def MM_E_step(x, K, opts, tmp_mu, tmp_v, tmp_PI, xpos, xneg):
#PS=np.zeros([K,size(x)])
#D=np.zeros([K,size(x)]) # storages probability of samples wrt distributions
PS = np.zeros([K, x.shape[0]])
D = np.zeros([K, x.shape[0]
]) # storages probability of samples wrt distributions
tmp_a = np.zeros(
K) #it will remain zero for non-gamma or inv gamma distributions
tmp_b = np.zeros(
K) #it will remain zero for non-gamma or inv gamma distributions
for k in range(K):
if opts['Components_Model'][k] == 'Gauss':
Nobj = scipy.stats.norm(tmp_mu[k], np.power(tmp_v[k], 0.5))
PS[k, :] = Nobj.pdf(x)
elif opts['Components_Model'][k] == 'Gamma':
tmp_a[k] = alb.alphaGm(tmp_mu[k], tmp_v[k])
tmp_b[k] = alb.betaGm(tmp_mu[k], tmp_v[k])
PS[k, :] = alb.gam_self(x, tmp_a[k], tmp_b[k])
PS[k, xneg] = 0
elif opts['Components_Model'][k] == '-Gamma':
tmp_a[k] = alb.alphaGm(-1 * tmp_mu[k], tmp_v[k])
tmp_b[k] = alb.betaGm(-1 * tmp_mu[k], tmp_v[k])
PS[k, :] = alb.gam_self(-1 * x, tmp_a[k], tmp_b[k])
PS[k, xpos] = 0
elif opts['Components_Model'][k] == 'InvGamma':
tmp_a[k] = alb.alphaIG(tmp_mu[k], tmp_v[k])
tmp_b[k] = alb.betaIG(tmp_mu[k], tmp_v[k])
PS[k, :] = alb.invgam(x, tmp_a[k], tmp_b[k])
PS[k, xneg] = 0
elif opts['Components_Model'][k] == '-InvGamma':
tmp_a[k] = alb.alphaIG(-1 * tmp_mu[k], tmp_v[k])
tmp_b[k] = alb.betaIG(-1 * tmp_mu[k], tmp_v[k])
PS[k, :] = alb.invgam(-1 * x, tmp_a[k], tmp_b[k])
PS[k, xpos] = 0
elif opts['Components_Model'][k] == 'Beta':
tmp_a[k] = alb.a_beta_distr(tmp_mu[k], tmp_v[k])
tmp_b[k] = alb.b_beta_distr(tmp_mu[k], tmp_v[k])
PS[k, :] = scipy.stats.beta.pdf(x, tmp_a[k], tmp_b[k])
PS[np.isnan(PS)] = 0
PS[np.isinf(PS)] = 0
D = np.multiply(PS, np.matrix(tmp_PI).T)
resp = np.divide(D, np.matrix(np.sum(D, 0)))
N = np.sum(resp, 1)
tmp_PI = np.divide(N, np.sum(resp)).T
if 0:
dum = np.add(np.log(PS), np.log(tmp_PI).T)
dum[np.isinf(dum)] = 0
dum[np.isinf(dum)] = 0
Exp_lik = np.sum(np.multiply(resp, dum))
else:
dum = np.multiply(tmp_PI.T, PS) #add(np.log(PS),np.log(tmp_PI).T)
dum[np.isinf(dum)] = 1
dum[np.isinf(dum)] = 1
dum[dum == 0] = 1
Exp_lik = np.sum(np.log(dum))
return PS, resp, tmp_PI, N, Exp_lik
def init_ML(x, opts):
tol = opts['tol']
maxiters = opts['maxits']
K = opts['Number_of_Components']
#Exp_lik=np.zeros(maxiters+1)
opts_MM = copy.deepcopy(opts)
#opts_MM['maxits']=np.int(1)
Model = alb.Mix_Mod_MethodOfMoments(x, opts_MM)
Exp_lik = Model['Likelihood']
tmp_mu = Model['mu1']
tmp_v = Model['variances']
tmp_PI = Model['Mixing Prop.']
param1 = np.zeros(K)
param2 = np.zeros(K)
for k in range(K):
if opts['Components_Model'][k] == 'Gauss':
param1[k] = tmp_mu[k]
param2[k] = tmp_v[k]
elif opts['Components_Model'][k] == 'Gamma':
param1[k] = alb.alphaGm(tmp_mu[k], tmp_v[k])
param2[k] = np.divide(1., alb.betaGm(tmp_mu[k], tmp_v[k]))
elif opts['Components_Model'][k] == '-Gamma':
param1[k] = alb.alphaGm(-1 * tmp_mu[k], tmp_v[k])
param2[k] = np.divide(1., alb.betaGm(-1 * tmp_mu[k], tmp_v[k]))
elif opts['Components_Model'][k] == 'InvGamma':
param1[k] = alb.alphaIG(tmp_mu[k], tmp_v[k])
param2[k] = alb.betaIG(tmp_mu[k], tmp_v[k])
elif opts['Components_Model'][k] == '-InvGamma':
param1[k] = alb.alphaIG(-1 * tmp_mu[k], tmp_v[k])
param2[k] = alb.betaIG(-1 * tmp_mu[k], tmp_v[k])
elif opts['Components_Model'][k] == 'Beta':
param1[k] = alb.a_beta_distr(tmp_mu[k], tmp_v[k])
param2[k] = alb.b_beta_distr(tmp_mu[k], tmp_v[k])
return param1, param2, maxiters, tol, K, tmp_PI, Exp_lik
def Mix_Mod_MethodOfMoments(
x,
opts={
'Number_of_Components': 3,
'Components_Model': ['Gauss', 'Gamma', '-Gamma'],
'init_params': [0, 1, 3, 1, -3, 1],
'maxits': np.int(100),
'tol': 0.00001,
'init_pi': np.true_divide(np.ones(3), 3)
}):
tmp_mu, tmp_v, maxiters, tol, K, tmp_PI, Exp_lik = init_MM(x, opts)
#indexes of samples to assign 0 prob wrt each positive definite distr.
#xneg=find(x<pow(10,-14))
#xpos=find(x>-pow(10,-14))
xneg = np.argwhere(x < pow(10, -14))[:, 0]
xpos = np.argwhere(x > -pow(10, -14))[:, 0]
#ITERATE
flag = 0
it = 0
while flag == 0:
# E-step
PS, resp, tmp_PI, N, Exp_lik[it] = MM_E_step(x, K, opts, tmp_mu, tmp_v,
tmp_PI, xpos, xneg)
#M-step
tmp_mu, tm_v = MM_M_step(x, K, tmp_mu, tmp_v, resp, N)
#convergence criterium
if it > 0:
if (abs((Exp_lik[it] - Exp_lik[it - 1]) / Exp_lik[it - 1]) <
tol) | (it > maxiters - 1):
flag = 1
#print(it)
it = it + 1
#gather output
tmp_a = np.zeros(
K) #it will remain zero for non-gamma or inv gamma distributions
tmp_b = np.zeros(
K) #it will remain zero for non-gamma or inv gamma distributions
tmp_c = np.zeros(K)
for k in range(K):
if opts['Components_Model'][k] == 'Gamma':
tmp_a[k] = alb.alphaGm(tmp_mu[k], tmp_v[k])
tmp_b[k] = alb.betaGm(tmp_mu[k], tmp_v[k])
elif opts['Components_Model'][k] == '-Gamma':
tmp_a[k] = alb.alphaGm(-1 * tmp_mu[k], tmp_v[k])
tmp_b[k] = alb.betaGm(-1 * tmp_mu[k], tmp_v[k])
elif opts['Components_Model'][k] == 'InvGamma':
tmp_a[k] = alb.alphaIG(tmp_mu[k], tmp_v[k])
tmp_c[k] = alb.betaIG(tmp_mu[k], tmp_v[k])
elif opts['Components_Model'][k] == '-InvGamma':
tmp_a[k] = alb.alphaIG(-1 * tmp_mu[k], tmp_v[k])
tmp_c[k] = alb.betaIG(-1 * tmp_mu[k], tmp_v[k])
elif opts['Components_Model'][k] == 'Beta':
tmp_a[k] = alb.a_beta_distr(tmp_mu[k], tmp_v[k])
tmp_c[k] = alb.b_beta_distr(tmp_mu[k], tmp_v[k])
output_dict = {
'means': tmp_mu,
'mu1': tmp_mu,
'variances': tmp_v,
'taus1': np.divide(1, tmp_v),
'Mixing Prop.': np.asarray(tmp_PI)[0],
'Likelihood': Exp_lik[0:it],
'its': it,
'Final responsibilities': resp,
'opts': opts,
'shapes': tmp_a,
'scales': tmp_c,
'rates': np.divide(1., tmp_b)
}
return output_dict