def CA_iteration(z1, z2, prev_theta, max_iter,
fix_mu=False, fix_sigma=False, eps=1e-12):
"""Fit the gaussian model params via coordinate ascent.
"""
init_lhd = calc_gaussian_mix_log_lhd(prev_theta, z1, z2)
prev_lhd = init_lhd
min_vals = [MIN_MU, MIN_SIGMA, MIN_RHO, MIN_MIX_PARAM]
max_vals = [MAX_MU, MAX_SIGMA, MAX_RHO, MAX_MIX_PARAM]
theta = numpy.array(prev_theta).copy()
for i in range(max_iter):
for index, (min_val, max_val) in enumerate(zip(min_vals, max_vals)):
if index == 0 and fix_mu: continue
if index == 1 and fix_sigma: continue
theta, new_lhd = CA_step(z1, z2, theta, index, min_val, max_val)
theta, changed_params = clip_model_params(theta)
assert changed_params == False
if not changed_params:
assert new_lhd + 1e-6 >= prev_lhd
if new_lhd - prev_lhd < eps:
return theta, new_lhd
prev_theta = theta
prev_lhd = new_lhd
return theta, new_lhd
def EM_iteration(z1, z2, prev_theta, max_iter,
fix_mu=False, fix_sigma=False, eps=1e-12):
"""Fit the gaussian model params via EM.
"""
init_lhd = calc_gaussian_mix_log_lhd(prev_theta, z1, z2)
prev_lhd = init_lhd
for i in range(max_iter):
theta = EM_step(z1, z2, prev_theta)
theta, changed_params = clip_model_params(theta)
new_lhd = calc_gaussian_mix_log_lhd(theta, z1, z2)
# if the model is at the boundary, abort
if changed_params:
return theta, new_lhd, True
assert new_lhd + 1e-6 >= prev_lhd
if new_lhd - prev_lhd < eps:
return theta, new_lhd, False
prev_theta = theta
prev_lhd = new_lhd
return theta, new_lhd, False
def grid_search(r1, r2 ):
res = []
best_theta = None
max_log_lhd = -1e100
for mu in numpy.linspace(0.1, 5, num=10):
for sigma in numpy.linspace(0.5, 3, num=10):
for rho in numpy.linspace(0.1, 0.9, num=10):
for pi in numpy.linspace(0.1, 0.9, num=10):
z1 = compute_pseudo_values(r1, mu, sigma, pi)
z2 = compute_pseudo_values(r2, mu, sigma, pi)
log_lhd = calc_gaussian_mix_log_lhd((mu, sigma, rho, pi), z1, z2)
if log_lhd > max_log_lhd:
best_theta = ((mu,mu), (sigma,sigma), rho, pi)
max_log_lhd = log_lhd
return best_theta
def f(alpha):
inner_theta[index] = theta[index] + alpha
return -calc_gaussian_mix_log_lhd(inner_theta, z1, z2)
def log_lhd_loss(r1, r2, theta):
mu, sigma, rho, p = theta
z1 = compute_pseudo_values(r1, mu, sigma, p)
z2 = compute_pseudo_values(r2, mu, sigma, p)
return -calc_gaussian_mix_log_lhd(theta, z1, z2)
