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SC-GMM.py
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SC-GMM.py
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import torch
import torch.nn as nn
import torch.nn.functional as F
import numpy as np
import random
import matplotlib
import matplotlib.pyplot as plt
import matplotlib.animation as manimation
from matplotlib.patches import Ellipse
import pickle
import math
import time
from lion_pytorch import Lion
torch.set_default_dtype(torch.float64)
def set_seed(seed):
torch.manual_seed(seed)
torch.cuda.manual_seed_all(seed)
np.random.seed(seed)
random.seed(seed)
torch.backends.cudnn.deterministic = True
class CramerUnit(nn.Module):
def __init__(self):
super().__init__()
# antiderivative of Phi (CDF of N(0,1)) is F.gelu(z) + sqrt(1/(2*pi)) * exp(-z**2/2)
self.unit = lambda z: 2 * F.gelu(z) - z + 0.7978845608028654 * torch.exp(-z**2/2)
def forward(self, m1, s1, m2, s2):
v = torch.sqrt(s1**2 + s2**2 + 1e-20)
return v*self.unit((m1-m2)/v)
# This function is 1-Lipschitz
cramer = CramerUnit()
def calc_loss(pi, mu, sigma, pi2, mu2, sigma2):
# pi, mu, sigma: (batch_size, n)
# pi2, mu2, sigma2: (batch_size, n2)
n=pi.size(-1)
n2=pi2.size(-1)
def r(T, d, N):
return T.unsqueeze(d).repeat(
[1,N,1] if d==-2 else [1,1,N] if d==-1 else None
)
I1 = r(pi, -1,n ) * r(pi, -2,n ) * cramer(r(mu, -1,n ), r(sigma, -1,n ), r(mu, -2,n ), r(sigma, -2,n ))
I2 = r(pi2,-1,n2) * r(pi2,-2,n2) * cramer(r(mu2,-1,n2), r(sigma2,-1,n2), r(mu2,-2,n2), r(sigma2,-2,n2))
I3 = r(pi, -1,n2) * r(pi2,-2,n ) * cramer(r(mu, -1,n2), r(sigma, -1,n2), r(mu2,-2,n ), r(sigma2,-2,n ))
#I4 = r(pi2,-1,n ) * r(pi, -2,n2) * cramer(r(mu2,-1,n ), r(sigma2,-1,n ), r(mu, -2,n2), r(sigma, -2,n2))
# We don't want sigmas to be negative. That has no mathematical meaning.
penalty_item = nn.ReLU()(-10*sigma).sum()
#print(I3.sum(), I4.sum())
loss = (I3.sum() - I1.sum() + I3.sum() - I2.sum() + penalty_item) # / batch_size
return loss
class GaussianMixture(nn.Module):
def __init__(self, n, m, p=None, mu=None, s=None, target=False):
# m: dim
# n: number of gaussians
# p: proportions
# mu: expectation
# s: variance matrix params
super().__init__()
self.n = n
self.m = m
self.p = nn.Parameter(0.05*torch.randn((n,)) if p is None else(
torch.zeros((n,)) if isinstance(p, int) or isinstance(p, float) else torch.DoubleTensor(p)
))
self.mu = nn.Parameter(1*torch.randn((n, m)) if mu is None else(
torch.zeros((n,m)) if isinstance(mu, int) or isinstance(mu, float) else torch.DoubleTensor(mu)
))
self.s = nn.Parameter(0.2*torch.randn((n, m, m))/m if s is None else (
torch.zeros((n, m, m)) if (isinstance(s, int) or isinstance(s, float)) and s==0 else (
torch.eye(m).unsqueeze(0).repeat([n, 1, 1]) if (
isinstance(s, int) or isinstance(s, float)) and s==1
else torch.DoubleTensor(s)
)
))
if target:
for param in self.parameters():
param.requires_grad_(False)
else:
for param in self.parameters():
param.requires_grad_(True)
def forward(self, x: torch.Tensor):
# (batch_size, self.m) -> (batch_size, self.n, self.m, 1)
batch_size = x.shape[0]
x = x.unsqueeze(1).repeat([1, self.n, 1]).unsqueeze(-1)
# pi to (batch_size, self.n)
pis = (nn.Softmax(dim=-1)(self.p)).unsqueeze(0).repeat([batch_size, 1])
# mu_temp to (batch_size, self.n, 1, self.m)
mu_temp = self.mu.unsqueeze(0).repeat([batch_size, 1, 1]).unsqueeze(-2)
# s_temp to (batch_size, self.n, self.m, self.m)
s_temp = self.s.unsqueeze(0).repeat([batch_size, 1, 1, 1])
# mus (batch_size, self.n, 1, 1) -> (batch_size, self.n)
mus = torch.matmul(mu_temp, x).squeeze(-1).squeeze(-1)
s_temp = torch.matmul(s_temp, x)
sigmas = torch.matmul(s_temp.mT, s_temp).squeeze(-1).squeeze(-1)
sigmas = torch.sqrt(sigmas)
return pis, mus, sigmas
def forward2(self, x):
# x is of shape (m,), an m-dim vector
# please implement the (negative) log-likelihood here
# using logsumexp, softmax or other functions
# Compute the log-probabilities of each Gaussian component
log_p = torch.log_softmax(self.p, dim=0) # shape (n,)
log_gauss = torch.empty(self.n) # shape (n,)
for i in range(self.n):
# Compute the Mahalanobis distance between x and mu[i]
d_temp = torch.matmul(x - self.mu[i], self.s_inv[i]) # sigma = s^T s, sigma^-1 = s_inv s_inv^T
nrm = torch.linalg.vector_norm(d_temp) # shape ()
_, absdet = torch.slogdet(self.s_inv[i])
# Compute the log-density of the multivariate normal distribution
log_norm = -0.91893853320467274 * self.m + absdet # shape ()
log_gauss[i] = log_norm - nrm # shape ()
# Compute the log-likelihood using logsumexp
log_likelihood = torch.logsumexp(log_p + log_gauss, dim=0) # shape ()
# Return the negative log-likelihood
return -log_likelihood
def transfer_to_s_inv(self):
# Compute the inverse of each s matrix and detach from the computation graph
s_inv_list = [torch.inverse(s).detach() for s in self.s] # list of tensors of shape (m, m)
# Stack the inverse matrices into a tensor of shape (n, m, m)
s_inv_tensor = torch.stack(s_inv_list, dim=0) # tensor of shape (n, m, m)
# Create a new parameter for s_inv and assign it to self.s_inv
self.s_inv = nn.Parameter(s_inv_tensor) # parameter of shape (n, m, m)
self.s = None
def generate_unit_vectors(batch_size, m):
if m==2:
phi = 2*math.pi/batch_size
u=random.uniform(0,2*math.pi)
s=u+phi*torch.arange(batch_size)
return torch.stack([torch.cos(s), torch.sin(s)], dim=-1)
data=np.loadtxt('./data/ring-line-square.txt',delimiter=' ')
data-=data.mean(axis=0)
print(data.shape)
target_model = GaussianMixture(data.shape[0], data.shape[1], p=0, mu=data, s=0, target=True)
target_model.train(False)
def plot_cov_ellipse(pos,cov, nstd=2, ax=None, c='r'):
def eigsorted(cov):
vals, vecs = np.linalg.eigh(cov)
order = vals.argsort()[::-1]
return vals[order], vecs[:,order]
if ax is None:
ax = plt.gca()
vals, vecs = eigsorted(cov)
theta = np.degrees(np.arctan2(*vecs[:,0][::-1]))
# Width and height are "full" widths, not radius
width, height = 2 * nstd * np.sqrt(vals)
ellip = Ellipse(xy=pos, width=width, height=height, angle=theta, facecolor=c, edgecolor=c, linewidth=2,zorder=25, alpha = 0.2)
ax.add_artist(ellip)
return ellip
n=10
m=2
def experiment(seed, SC2):
set_seed(seed)
model=GaussianMixture(n,m)
plt.figure(figsize=(6,5))
plt.plot(data[:,0],data[:,1],'x',zorder=0)
for k in range(n):
mu = model.mu[k].detach().numpy()
sigma = torch.matmul(model.s[k].mT, model.s[k]).detach().numpy()
plot_cov_ellipse(mu, sigma, nstd=2, ax=None)
plt.scatter(mu[0],mu[1],c='r',marker='.',linewidth=0.7,zorder=5)
plt.savefig(f"init_{seed}.jpg")
FFMpegWriter = manimation.writers['ffmpeg']
metadata = dict(title='SlicedCramerGMM',
comment='Sliced Cramer GMM learning process')
writer = FFMpegWriter(fps=10, metadata=metadata)
if SC2:
opt = Lion([
{'params': model.p, 'lr': 5e-6},
{'params': model.mu, 'lr': 0.02},
{'params': model.s, 'lr': 3e-3},
])
batch_size=7
losses=[]
with writer.saving(plt.figure(figsize=(20.2, 6)), f"SlicedCramerLearning_{seed}.mp4", 100):
for i in range(1200):
if i % 10 == 0: print(i)
opt.zero_grad()
rand_vecs = generate_unit_vectors(batch_size, model.m)
pi, mu, sigma = model.forward(rand_vecs)
pi2, mu2, sigma2 = target_model.forward(rand_vecs)
loss = calc_loss(pi, mu, sigma, pi2, mu2, sigma2)
loss.backward()
losses.append(math.log(float(loss)))
opt.step()
if i%4 == 0:
plt.subplot(1,3,1)
plt.cla()
plt.plot(data[:,0],data[:,1],'x',zorder=0)
for k in range(n):
mu = model.mu[k].detach().numpy()
sigma = torch.matmul(model.s[k].mT, model.s[k]).detach().numpy()
plot_cov_ellipse(mu, sigma)
plt.scatter(mu[0],mu[1], c='r',marker='.',linewidth=0.7,zorder=5)
plt.title('Data & GMM',fontsize=15)
plt.subplot(1,3,2)
plt.cla()
circle = plt.Circle((0, 0), 1.0, color='k',linewidth=0.8, fill=False)
plt.gca().add_artist(circle)
vecs = rand_vecs.detach().numpy()
plt.plot(vecs[:,0],vecs[:,1],'o',markersize=10,linewidth=3,markerfacecolor='None',markeredgecolor='r',markeredgewidth=3)
plt.xlim(-1.2,1.2)
plt.ylim(-1.2,1.2)
plt.title('Random projections',fontsize=15)
plt.subplot(1,3,3)
plt.cla()
plt.plot(np.asarray(losses),c='k',linewidth=1)
plt.title('Log (Sliced Cramer 2-loss)',fontsize=15)
writer.grab_frame()
plt.figure(figsize=(6,5))
plt.plot(data[:,0],data[:,1],'x',zorder=0)
for k in range(n):
mu = model.mu[k].detach().numpy()
sigma = torch.matmul(model.s[k].mT, model.s[k]).detach().numpy()
plot_cov_ellipse(mu, sigma, nstd=2, ax=None)
plt.scatter(mu[0],mu[1],c='r',marker='.',linewidth=0.7,zorder=5)
plt.savefig(f"sc2_{seed}.jpg")
plt.figure(figsize=(6,5))
plt.plot(np.asarray(losses),c='k',linewidth=0.6)
plt.title('Log (Sliced Cramer 2-loss)',fontsize=15)
plt.savefig(f"sc2_{seed}_loss.jpg")
model.transfer_to_s_inv()
opt = Lion([
{'params': model.p, 'lr': 5e-6},
{'params': model.mu, 'lr': 0.02},
{'params': model.s_inv, 'lr': 3e-3},
])
batch_size=256
losses=[]
with writer.saving(plt.figure(figsize=(13.4, 6)), f"LikelihoodLearning_{seed}_{SC2}.mp4", 100):
for i in range(200 if SC2 else 1200):
if i % 10 == 0: print(i)
opt.zero_grad()
idxs = np.random.choice(len(data), batch_size)
loss = torch.empty(1)
for j in idxs:
loss += model.forward2(torch.tensor(data[j]))
loss /= 16
if math.isnan(float(loss)) or loss >= 1000 or loss <= 0:
losses.append(float('nan'))
else:
loss.backward()
losses.append(float(loss))
opt.step()
if i%4 == 0:
plt.subplot(1,2,1)
plt.cla()
plt.plot(data[:,0],data[:,1],'x',zorder=0)
for k in range(n):
mu = model.mu[k].detach().numpy()
sigma = np.linalg.inv(torch.matmul(model.s_inv[k], model.s_inv[k].mT).detach().numpy())
plot_cov_ellipse(mu, sigma)
plt.scatter(mu[0],mu[1], c='r',marker='.',linewidth=0.7,zorder=5)
plt.title('Data & GMM',fontsize=15)
plt.subplot(1,2,2)
plt.cla()
plt.plot(np.asarray(losses),c='k',linewidth=1)
plt.title('-Log(Likelihood)',fontsize=15)
writer.grab_frame()
plt.figure(figsize=(6,5))
plt.plot(data[:,0],data[:,1],'x',zorder=0)
for k in range(n):
mu = model.mu[k].detach().numpy()
sigma = np.linalg.inv(torch.matmul(model.s_inv[k], model.s_inv[k].mT).detach().numpy())
plot_cov_ellipse(mu, sigma)
plt.scatter(mu[0],mu[1], c='r',marker='.',linewidth=0.7,zorder=5)
plt.savefig(f"nll_{seed}_{SC2}.jpg")
plt.figure(figsize=(6,5))
plt.plot(np.asarray(losses),c='k',linewidth=0.6)
plt.title('-Log(Likelihood)',fontsize=15)
plt.savefig(f"nll_{seed}_loss.jpg")
experiment(123, True)