-
Notifications
You must be signed in to change notification settings - Fork 0
/
banana.py
149 lines (113 loc) · 4.49 KB
/
banana.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
import math
import torch
import torch.distributions as D
import matplotlib.pyplot as plt
__all__ = ['BananaDistribution', ]
def rotate(x, angle):
"""Rotate a 2D tensor by a certain angle (in degrees)."""
angle = torch.as_tensor([angle * math.pi / 180])
cos, sin = torch.cos(angle), torch.sin(angle)
rot_mat = torch.as_tensor([[cos, sin], [-sin, cos]])
return x @ rot_mat
# Borrowed from Yann Dubois
class BananaTransform(D.Transform):
"""Transform from gaussian to banana."""
def __init__(self, curvature, factor=10):
super().__init__()
self.bijective = True
self.curvature = curvature
self.factor = factor
self.domain = D.constraints.Constraint()
self.codomain = D.constraints.Constraint()
def _call(self, x):
shift = torch.zeros_like(x)
shift[..., 1] = self.curvature * (torch.pow(x[..., 0], 2) - self.factor ** 2)
return x + shift
def _inverse(self, y):
shift = torch.zeros_like(y)
shift[..., 1] = self.curvature * (torch.pow(y[..., 0], 2) - self.factor ** 2)
return y - shift
def log_abs_det_jacobian(self, x, y):
return torch.zeros_like(x)
class RotateTransform(D.Transform):
"""Rotate a distribution from `angle` degrees."""
def __init__(self, angle):
super().__init__()
self.bijective = True
self.angle = angle
self.domain = D.constraints.Constraint()
self.codomain = D.constraints.Constraint()
def _call(self, x):
return rotate(x, self.angle)
def _inverse(self, y):
return rotate(y, -self.angle)
def log_abs_det_jacobian(self, x, y):
return torch.zeros_like(x)
class BananaDistribution(D.TransformedDistribution):
"""2D banana distribution.
Parameters
----------
curvature : float, optional
Controls the strength of the curvature of the banana-shape.
factor : float, optional
Controls the elongation of the banana-shape.
location : torch.Tensor, optional
Controls the location of the banana-shape.
angles : float, optional
Controls the angle rotation of the banana-shape.
scale : float, optional
Rescales the entire distribution (while keeping entropy of underlying distribution correct)
This is useful to make sure that the inputs during training are not too large / small.
"""
arg_constraints = {}
has_rsample = True
def __init__(
self,
curvature=0.05,
factor=6,
location=torch.as_tensor([-1.5, -2.0]),
angle=-40,
scale=1 / 2,
):
std = torch.as_tensor([factor * scale, scale])
base_dist = D.Independent(D.Normal(loc=torch.zeros(2), scale=std), 1)
transforms = D.ComposeTransform(
[
BananaTransform(curvature / scale, factor=factor * scale),
RotateTransform(angle),
D.AffineTransform(location * scale, 1),
]
)
super().__init__(base_dist, transforms)
self.curvature = curvature
self.factor = factor
self.rotate = rotate
self.domain = D.constraints.Constraint()
def entropy(self):
return self.base_dist.entropy() # log det is zero => same entropy
if __name__ == "__main__":
laplace = D.Laplace(loc=0, scale=1)
banana = BananaDistribution()
laplace_data = laplace.sample((200, ))
banana_data = banana.sample((1000, ))
laplace_limit = torch.linspace(-5, 5, 1000)
banana_limit_1 = torch.linspace(-5, 6, 1000)
banana_limit_2 = torch.linspace(-5, 6, 1000)
banana_grid_1, banana_grid_2 = torch.meshgrid(banana_limit_1, banana_limit_2)
xy = torch.vstack((banana_grid_1.flatten(), banana_grid_2.flatten())).T
fig, ax = plt.subplots(1, 2, figsize=(10, 5))
ax[0].plot(laplace_limit, torch.exp(laplace.log_prob(laplace_limit)), label="density")
# ax[0].hist(laplace_data, bins=100, density=True, color='gray')
ax[0].eventplot(laplace_data, lineoffsets=0, linelengths=0.03, color='red', alpha=.3, label="samples")
ax[0].set_ylim(0, 0.55)
ax[0].set_xlim(-5, 5)
ax[0].legend()
ax[1].contourf(banana_grid_1, banana_grid_2, torch.exp(banana.log_prob(xy).view(1000, 1000)),
levels=100, label="density", cmap='gist_yarg')
ax[1].scatter(banana_data[:, 0], banana_data[:, 1], color='red', s=1, alpha=.3, label="samples")
ax[1].set_ylim(-5, 6)
ax[1].set_xlim(-5, 6)
ax[1].legend()
plt.tight_layout()
plt.legend()
plt.show()