as plt
fig = plt.figure()
plt.plot(d[T==0], z[T==0], 'r.')
plt.plot(d[T==1], z[T==1], 'k.')
plt.plot(d[T==2], z[T==2], 'g.')
plt.plot(d, g, 'k-', linewidth=3, alpha=.5)
plt.plot(d, g+h, 'g-', linewidth=3, alpha=.5)
#plt.fill_between(d, g-1.96*sigma_g, g+1.96*sigma_g, color='k', alpha=.3)
def moveon(event):
plt.close()
fig.canvas.mpl_connect('key_press_event', moveon)
plt.show()