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distributions.py
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distributions.py
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import numpy as np
import torch
from torch.distributions import Normal, MultivariateNormal
import matplotlib.pyplot as plt
from scipy.stats import gaussian_kde
import torch.nn as nn
import torch.distributions as D
torch.manual_seed(926)
class Funnel(object):
"""
Funnel distribution.
“Slice sampling”. R. Neal, Annals of statistics, 705 (2003) https://doi.org/10.1214/aos/1056562461
Args:
dim - dimension
"""
def __init__(self, num_dims=2):
self.num_dims = num_dims
self.normal_first = Normal(0, 1)
@property
def dim(self) -> int:
return self.num_dims
def log_prob(self, x: torch.FloatTensor) -> torch.FloatTensor:
"""
Returns:
log p(x)
"""
normal_last = Normal(torch.zeros(x.shape[:-1], device=x.device), torch.exp(x[..., 0] / 2.))
return normal_last.log_prob(x[..., 1:].permute(-1, *range(x.ndim-1))).sum(0) + self.normal_first.log_prob(x[..., 0])
def likelihood(self, x: torch.FloatTensor) -> torch.FloatTensor:
"""
Returns:
p(x)
"""
return torch.exp(self.log_prob(x))
def plot_2d_countour(self, ax):
"""
Visualizes contour plot of Funnel distribution using log p(x)
"""
x = np.linspace(-15, 15, 100)
y = np.linspace(-10, 10, 100)
X, Y = np.meshgrid(x, y)
inp = torch.from_numpy(np.stack([X, Y], -1))
Z = self.log_prob(inp.reshape(-1, 2)).reshape(inp.shape[:-1])
ax.contour(Y, X, Z.exp(),
levels=3,
alpha=1., colors='midnightblue', linewidths=1)
def visualize_dist(self, ax, s=1000, alpha=1.0, cmap="magma"):
"""
Visualizes Banana distribution using sampled points
"""
# Generate points from distribution
points = self.sample(s)
X = points[:, 0]
Y = points[:, 1]
# Calculate the point density
XY = torch.stack([points[:, 0], points[:, 1]], dim=0).numpy()
Z = gaussian_kde(XY)(XY)
# Sort the points by density, so that the densest points are plotted last
idx = Z.argsort()
X, Y, Z = X[idx], Y[idx], Z[idx]
ax.scatter(X, Y, c=Z, label=Z, alpha=alpha, cmap=cmap)
def sample(self, num_samples: int) -> torch.Tensor:
"""
Sample from the Funnel distribution
"""
all_c = torch.randn((num_samples, self.dim))
all_c[:, 0] = all_c[:, 0] * 1**0.5
all_c[:, 1:] = all_c[:, 1:]*(torch.exp(1*all_c[:, 0]))[:, None]
return all_c
def estimate_dist(self, s=100000):
"""
Estimates mean and standard deviation of the Funnel distribution
by sampling from it
"""
target_samp = self.sample(s)
std = torch.std(target_samp, dim=0).numpy()
m = torch.mean(target_samp, dim=0).numpy()
return [m, std]
class Banana:
def __init__(self, b=0.02, dim=2, sigma=10):
self.b = b
self.dim = dim
self.sigma = sigma
def log_prob(self, x: torch.FloatTensor) -> torch.FloatTensor:
"""
Returns:
log p(x)
"""
even = np.arange(0, x.shape[-1], 2)
odd = np.arange(1, x.shape[-1], 2)
ll = -0.5 * (x[..., odd] - self.b * x[..., even]**2 + (self.sigma**2) * self.b)**2 - ((x[..., even])**2)/(2 * self.sigma**2)
return ll.sum(-1)
def likelihood(self, x: torch.FloatTensor) -> torch.FloatTensor:
"""
Returns:
p(x)
"""
return torch.exp(self.log_prob(x))
def sample(self, s):
"""
Sample from the Banana distribution
"""
torch.manual_seed(926)
even = np.arange(0, self.dim, 2)
odd = np.arange(1, self.dim, 2)
var = torch.ones(self.dim)
var[..., even] = self.sigma**2
base_dist = D.MultivariateNormal(torch.zeros(self.dim), torch.diag(var))
samples = base_dist.sample((s,))
samples[..., odd] += self.b * samples[..., even]**2 - self.b * self.sigma**2
return samples
def plot_2d_countour(self, ax):
"""
Visualizes contour plot of Banana distribution using log p(x)
"""
x = np.linspace(-20, 20, 100)
y = np.linspace(-10, 10, 100)
X, Y = np.meshgrid(x, y)
inp = torch.from_numpy(np.stack([X, Y], -1))
Z = self.log_prob(inp.reshape(-1, 2)).reshape(inp.shape[:-1])
ax.contour(X, Y, Z.exp(),
levels=5,
alpha=1., colors='midnightblue', linewidths=1)
def visualize_dist(self, ax, s=1000, alpha=1.0, cmap="magma"):
"""
Visualizes Banana distribution using sampled points
"""
# Generate points from distribution
points = self.sample(s)
X = points[:, 0]
Y = points[:, 1]
# Calculate the point density
XY = torch.stack([points[:, 0], points[:, 1]], dim=0).numpy()
Z = gaussian_kde(XY)(XY)
# Sort the points by density, so that the densest points are plotted last
idx = Z.argsort()
X, Y, Z = X[idx], Y[idx], Z[idx]
ax.scatter(X, Y, c=Z, label=Z, alpha=alpha, cmap=cmap)
def visualize_dist_nf(self, ax, s=1000, alpha=1.0, nf = None, cmap="magma"):
"""
Visualizes GMM distribution using sampled points and NF
"""
# Generate points from distribution
points = self.sample(s)
if nf:
points = nf(points).detach()
X = points[:, 0]
Y = points[:, 1]
# Calculate the point density
XY = torch.stack([points[:, 0], points[:, 1]], dim=0).numpy()
Z = gaussian_kde(XY)(XY)
# Sort the points by density, so that the densest points are plotted last
idx = Z.argsort()
X, Y, Z = X[idx], Y[idx], Z[idx]
ax.scatter(X, Y, c=Z, label=Z, alpha=alpha, cmap=cmap)
# ax.colorbar()
# ax.show()
# ax.close()
def estimate_dist(self, s=10000000):
"""
Estimates mean and standard deviation of the Banana distribution
by sampling from it
"""
target_samp = self.sample(s)
std = torch.std(target_samp, dim=0).numpy()
m = torch.mean(target_samp, dim=0).numpy()
return [m, std]