/
gaussian_hmm.py
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gaussian_hmm.py
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# A few issues in this code could be initialization prior, pi, is not used in alpha step
# P(X) does not seems correct
# the scaling factors for alpha and beta need to be re-written
# np.set_printoptions(threshold=np.inf)
import numpy as np
import pandas as pd
from pandas import Series,DataFrame
from scipy.stats import norm
X = np.random.normal(10, 1, 120)
Y = np.random.normal(0, 1, 120)
Z = np.random.normal(3,2,50)
X = np.concatenate(( X, Y, X, Z))
#The parameters only for Gaussian
A=np.random.rand(3, 3); A = A/A.sum(axis=1)[:, np.newaxis]
phi = [[0, 1.2],[5, 2], [1, 2]]
class gaussian_hmm:
A = []
X = []
k_states = []
N = []
phi = []
alpha = []
beta = []
alpha_prime = []
beta_prime = []
scaling_c = []
z_X = []
likelihood = []
eata = []
def __init__(self, A, X, phi):
self.A = A
self.X = X
self.k_states = A.shape[0]
self.N = X.shape[0]
self.phi = phi
self.alpha = np.zeros((self.N, self.k_states))
self.beta = np.zeros((self.N, self.k_states))
self.beta[self.N-1,]=1
self.alpha_prime = self.alpha
self.beta_prime = self.beta
self.scaling_c = np.zeros(X.shape[0])
def get_emission( self, n, state):
X = self.X
phi = self.phi
prior = norm.pdf(X[n],phi[state][0], phi[state][1])
return(prior)
def get_alpha_N_1(self, n, state):
alpha = self.alpha
A = self.A
sum = 0
for i in np.arange(self.k_states):
sum = sum + alpha[n-1][state]*A[i][state]
return(sum)
def get_alpha_prime_N_1(self, n, state):
alpha_prime = self.alpha_prime
A = self.A
sum = 0
for i in np.arange(self.k_states):
sum = sum + alpha_prime[n-1][state]*A[i][state]
return(sum)
def alpha_recursion(self):
X = self.X
N = self.N
alpha = self.alpha
k_states = self.k_states
for state in np.arange(k_states):
alpha[0][state] = self.get_emission(0,state) #requires changing once we know pi
for i in np.arange(1,N):
alpha[i][state] = self.get_emission(i, state) * self.get_alpha_N_1(i,state)
self.alpha = alpha
def beta_recursion(self):
beta = self.beta
X = self.X
N = self.N
A = self.A
k_states = self.k_states
for state in np.arange(k_states):
counter = np.arange(0,N-1)
counter = counter[::-1]
for n in counter:
beta[n][state] = sum(beta[n+1][state]*self.get_emission(n+1, state)*A[state][:])
self.beta[n][state] = beta[n][state]
def beta_prime_recursion(self):
beta_prime = self.beta_prime
X = self.X
N = self.N
A = self.A
k_states = self.k_states
cn = self.scaling_c
counter = np.arange(0, N - 1)
counter = counter[::-1]
for n in counter:
for state in np.arange(k_states):
beta_prime[n][state] = sum(beta_prime[n+1][state]*self.get_emission(n+1, state)*A[state][:]) +2e-20
self.beta_prime[n][:] = beta_prime[n][:]/sum(beta_prime[n][:])
def alpha_prime_recursion(self):
X = self.X
N = self.N
alpha_prime = self.alpha_prime
k_states = self.k_states
cn = self.scaling_c
alpha_prime[0][:] = 1 #change once pi is introduced
cn[0] = 1
for i in np.arange(1,N):
for state in np.arange(k_states):
alpha_prime[i][state] = 2e-20 + self.get_emission(i, state) * self.get_alpha_prime_N_1(i,state)
try:
cn[i] = sum(alpha_prime[i][:])
alpha_prime[i][:] = alpha_prime[i][:]/cn[i]
except:
print(i)
self.alpha_prime = alpha_prime
self.scaling_c = cn
def expectation_step(self):
self.alpha_recursion()
self.beta_recursion()
k_states = self.k_states
N = self.N
X = self.X
beta = self.beta
alpha = self.alpha
likelihood = (alpha*beta).sum(axis = 1) # This may be an error
z_X = (alpha*beta)/likelihood[:, np.newaxis]
self.z_X = np.asarray(z_X)
self.likelihood = likelihood
eata = ['']
for n in np.arange(1,N):
M = np.zeros((k_states, k_states))
for stateN_1 in np.arange(k_states):
for stateN in np.arange(k_states):
M[stateN_1][stateN]=alpha[n-1][stateN_1]*norm.pdf(X[n],phi[stateN][0], phi[stateN][1])*A[stateN_1][stateN]*beta[n][stateN]
M = M/ M.sum(axis=1)[:, np.newaxis]
eata.append(M)
eata.pop(0)
self.eata = eata
def expectation_prime_step(self):
self.alpha_prime_recursion()
self.beta_prime_recursion()
k_states = self.k_states
N = self.N
X = self.X
beta = self.beta_prime
alpha = self.alpha_prime
likelihood = (alpha * beta).sum(axis=1) # This may be an error
z_X = (alpha * beta) / likelihood[:, np.newaxis]
self.z_X = np.asarray(z_X)
self.likelihood = likelihood
eata = ['']
for n in np.arange(1, N):
M = np.zeros((k_states, k_states))
for stateN_1 in np.arange(k_states):
for stateN in np.arange(k_states):
M[stateN_1][stateN] = 2e-20 + alpha[n - 1][stateN_1] * self.get_emission(n,stateN) * \
A[stateN_1][stateN] * beta[n][stateN]
M = M / M.sum(axis=1)[:, np.newaxis]
eata.append(M)
eata.pop(0)
self.eata = eata
def recalculate_A(self):
eata = self.eata
k_states = self.k_states
l = len(eata)
A = np.zeros((k_states,k_states))
for i in np.arange(l):
A = A+eata[i]
A = A / A.sum(axis=1)[:, np.newaxis]
self.A = A
def get_emission_parameters(self):
X = self.X
N = self.N
z_X = self.z_X
K = self.k_states
phi = self.phi
#X = X.reshape(N,1)
for k in np.arange(K):
phi[k][0] = sum(z_X[:, k] * X) / sum(z_X[:, k])
phi[k][1] = sum((X - phi[k][0])*(X-phi[k][0])*z_X[:,k])/sum(z_X[:,k])
self.phi = phi
def maximization_step(self):
self.recalculate_A()
self.get_emission_parameters()
def fit(self):
for i in np.arange(15):
self.expectation_prime_step()
self.maximization_step()
######Testing scrip here
model = gaussian_hmm(A, X, phi)
model.fit()
#model.alpha_prime_recursion()
#model.beta_prime_recursion()
#model.alpha_recursion()
#model.beta_recursion()
#model.expectation_prime_step()
#model.maximization_step()
#model.expectation_prime_step()
#model.maximization_step()
#print(model.A)
np.set_printoptions(threshold=np.inf)
#print(model.z_X)
print(model.phi)
#z_X = model.z_X
#k = 0