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
def SIN_init_VB_MM(data, opts):
K = opts['Number_of_Components']
opts2 = copy.deepcopy(opts)
opts2['maxits'] = 10
#SET PRIORS
#set mixing priors.
mmm = 3
#(the mean of non gauss component)
vvv = 10
#(the variance of the component)\
m0 = np.zeros(K)
tau0 = np.zeros(K)
b0 = np.zeros(K)
c0 = np.zeros(K)
b_0 = np.zeros(K)
c_0 = np.zeros(K)
d_0 = np.zeros(K)
e_0 = np.zeros(K)
Erate = np.zeros(K)
Eshape = np.zeros(K)
loga_0 = np.zeros(K)
Escale = np.zeros(K)
for k in range(K):
if opts['Components_Model'][k] == 'Gamma' or (
opts['Components_Model'][k] == '-Gamma'):
#set GAMMA prior on rates (shape and rate)
Erate[k] = np.true_divide(1, betaGm(mmm, vvv))
d_0[k] = copy.deepcopy(Erate[k])
e_0[k] = 1
Erate[k] = np.true_divide(d_0[k], e_0[k])
#set shapes conditional prior (fancy)
Eshape[k] = alphaGm(mmm, vvv)
dum_v = np.copy(Eshape[k])
#allow variance on shape to be of size of mean shape
dum_p = np.true_divide(1, dum_v)
#from laplace approx b=prec/psi'(map(s))
b_0[k] = np.true_divide(dum_p, sp.polygamma(1, Eshape[k]))
c_0[k] = copy.deepcopy(b_0[k])
loga_0[k] = ((b_0[k] * sp.polygamma(0, Eshape[k])) -
(c_0[k] * np.log(Erate[k])))
if opts['Components_Model'][k] == 'InvGamma' or (
opts['Components_Model'][k] == '-InvGamma'):
#set GAMMA prior on scale (shape d and rate e)
Escale[k] = betaIG(mmm, vvv)
d_0[k] = copy.deepcopy(Escale[k])
#shape
e_0[k] = 1
#rate
Escale[k] = np.true_divide(d_0[k], e_0[k])
#set component 2 and 3 shape conditional prior (fancy)
Eshape[k] = alphaIG(mmm, vvv)
dum_v = np.copy(Eshape[k])
#allow variance on shape to be of size of mean shape
dum_p = np.true_divide(1, dum_v)
b_0[k] = np.true_divide(dum_p, sp.polygamma(1, Eshape[k]))
#from laplace approx b=prec/psi'(map(s))
c_0[k] = copy.deepcopy(b_0[k])
loga_0[k] = (-(b_0[k] * sp.polygamma(0, Eshape[k])) +
(c_0[k] * np.log(Escale[k])))
Prior = {
'lambda_0': 5,
'm_0': 0,
'tau_0': 100,
'c0': 0.001,
'b0': 100,
'd_0': d_0,
'e_0': e_0,
'loga_0': loga_0,
'b_0': b_0,
'c_0': c_0
}
# #SET POSTERIORS initializations using ML mixture models
init_ML = Mix_Mod_MethodOfMoments(data, opts2)
resp = init_ML['Final responsibilities']
lambdap = np.sum(resp, 1)
Escales = np.zeros(K)
for k in range(K):
if opts['Components_Model'][k] == 'Gauss':
m0[k] = init_ML['means'][k]
tau0[k] = np.mean(np.absolute(init_ML['means']))
#hyperparam. on precission
init_prec = np.true_divide(1, init_ML['variances'][k])
init_var_prec = np.var(np.true_divide(1, init_ML['variances']),
ddof=1)
c0[k] = alphaGm(init_prec, init_var_prec)
#shape
b0[k] = betaGm(init_prec, init_var_prec)
#scale
if (opts['Components_Model'][k]
== 'Gamma') or (opts['Components_Model'][k] == '-Gamma'):
##hyperparam. on rates
init_rates = np.true_divide(
1,
betaGm(np.absolute(init_ML['means'][k]),
init_ML['variances'][k])
) # , np.true_divide(1,alb.betaGm(np.absolute(ML_param[4]), ML_param[5])) ] ;
dum_var_r = np.multiply(
0.1, init_rates) #(init_rates)* 0.1;# var(init_rates);
d_0[k] = alphaGm(init_rates, dum_var_r)
#shape
e_0[k] = np.true_divide(1, betaGm(init_rates, dum_var_r))
#rate
Erate[k] = np.true_divide(d_0[k], e_0[k]) # == init_rates
#hyperparam. on shapes
init_shapes = alphaGm(np.absolute(init_ML['means'][k]),
init_ML['variances'][k])
b_0[k] = np.sum(resp[k, :])
c_0[k] = b_0[k]
#loga_0=((b_0* sp.polygamma(0,init_shapes)-(c_0*log(Erates)));
loga_0[k] = np.multiply(b_0[k], sp.polygamma(
0, init_shapes)) - (np.multiply(c_0[k], np.log(Erate[k])))
#MAP_shapes=invpsi((loga_0+ (c_0 .* log(Erates))) ./ b_0) # == init_shapes
if (opts['Components_Model'][k]
== 'InvGamma') or (opts['Components_Model'][k] == '-InvGamma'):
#hyperparam. on scales (inverse gamma) --> scale is r in the text, #r ~ inv gamma distr
init_scales = betaIG(np.absolute(init_ML['means'][k]),
init_ML['variances'][k])
dum_var_sc = np.multiply(0.1, init_scales)
d_0[k] = alphaGm(init_scales, dum_var_sc) #gamma shape
e_0[k] = np.divide(1., betaGm(init_scales,
dum_var_sc)) #gamma rate
Escales[k] = np.divide(d_0[k], e_0[k])
#hyperparam. on shapes
init_shapes = alphaIG(np.absolute(init_ML['means'][k]),
init_ML['variances'][k])
sumgam = np.sum(resp, 1)
b_0[k] = sumgam[k]
c_0[k] = copy.deepcopy(b_0[k])
loga_0[k] = -np.multiply(b_0[k], sp.polygamma(0, init_shapes)) + (
np.multiply(c_0[k], np.log(Escales[k])))
#MAP_shapes=invpsi((-loga_0+ (c_0 .* log(Escales))) ./ b_0) # == init_shapes
shapes = np.zeros(K)
rates = np.zeros(K)
scales = np.zeros(K)
for k in range(K):
if (opts['Components_Model'][k]
== 'Gamma') or (opts['Components_Model'][k] == '-Gamma'):
shapes[k] = alphaGm(np.absolute(init_ML['means'][k]),
init_ML['variances'][k])
rates[k] = np.divide(
1,
betaGm(np.absolute(init_ML['means'][k]),
init_ML['variances'][k]))
if (opts['Components_Model'][k]
== 'InvGamma') or (opts['Components_Model'][k] == '-InvGamma'):
shapes[k] = alphaIG(np.absolute(init_ML['means'][k]),
init_ML['variances'][k])
scales[k] = betaIG(np.absolute(init_ML['means'][k]),
init_ML['variances'][k])
#Save posterior expectations for initialization of VB mixModel
Posterior = {
'gammas': resp,
'pi': init_ML['Mixing Prop.'],
'mus': init_ML['means'],
'tau1s': np.true_divide(1, init_ML['variances']),
'shapes': shapes,
'rates': rates,
'scales': scales,
'lambda': lambdap,
'm_0': m0,
'tau_0': tau0,
'c0': c0,
'b0': b0,
'd_0': d_0,
'e_0': e_0,
'loga_0': loga_0,
'b_0': b_0,
'c_0': c_0
}
return Prior, Posterior
def SIN_init_VB_MM(data, opts):
import scipy.special as sp
import copy
#SIN_init_VB_MM does
# - fit a mixture model using ML (EM + MM algorithms (mmfit.m))
# - initialize VB parameters of mixture model using EM fit as
# initial posteriors
#inputs: -data : vector normalized to mean zero and unit std
# -opts: list with options and values
# -MM = GIM or GGM( default =GIM)
# -MLMMits = max number of iterations allowed to ML algorithm before initialize VB (default =1)
# -MLMMtol = tolerance for convergence of ML algorithm before initialize VB
#ouptput: mix1 is a list containg the initialized priors, and the posterior estimations given the ML initialization
#example:opts=[];opts.append({'MM': 'GIM', 'MLMMits': 1, 'MLMMtol': 10^-5});
#mix=SIN_init_VB_MM(data,opts);
#From matlab...IN PROGRESS
if 'MM' not in opts[0]:
MM = 'GIM'
else:
MM = opts[0]['MM']
if 'MLMMits' not in opts[0]:
MLMMits = 1
else:
MLMMits = opts[0]['MLMMits']
if 'MLMMtol' not in opts[0]:
MLMMtol = 0.00001
else:
MLMMtol = opts[0]['MLMMtol']
#SET PRIORS
#set mixing priors.
prior = []
mmm = 10
#(the mean of component)
vvv = 10
#(the variance of the component)
if MM == 'GGM':
#set GAMMA prior on rates (shape and rate)
Erate = np.true_divide(1, alb.betaGm(mmm, vvv))
d_0 = copy.deepcopy(Erate)
e_0 = 1
Erate = np.true_divide(d_0, e_0)
#set shapes conditional prior (fancy)
Eshape = alb.alphaGm(mmm, vvv)
dum_v = np.copy(Eshape)
#allow variance on shape to be of size of mean shape
dum_p = np.true_divide(1, dum_v)
#from laplace approx b=prec/psi'(map(s))
b_0 = np.true_divide(dum_p, sp.polygamma(1, Eshape))
c_0 = copy.deepcopy(b_0)
loga_0 = ((b_0 * sp.polygamma(0, Eshape)) - (c_0 * log(Erate)))
elif MM == 'GIM':
#set GAMMA prior on scale (shape d and rate e)
Escale = alb.betaIG(mmm, vvv)
d_0 = copy.deepcopy(Escale)
#shape
e_0 = 1
#rate
Escale = np.true_divide(d_0, e_0)
#set component 2 and 3 shape conditional prior (fancy)
Eshape = alb.alphaIG(mmm, vvv)
dum_v = np.copy(Eshape)
#allow variance on shape to be of size of mean shape
dum_p = np.true_divide(1, dum_v)
b_0 = np.true_divide(dum_p, sp.polygamma(1, Eshape))
#from laplace approx b=prec/psi'(map(s))
c_0 = copy.deepcopy(b_0)
loga_0 = (-(b_0 * sp.polygamma(0, Eshape)) + (c_0 * np.log(Escale)))
prior.append({
'lambda_0': 5,
'm_0': 0,
'tau_0': 100,
'c0': 0.001,
'b0': 100,
'd_0': d_0,
'e_0': e_0,
'loga_0': loga_0,
'b_0': b_0,
'c_0': c_0
})
prior = prior[0]
#SET POSTERIORS initializations using ML mixture models
if MM == 'GGM':
mmtype = 2
elif MM == 'GIM':
mmtype = 3
else:
mmtype = 1
#dummy, never used gmm
ML = []
[mu1, v1, mu2, v2, mu3, v3, pipi, lik, numits,
resp] = alb.mmfit3(data, MLMMits, MLMMtol, mmtype)
ML_param = [mu1, v1, mu2, v2, mu3, v3]
ML.append({'init': ML_param, 'pi': pipi, 'LIK': lik})
ML = ML[0]
#mix1.ML
#INIT POSTERIORS BASED IN ML MIX MODEL
post = []
#[dum; b]=max(resp)
q = resp.argmax(1)
gammas = np.copy(resp)
#lambda=sum(resp,2)'
lambdap = resp.sum(0)
#COMPONENT 1: Gaussian component
#hyperparam. on mean
m0 = ML_param[0]
tau0 = np.true_divide(
1,
np.true_divide(ML_param[0] + ML_param[2] + np.absolute(ML_param[4]),
3))
#hyperparam. on precission
init_prec = np.true_divide(1, ML_param[1])
init_var_prec = np.var([
np.true_divide(1, ML_param[1]),
np.true_divide(1, ML_param[3]),
np.true_divide(1, ML_param[5])
],
ddof=1)
c0 = alb.alphaGm(init_prec, init_var_prec)
#shape
b0 = alb.betaGm(init_prec, init_var_prec)
#scale
#COMPONENTS 2 AND 3: gamma or inverse gamma
if MM == 'GGM':
#hyperparam. on rates
init_rates = [
np.true_divide(1, alb.betaGm(np.absolute(ML_param[2]),
ML_param[3])),
np.true_divide(1, alb.betaGm(np.absolute(ML_param[4]),
ML_param[5]))
]
dum_var_r = np.multiply(
0.1, init_rates) #(init_rates)* 0.1;# var(init_rates);
d_0 = alb.alphaGm(init_rates, dum_var_r)
#shape
e_0 = np.true_divide(1, alb.betaGm(init_rates, dum_var_r))
#rate
Erates = np.true_divide(d_0, e_0) # == init_rates
#hyperparam. on shapes
init_shapes = [
alb.alphaGm(np.absolute(ML_param[2]), ML_param[3]),
alb.alphaGm(np.absolute(ML_param[4]), ML_param[5])
]
#b_0=[1 1];c_0=b_0;
#b_0=sum(resp(2:3,:),2)';c_0=b_0;
b_0 = resp.sum(0)[1:3]
c_0 = b_0
#loga_0=((b_0* sp.polygamma(0,init_shapes)-(c_0*log(Erates)));
loga_0 = np.multiply(b_0, sp.polygamma(0, init_shapes)) - (np.multiply(
c_0, np.log(Erates)))
#MAP_shapes=invpsi((loga_0+ (c_0 .* log(Erates))) ./ b_0) # == init_shapes
elif MM == 'GIM':
#hyperparam. on scales (inverse gamma) --> scale is r in the text,
#r ~ inv gamma distr
init_scales = [
alb.betaIG(np.absolute(ML_param[2]), ML_param[3]),
alb.betaIG(np.absolute(ML_param[4]), ML_param[5])
]
dum_var_sc = np.multiply(0.1, init_scales)
#var(init_scales);
d_0 = alb.alphaGm(init_scales, dum_var_sc)
#gamma shape
e_0 = np.divide(1, alb.betaGm(init_scales, dum_var_sc))
#gamma rate
Escales = np.divide(d_0, e_0)
# == init_scales
#hyperparam. on shapes
init_shapes = [
alb.alphaIG(np.absolute(ML_param[2]), ML_param[3]),
alb.alphaIG(np.absolute(ML_param[4]), ML_param[5])
]
#b_0=[1 1];c_0=b_0;
sumgam = resp.sum(0)
b_0 = sumgam[1:3]
c_0 = b_0
loga_0 = -np.multiply(b_0, sp.polygamma(0, init_shapes)) + (
np.multiply(c_0, np.log(Escales)))
#MAP_shapes=invpsi((-loga_0+ (c_0 .* log(Escales))) ./ b_0) # == init_shapes
post.append({
'lambda': lambdap,
'm_0': m0,
'tau_0': tau0,
'c0': c0,
'b0': b0,
'd_0': d_0,
'e_0': e_0,
'loga_0': loga_0,
'b_0': b_0,
'c_0': c_0
})
post = post[0]
#Save posterior expectations for initialization of VB mixModel
mix1 = []
if MM == 'GGM':
shapes = [0, 0]
rates = [0, 0]
#shapes=alphaGm(ML_param[2:3], ML_param(2:3,2))';
#rates= 1./ betaGm(ML_param(2:3,1), ML_param(2:3,2))' ;
shapes[0] = alb.alphaGm(abs(ML_param[2]), ML_param[3])
shapes[1] = alb.alphaGm(abs(ML_param[4]), ML_param[5])
rates[0] = np.divide(1, betaGm(abs(ML_param[2]), ML_param[3]))
rates[1] = np.divide(1, betaGm(abs(ML_param[4]), ML_param[5]))
mix1.append({
'gammas': resp,
'lambda': lambdap,
'pi': pipi,
'mu1': ML_param[0],
'tau1': np.true_divide(1, ML_param[1]),
'shapes': shapes,
'rates': rates,
'q': q,
'prior': prior,
'post': post,
'ML': ML,
'opts': opts
})
elif MM == 'GIM':
shapes = [0, 0]
scales = [0, 0]
shapes[0] = [alphaIG(abs(ML_param[2]), ML_param[3])]
shapes[1] = [alphaIG(abs(ML_param[4]), ML_param[5])]
scales[0] = [betaIG(abs(ML_param[2]), ML_param[3])]
# betaIG(ML_param(3,1), ML_param(3,2)) ];
scales[1] = [betaIG(abs(ML_param[4]), ML_param[5])]
mix1.append({
'gammas': resp,
'lambda': lambdap,
'pi': pipi,
'mu1': ML_param[0],
'tau1': np.true_divide(1, ML_param[1]),
'shapes': shapes,
'scales': scales,
'q': q,
'prior': prior,
'post': post,
'ML': ML,
'opts': opts
})
mix1 = mix1[0]
return mix1
def mmfit2(x, maxiters, tol, MM):
print MM
all_params = [0, 1, 2, 1]
init_mu1 = all_params[0]
init_v1 = all_params[1]
init_mu2 = all_params[2]
init_v2 = all_params[3]
init_PI = np.zeros(2)
init_PI[0] = 0.5
init_PI[1] = 0.5
#First estimation initial parameters for inv gammas: alphas y betas
#if MM==1:
# 1#fix for gmm
#el
if MM == 2:
init_a1 = alb.alphaGm(init_mu2, init_v2)
init_b1 = alb.betaGm(init_mu2, init_v2)
elif MM == 3:
init_a1 = alb.alphaIG(init_mu2, init_v2)
init_b1 = alb.betaIG(init_mu2, init_v2)
#rename parameters for iteration
tmp_mu1 = init_mu1
tmp_v1 = init_v1
tmp_mu2 = init_mu2
tmp_v2 = init_v2
tmp_a1 = init_a1
tmp_b1 = init_b1
tmp_PI = init_PI
#make structures to save the parameters estimates at each iteration
mu1 = np.zeros(maxiters + 2)
v1 = np.zeros(maxiters + 2)
mu2 = np.zeros(maxiters + 2)
v2 = np.zeros(maxiters + 2)
a1 = np.zeros(maxiters + 2)
b1 = np.zeros(maxiters + 2)
tmp_lik = np.zeros(maxiters + 2)
real_lik = np.zeros(maxiters + 2)
PI = np.zeros(2 * (maxiters + 2))
#3 because we fit 2 components
PI = np.reshape(PI, [maxiters + 2, 2])
#save first values of this structures as the initialized values
mu1[0] = tmp_mu1
v1[0] = tmp_v1
mu2[0] = tmp_mu2
v2[0] = tmp_v2
a1[0] = tmp_a1
b1[0] = tmp_b1
PI[0, 0] = tmp_PI[0]
PI[0, 1] = tmp_PI[1]
flag = 0
it = -1
#indexes of samples to assign 0 prob wrt non-gauss components
xneg = find(x < pow(10, -14))
while flag == 0:
it = it + 1
#print it
#for it in range (0,maxiters):
#print 'it1',it
Nobj = sc.stats.norm(tmp_mu1, pow(tmp_v1, (1 / 2)))
pGa = Nobj.pdf(x)
pGa[pGa == 0] = pow(10, -14)
if MM == 1:
1
elif MM == 2:
dum2 = alb.gam(x, tmp_a1, tmp_b1)
elif MM == 3:
dum2 = alb.invgam(x, tmp_a1, tmp_b1)
dum2[xneg] = 0
dum2[np.isnan(dum2)] = 0
dum2[np.isinf(dum2)] = 0
dum2[dum2 == 0] = pow(10, -14)
D1 = np.multiply(np.ones(size(x)) * tmp_PI[0], pGa)
D2 = np.multiply(np.ones(size(x)) * tmp_PI[1], dum2)
D2[xneg] = 0
D = D1 + D2
R1 = np.divide(D1,
np.ones(size(x)) * D)
R2 = np.divide(D2,
np.ones(size(x)) * D)
resp = sc.column_stack([R1, R2])
#tmp_lik[it]=sum( np.multiply(resp[:,0],(log(tmp_PI[0])+log(pGa))) + np.multiply(resp[:,1],(log(tmp_PI[1])+log(dum2))));#bishop
real_lik[it] = sum(
log(np.multiply(tmp_PI[0], pGa) + np.multiply(tmp_PI[1], dum2)))
#N=np.ones(2)
#N[0]=sum(R1)
#N[1]=sum(R2)
#PI[0,0]=N[0]/sum(N)
#PI[0,1]=N[1]/sum(N)
#if it < maxiters-1:
#M step
N = np.ones(2)
N[0] = sum(R1)
N[1] = sum(R2)
tmp_PI[0] = N[0] / sum(N)
tmp_PI[1] = N[1] / sum(N)
#print tmp_PI
#print tmp_lik[it]
#update gaussian mean and variance
tmp_mu1 = []
tmp_mu1 = sum(np.multiply(resp[:, 0], x)) / N[0]
tmp_v1 = []
tmp_v1 = sum(np.multiply(resp[:, 0], pow(x - tmp_mu1, 2))) / N[0]
#if tmp_v <= 0.5:
# tmp_v=0.5
#UPDATE EACH INVERSE GAMMA.
tmp_mu2 = []
tmp_mu2 = sum(np.multiply(resp[:, 1], x)) / N[1]
tmp_v2 = []
tmp_v2 = sum(np.multiply(resp[:, 1], pow(x - tmp_mu2, 2))) / N[1]
if tmp_v2 < 0.2:
tmp_v2 = 0.2
if MM == 2:
tmp_a1 = alb.alphaGm(tmp_mu2, tmp_v2)
tmp_b1 = alb.betaGm(tmp_mu2, tmp_v2)
elif MM == 3:
tmp_a1 = alb.alphaIG(tmp_mu2, tmp_v2)
tmp_b1 = alb.betaIG(tmp_mu2, tmp_v2)
if it > 20:
if abs(real_lik[it] - real_lik[it - 1]) < tol:
flag = 1
print it
if it > (maxiters - 1):
flag = 1
#print it
if flag == 0:
mu1[it + 1] = tmp_mu1
v1[it + 1] = tmp_v1
mu2[it + 1] = tmp_mu2
v2[it + 1] = tmp_v2
a1[it + 1] = alphaIG(tmp_mu2, tmp_v2)
b1[it + 1] = betaIG(tmp_mu2, tmp_v2)
PI[it + 1, :] = tmp_PI
stmu1 = mu1[it]
stv1 = v1[it]
stmu2 = mu2[it]
stv2 = v2[it]
stPI = PI[it, :]
lik = tmp_lik[it]
stPI = PI[it, :]
return stmu1, stv1, stmu2, stv2, stPI, lik, it, resp
def mmfit3(x, maxiters, tol, MM):
import copy
import numpy as np
all_params = [0, 1, 3, 1, -3, 1]
init_mu1 = all_params[0]
init_v1 = all_params[1]
init_mu2 = all_params[2]
init_v2 = all_params[3]
init_mu3 = all_params[4]
init_v3 = all_params[5]
init_PI = np.zeros(3)
init_PI[0] = np.true_divide(1, 3)
init_PI[1] = np.true_divide(1, 3)
init_PI[2] = np.true_divide(1, 3)
#First estimation initial parameters for inv gammas: alphas y betas
#if MM==1:
# 1#fix for gmm
#el
if MM == 2:
init_a1 = alb.alphaGm(init_mu2, init_v2)
init_b1 = alb.betaGm(init_mu2, init_v2)
init_a2 = alb.alphaGm(-1 * init_mu3, init_v3)
init_b2 = alb.betaGm(-1 * init_mu3, init_v3)
elif MM == 3:
init_a1 = alb.alphaIG(init_mu2, init_v2)
init_b1 = alb.betaIG(init_mu2, init_v2)
init_a2 = alb.alphaIG(-1 * init_mu3, init_v3)
init_b2 = alb.betaIG(-1 * init_mu3, init_v3)
#rename parameters for iteration
tmp_mu1 = copy.deepcopy(init_mu1)
tmp_v1 = copy.deepcopy(init_v1)
tmp_mu2 = copy.deepcopy(init_mu2)
tmp_v2 = copy.deepcopy(init_v2)
tmp_mu3 = copy.deepcopy(init_mu3)
tmp_v3 = copy.deepcopy(init_v3)
tmp_a1 = copy.deepcopy(init_a1)
tmp_b1 = copy.deepcopy(init_b1)
tmp_a2 = copy.deepcopy(init_a2)
tmp_b2 = copy.deepcopy(init_b2)
tmp_PI = copy.deepcopy(init_PI)
#make structures to save the parameters estimates at each iteration
mu1 = np.zeros(maxiters + 2)
v1 = np.zeros(maxiters + 2)
mu2 = np.zeros(maxiters + 2)
v2 = np.zeros(maxiters + 2)
mu3 = np.zeros(maxiters + 2)
v3 = np.zeros(maxiters + 2)
a1 = np.zeros(maxiters + 2)
b1 = np.zeros(maxiters + 2)
a2 = np.zeros(maxiters + 2)
b2 = np.zeros(maxiters + 2)
tmp_lik = np.zeros(maxiters + 2)
real_lik = np.zeros(maxiters + 2)
PI = np.zeros(3 * (maxiters + 2))
#3 because we fit 3 components
PI = np.reshape(PI, [maxiters + 2, 3])
#save first values of this structures as the initialized values
mu1[0] = tmp_mu1
v1[0] = tmp_v1
mu2[0] = tmp_mu2
v2[0] = tmp_v2
mu3[0] = tmp_mu2
v3[0] = tmp_v2
a1[0] = tmp_a1
b1[0] = tmp_b1
a2[0] = tmp_a2
b2[0] = tmp_b2
#indexes of samples to assign 0 prob wrt each inv gammas
xneg = find(x < pow(10, -14))
xpos = find(x > -pow(10, -14))
eps = np.finfo(float).eps
#First Expectation step to evaluate initilization it=0
it = 0
Nobj = sc.stats.norm(tmp_mu1, np.power(tmp_v1, 0.5))
pGa = Nobj.pdf(x)
pGa[pGa == 0] = 10**-14
if MM == 1:
1
elif MM == 2:
dum2 = alb.gam(x, tmp_a1, tmp_b1)
dum3 = alb.gam(-1 * x, tmp_a2, tmp_b2)
elif MM == 3:
dum2 = alb.invgam(x, tmp_a1, tmp_b1)
dum3 = alb.invgam(-1 * x, tmp_a2, tmp_b2)
dum2[xneg] = 0
dum3[xpos] = 0
D1 = np.multiply(np.ones(size(x)) * tmp_PI[0], pGa)
D1[np.where(D1 < 10**-14)] = eps
D2 = np.multiply(np.ones(size(x)) * tmp_PI[1], dum2)
D2[np.where(D2 < 10**-14)] = eps
D3 = np.multiply(np.ones(size(x)) * tmp_PI[2], dum3)
D3[np.where(D3 < 10**-14)] = eps
D = D1 + D2 + D3
R1 = np.divide(D1,
np.ones(size(x)) * D)
R2 = np.divide(D2,
np.ones(size(x)) * D)
R3 = np.divide(D3,
np.ones(size(x)) * D)
resp = sc.column_stack([R1, R2, R3])
#M step
N = np.ones(3)
N[0] = sum(R1)
N[1] = sum(R2)
N[2] = sum(R3)
tmp_PI[0] = N[0] / sum(N)
tmp_PI[1] = N[1] / sum(N)
tmp_PI[2] = N[2] / sum(N)
#tmp_lik[it]=sum( np.multiply(resp[:,0],(log(tmp_PI[0])+log(pGa))) + np.multiply(resp[:,1],(log(tmp_PI[1])+log(dum2))) + np.multiply(resp[:,2],(log(tmp_PI[2])+log(dum3))) );#bishop
real_lik[it] = sum(
log(
np.multiply(tmp_PI[0], pGa) + np.multiply(tmp_PI[1], dum2) +
np.multiply(tmp_PI[2], dum3)))
trol = np.zeros([3, x.shape[0]])
trol[0, :] = np.multiply(D1, tmp_PI[0])
trol[1, :] = np.multiply(D2, tmp_PI[1])
trol[2, :] = np.multiply(D3, tmp_PI[2])
real_lik[it] = np.sum(np.log(trol.sum(0)))
#ITERATE
flag = 0
while flag == 0:
it = it + 1
#update gaussian mean and variance
tmp_mu1 = []
tmp_mu1 = sum(np.multiply(resp[:, 0], x)) / N[0]
tmp_v1 = []
tmp_v1 = sum(np.multiply(resp[:, 0], pow(x - tmp_mu1, 2))) / N[0]
#if tmp_v <= 0.5:
# tmp_v=0.5
#UPDATE EACH INVERSE GAMMA.
tmp_mu2 = []
tmp_mu2 = sum(np.multiply(resp[:, 1], x)) / N[1]
tmp_v2 = []
tmp_v2 = sum(np.multiply(resp[:, 1], pow(x - tmp_mu2, 2))) / N[1]
#if tmp_v2< 0.1:#pow(10,-1):
#tmp_v2=0.1
tmp_mu3 = []
tmp_mu3 = sum(np.multiply(resp[:, 2], x)) / N[2]
tmp_v3 = []
tmp_v3 = sum(np.multiply(resp[:, 2], pow(x - tmp_mu3, 2))) / N[2]
#if tmp_v3< 0.1:
#tmp_v3=0.1
if MM == 2:
tmp_a1 = alb.alphaGm(tmp_mu2, tmp_v2)
tmp_b1 = alb.betaGm(tmp_mu2, tmp_v2)
tmp_a2 = alb.alphaGm(-1 * tmp_mu3, tmp_v3)
tmp_b2 = alb.betaGm(-1 * tmp_mu3, tmp_v3)
elif MM == 3:
tmp_a1 = alb.alphaIG(tmp_mu2, tmp_v2)
tmp_b1 = alb.betaIG(tmp_mu2, tmp_v2)
tmp_a2 = alb.alphaIG(-1 * tmp_mu3, tmp_v3)
tmp_b2 = alb.betaIG(-1 * tmp_mu3, tmp_v3)
#print 'it_num',it
Nobj = sc.stats.norm(tmp_mu1, np.power(tmp_v1, 0.5))
pGa = Nobj.pdf(x)
pGa[pGa == 0] = 10**-14
if MM == 1:
1
elif MM == 2:
dum2 = alb.gam(x, tmp_a1, tmp_b1)
dum3 = alb.gam(-1 * x, tmp_a2, tmp_b2)
elif MM == 3:
dum2 = alb.invgam(x, tmp_a1, tmp_b1)
dum3 = alb.invgam(-1 * x, tmp_a2, tmp_b2)
dum2[xneg] = 0
dum3[xpos] = 0
dum2[np.isnan(dum2)] = 0
dum2[np.isinf(dum2)] = 0
dum2[dum2 == 0] = 10**-14
dum3[np.isnan(dum3)] = 0
dum3[np.isinf(dum3)] = 0
dum3[dum3 == 0] = 10**-14
D1 = np.multiply(np.ones(size(x)) * tmp_PI[0], pGa)
D1[np.where(D1 < 10**-14)] = eps
D2 = np.multiply(np.ones(size(x)) * tmp_PI[1], dum2)
D2[np.where(D2 < 10**-14)] = eps
D3 = np.multiply(np.ones(size(x)) * tmp_PI[2], dum3)
D3[np.where(D3 < 10**-14)] = eps
#D3[xpos]=0;
#D2[xneg]=0;
D = D1 + D2 + D3
R1 = np.divide(D1,
np.ones(size(x)) * D)
R2 = np.divide(D2,
np.ones(size(x)) * D)
R3 = np.divide(D3,
np.ones(size(x)) * D)
resp = sc.column_stack([R1, R2, R3])
#M step
N = np.ones(3)
N[0] = sum(R1)
N[1] = sum(R2)
N[2] = sum(R3)
tmp_PI[0] = N[0] / sum(N)
tmp_PI[1] = N[1] / sum(N)
tmp_PI[2] = N[2] / sum(N)
tmp_PI[np.where(tmp_PI < 10**-14)] = eps
#tmp_lik[it]=sum( np.multiply(resp[:,0],(log(tmp_PI[0])+log(pGa))) + np.multiply(resp[:,1],(log(tmp_PI[1])+log(dum2))) + np.multiply(resp[:,2],(log(tmp_PI[2])+log(dum3))) );#bishop
real_lik[it] = sum(
log(
np.multiply(tmp_PI[0], pGa) + np.multiply(tmp_PI[1], dum2) +
np.multiply(tmp_PI[2], dum3)))
trol = np.zeros([3, x.shape[0]])
trol[0, :] = np.multiply(D1, tmp_PI[0])
trol[1, :] = np.multiply(D2, tmp_PI[1])
trol[2, :] = np.multiply(D3, tmp_PI[2])
real_lik[it] = np.sum(np.log(trol.sum(0)))
if (abs((real_lik[it] - real_lik[it - 1]) / real_lik[it - 1]) <
tol) | (it > maxiters):
flag = 1
stmu1 = tmp_mu1
#mu1[it];
stv1 = tmp_v1 #v1[it];
stmu2 = tmp_mu2 #mu2[it];
stv2 = tmp_v2 #v2[it];
stmu3 = tmp_mu3 #mu3[it];
stv3 = tmp_v3 #v3[it];
stPI = tmp_PI #PI[it,:];
lik = real_lik[0:it] #tmp_lik[it];
return stmu1, stv1, stmu2, stv2, stmu3, stv3, stPI, lik, it, resp