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November 21, 2020 00:04
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Attempted direct gradient descent on 2-state gaussian mixture model
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# gmm_gd.py | |
""" | |
Direct gradient descent on 2-state gaussian mixture model. | |
Not the best way to do this, typically use the EM algorithm instead. | |
Training is highly unstable. | |
model: | |
p(x) = pi * phi_1 + (1-pi) * phi_2 | |
phi_1, phi_2 ~ normal | |
pi = p(z = 0) | |
1 - pi = p(z = 1) | |
So -grad_theta log p = - grad_theta log(pi * phi_1 + (1-pi) * phi_2) | |
""" | |
import torch | |
pi_value = 3.14159265 | |
dtype = torch.float | |
device = torch.device('cpu') | |
N = 1000 | |
x1 = (torch.randn(N, device=device, dtype=dtype) * 2.) + 3. | |
x2 = (torch.randn(N, device=device, dtype=dtype) * 2.5) - 6. | |
x = torch.cat([x1, x2], dim=0) | |
# need sufficiently large sigma1, sigma2 values at initialization for numeric stability in loss function | |
mu1 = torch.randn(1, device=device, dtype=dtype, requires_grad=True) | |
sigma1 = torch.randn(1, device=device, dtype=dtype).clamp_min(1.5).requires_grad_() | |
mu2 = torch.randn(1, device=device, dtype=dtype, requires_grad=True) | |
sigma2 = torch.randn(1, device=device, dtype=dtype).clamp_min(1.5).requires_grad_() | |
pi = (torch.rand(1, device=device, dtype=dtype,) + 0.1).clamp_max(0.9).clamp_min(0.1).requires_grad_() | |
learning_rate = 1e-4 | |
for i in range(10**5): | |
loss = - torch.mean(torch.log(pi * 1./(sigma1 * (2*pi_value)**0.5)*torch.exp(-(x - mu1)**2/(2*sigma1**2)) + (1 - pi) | |
* 1./(sigma2 * (2*pi_value)**0.5) * torch.exp(-(x - mu2)**2/(2*sigma2**2)))) | |
if i % 10**3 == 0: | |
print(f'(i={i}) loss: {loss.item()} mu1: {mu1.item()}, mu2: {mu2.item()}, sigma1: {sigma1.item()}, sigma2: {sigma2.item()}, pi: {pi.item()}') | |
loss.backward() | |
with torch.no_grad(): | |
mu1 -= learning_rate * mu1.grad | |
sigma1 -= learning_rate * sigma1.grad | |
mu2 -= learning_rate * mu2.grad | |
sigma2 -= learning_rate * sigma2.grad | |
pi -= learning_rate * pi.grad | |
mu1.grad.zero_() | |
sigma1.grad.zero_() | |
mu2.grad.zero_() | |
sigma2.grad.zero_() | |
pi.grad.zero_() | |
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