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gradient descent solving mu, sigma for generative gaussian
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# -*- coding: utf-8 -*- | |
""" | |
generative gaussian model, minimizing <-log p>_data wrt. mu, sigma | |
with gradient descent | |
-log p = log sigma + log sqrt(2pi) + (x - mu)^2 / (2 sigma^2) | |
So | |
grad_mu (-log p) = - (x - mu) / sigma^2 | |
grad_sigma (-log p) = 1 / sigma - (x - mu)^2 / sigma^3 | |
""" | |
import numpy as np | |
N = 10000 | |
data = (np.random.randn(N, 1) + 0.9) * 1.5 | |
print(f'empirical mean: {np.mean(data)} empirical std: {np.std(data)}') | |
mu, sigma = 0.1, 0.5 | |
loss = np.mean(np.log(sigma) + np.log(np.sqrt(2*np.pi)) + (data - mu)**2 / (2 * sigma**2)) | |
lr = 1e-4 | |
for i in range(3*10**4): | |
grad_mu = np.mean(- (data - mu) / sigma**2) | |
grad_sigma = np.mean(1. / sigma - (data - mu)**2 / sigma**3) | |
mu -= lr * grad_mu | |
sigma -= lr * grad_sigma | |
if i % 10**3 == 0: | |
print(f'mu: {mu} sigma: {sigma}') |
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