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data_generation.py
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import numpy as np
import torch
from sklearn import datasets
def generate_prior_target(N, M, st, target):
targets = ['circles', 'cross', 'bananas', 'GMM', 'four_wells', 'circles', 'moons', 'swiss_roll_2d', 'swiss_roll_3d', 's_curve', 'annulus', 'low_dim_gaussian']
if target in targets:
return globals().get('generate_' + target)(N, M, st)
else:
raise ValueError("Invalid target specified. Currently, these are implemented: 'circles', 'cross', 'bananas', 'GMM', 'four_wells', 'circles', 'moons', 'swiss_roll_2d', 'swiss_roll_3d', 's_curve', 'annulus', 'low_dim_gaussian'")
def generate_low_dim_gaussian(N, M, st, d = 2):
m1 = 1/2*torch.ones(d)
M1 = torch.tensor([[1.0, 0.0], [0.0, -1.0]])
v = 1/200*torch.eye(d)
torch.manual_seed(st)
normal1 = torch.distributions.MultivariateNormal(m1, v)
target1 = normal1.sample((M,))
target = torch.cat( (target1, torch.zeros(M, 8)), dim=1)
prior = torch.cat( (torch.zeros((N, 8)), normal1.sample((N,)) ), dim=1 )
return target, prior
def generate_four_wells(N, M, st, d = 2):
if M % 4:
raise Exception(f'M must be divisible by 4, but M = {M}')
quarterM = int(M/4)
m1 = 1/2*torch.ones(d)
M1 = torch.tensor([[1.0, 0.0], [0.0, -1.0]])
m2 = torch.matmul(M1,m1)
v = 1/200*torch.eye(d)
torch.manual_seed(st)
normal1 = torch.distributions.MultivariateNormal(m1, v)
normal2 = torch.distributions.MultivariateNormal(-m1, v)
normal3 = torch.distributions.MultivariateNormal(m2, v)
normal4 = torch.distributions.MultivariateNormal(-m2, v)
target1 = normal1.sample((quarterM,))
target2 = normal2.sample((quarterM,))
target3 = normal3.sample((quarterM,))
target4 = normal4.sample((quarterM,))
target = torch.cat( (target1, target2, target3, target4) )
torch.manual_seed(st)
prior = normal1.sample((N,))
return target, prior
def generate_GMM(N, M, st, d = 2):
# target = sum of two Gaussians
# target and prior have the symmetry axis x = - y
linspace = torch.linspace(-.5, .5, N).unsqueeze(1)
prior = torch.cat( (linspace, - linspace), dim=1)
halfM = int(M/2)
m1 = 1/2*torch.ones(d)
v = 1/200*torch.eye(d)
torch.manual_seed(st)
normal = torch.distributions.MultivariateNormal(m1, v)
target = normal.sample((halfM,))
target = torch.cat( (target, - target) )
return target, prior
def neals_funnel(M, st=314):
# Generate samples from Neal's funnel
rs = np.random.RandomState(st)
y = rs.normal(0, 2, size=M)
x = rs.normal(0, np.exp(y/3), size=M)
y = (y+7.5)
return np.column_stack((x, y))
def generate_circles(N, M, st=42, r=.3, delta=.5):
'''
1. Generate three rings target, each ring has N points sampled uniformly.
The rings have a radius of r and a separation of delta.
2. Generate prior, which is a Gaussian with very small variance centered at
leftmost point of the rightmost ring.
Returns
-------
prior : np.array, shape = (N, 2) prior.
target : np.array, shape = (M, 2) three rings target
'''
if M % 3:
raise Exception(f'M should be divisible by 3, but you chose M={M}')
else:
n = int(M // 3)
# TODO: convert to pytorch code
X = np.c_[r * np.cos(np.linspace(0, 2 * np.pi, n + 1)), r * np.sin(np.linspace(0, 2 * np.pi, n + 1))][:-1] # noqa
for i in [1, 2]:
X = np.r_[X, X[:n, :]-i*np.array([0, (2 + delta) * r])]
target = torch.from_numpy(X).to(torch.float64)
torch.manual_seed(st)
m = torch.tensor([0.0, -r])
v = 1e-4*torch.eye(2)
normal = torch.distributions.MultivariateNormal(m, v)
prior = normal.sample((N,))
return target, prior
def generate_bananas(N, M, st, d=2):
u = int(M/2)
torch.manual_seed(st) # fix randomness
# layer 1
vert1 = torch.rand(u)
hori1 = torch.rand(u)
xs1 = torch.linspace(-1, 1, u) + vert1
squared1 = xs1**2 + hori1
# layer 2
vert2 = torch.rand(u)
hori2 = torch.rand(u)
xs2 = torch.linspace(-1.5, 1.5, u) + vert2
squared2 = 1/2*(xs2 - 1)**2 + hori2 - 4
xs = torch.cat((xs1, xs2))
squared = torch.cat((squared1, squared2))
target = torch.stack((xs, squared)).transpose(0, 1)
m_p = torch.tensor([0, 4.0])
v_p = 1 / 2000 * torch.eye(d)
norm = torch.distributions.MultivariateNormal(m_p, v_p)
prior = norm.sample((N,))
return target, prior
def generate_cross(N, M, st, d=2):
rot_num = 4 # number of rotations
samples = neals_funnel(int(M/rot_num), st=st)
rotations = (360/rot_num)*np.arange(rot_num)
new_samples = []
for rotation in rotations:
rotated_samples = rotate_points(samples, rotation)
new_samples.append(rotated_samples)
target = torch.from_numpy(np.concatenate(new_samples, axis=0))
m_p = torch.zeros(d)
v_p = 1/2000*torch.eye(d)
norm = torch.distributions.MultivariateNormal(m_p, v_p)
prior = norm.sample((N,))
return target, prior
def rotate_point(point, angle):
# rotate the point by angle (in radians)
x, y = point
angle = torch.tensor(angle)
new_x = x * torch.cos(angle) - y * torch.sin(angle)
new_y = x * torch.sin(angle) + y * torch.cos(angle)
return (new_x, new_y)
def rotate_points(points, angle):
return torch.tensor([rotate_point(point, angle) for point in points])
def generate_swiss_roll_2d(N, M, st):
torch.manual_seed(st)
theta = torch.sqrt(torch.rand(M)) * 4 * torch.pi # angles
X1 = theta.cos() * theta
X2 = theta.sin() * theta
target = torch.stack((X1, X2), dim=1)
m = torch.zeros(2)
v = 1/200*torch.eye(2)
torch.manual_seed(st)
normal = torch.distributions.MultivariateNormal(m, v)
prior = normal.sample((N,))
return target, prior
def generate_swiss_roll_3d(N, M, st):
target, _ = datasets.make_swiss_roll(n_samples=M, random_state=st, noise=.5)
target = torch.from_numpy(target)
m = torch.tensor([0.0, 10.0, -5.0])
v = 1/200*torch.eye(3)
torch.manual_seed(st)
normal = torch.distributions.MultivariateNormal(m, v)
prior = normal.sample((N,))
return target, prior
def generate_s_curve(N, M, st):
target, _ = datasets.make_s_curve(n_samples=M, random_state=st, noise=.1)
target = torch.from_numpy(target)
m = torch.zeros(3)
v = 1/200*torch.eye(3)
torch.manual_seed(st)
normal = torch.distributions.MultivariateNormal(m, v)
prior = normal.sample((N,))
return target, prior
def generate_annulus(N, M, st):
target, _ = datasets.make_circles(n_samples=M, random_state=st)
target = torch.from_numpy(target)
m = torch.zeros(2)
v = 1/200*torch.eye(2)
torch.manual_seed(st)
normal = torch.distributions.MultivariateNormal(m, v)
prior = normal.sample((N,))
return target, prior
def generate_moons(N, M, st):
target, _ = datasets.make_moons(n_samples=M, random_state=st, noise=.1)
target = torch.from_numpy(target)
m = 1/2*torch.tensor([2.0, 1.0])
v = 1/200*torch.eye(2)
torch.manual_seed(st)
normal = torch.distributions.MultivariateNormal(m, v)
prior = normal.sample((N,))
return target, prior