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v2infinitesadness.py
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v2infinitesadness.py
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#!/usr/bin/env python
from __future__ import division
import sys
import numpy as np
import random
import copy
from scipy.special import expit
import matplotlib
matplotlib.use('agg')
import matplotlib.pyplot as plt
from matplotlib.animation import ImageMagickFileWriter
from matplotlib.animation import FuncAnimation
def dirichlet_sample(alpha):
dirichlet_vector = np.random.gamma(alpha,1)
return np.divide(dirichlet_vector/np.sum(dirichlet_vector))
class hiddenModel:
def __init__(self,observations, alpha=1,gamma=1, alpha_a = 4, alpha_b = 2, gamma_a = 3, gamma_b = 6):
self.observations = observations
self.observation_set = set(self.observations)
self.observation_index_list = list(self.observation_set)
self.observation_array = np.asarray(map(lambda x: self.observation_index_list.index(x), observations))
self.state_list = []
self.state_assignments = []
self.state_array = np.zeros(self.observation_array.shape,dtype=int)
self.transition_matrix = np.zeros((0,0))
self.emission_matrix = np.zeros((0,len(self.observation_set)))
self.emission_priors = np.ones(0)
self.alpha0 = alpha
self.alpha0_a = alpha_a
self.alpha0_b = alpha_b
self.beta = None
self.gamma = gamma
self.gamma_a = gamma_a
self.gamma_b = gamma_b
self.hyper_resampling_num = 20
def initialize_test(self):
self.add_state()
self.add_state()
self.add_state()
self.add_state()
self.remove_state(1)
self.state_array = np.asarray([0,1,0,1,0,1])
for state in self.state_array:
self.state_assignments.append(self.state_list[state])
self.count_state_transitions()
self.count_state_emissions()
self.beta = np.ones(len(self.state_list)+1,dtype=float) / np.sum(len(self.state_list)+1)
# print "DEBUG COUNTS"
# print self.transition_matrix
# print self.emission_matrix
# print self.observation_array
def initialize_random(self,states=10):
for i in range(states+1):
self.add_state()
self.remove_state(0)
for i, observation in enumerate(self.observation_array):
self.state_assignments.append(random.choice(self.state_list))
self.state_array[i] = self.state_assignments[i].index
self.count_state_transitions()
self.count_state_emissions()
# print "DEBUG COUNTS"
# print self.transition_matrix
# print self.emission_matrix
# print self.observation_array
# print self.state_array
def add_state(self):
self.state_list.append(hiddenState(len(self.state_list),self))
self.transition_matrix = np.append(self.transition_matrix,np.zeros((1,self.transition_matrix.shape[1])),axis=0)
self.transition_matrix = np.append(self.transition_matrix,np.zeros((self.transition_matrix.shape[0],1)),axis=1)
self.emission_matrix = np.append(self.emission_matrix,np.zeros((1,self.emission_matrix.shape[1])),axis=0)
if self.beta != None:
new_beta = np.random.beta(1, self.gamma)
last_beta = self.beta[-1]
self.beta = np.append(self.beta,np.zeros(1))
self.beta[-2] = new_beta * last_beta
self.beta[-1] = (1.-new_beta) * last_beta
else:
self.beta = np.ones(1,dtype=float)
new_beta = np.random.beta(1, self.gamma)
last_beta = self.beta[-1]
self.beta = np.append(self.beta,np.zeros(1))
self.beta[-2] = new_beta * last_beta
self.beta[-1] = (1.-new_beta) * last_beta
self.emission_priors = np.append(self.emission_priors,np.ones(1))
def remove_state(self,r_state):
# print "REMOVE STATE DEBUG"
# print len(self.state_list)
# print self.transition_matrix.shape
del(self.state_list[r_state])
for i, item in enumerate(self.state_list):
item.index = i
for i, state in enumerate(self.state_assignments):
self.state_array[i] = state.index
self.transition_matrix = np.delete(self.transition_matrix, r_state, axis=0)
self.transition_matrix = np.delete(self.transition_matrix, r_state, axis=1)
print len(self.state_list)
print self.transition_matrix.shape
print self.alpha0
print self.gamma
self.emission_matrix = np.delete(self.emission_matrix, r_state, axis=0)
self.beta = np.delete(self.beta, r_state, axis=0)
self.emission_priors = np.delete(self.emission_priors, r_state, axis=0)
self.count_state_transitions()
self.count_state_emissions()
def count_state_transitions(self):
# print "TRANSITION COUNT DEBUG"
self.transition_matrix = np.zeros(self.transition_matrix.shape)
self.transition_matrix[1,1] = 1
for i in range(1,len(self.state_array)):
self.transition_matrix[self.state_array[i-1],self.state_array[i]] += 1
def count_state_emissions(self):
for state in self.state_list:
for i, observation in enumerate(self.observation_index_list):
# print self.state_array
# print self.observation_array
# print observation
# print i
# print i==observation
state_occurrences = self.state_array == state.index
observation_occurences = self.observation_array == i
state.emission_vector[i] = np.sum(np.logical_and(state_occurrences,observation_occurences))
self.emission_matrix[state.index,i] = state.emission_vector[i]
def sample_hypers(self,ialpha,ibeta,igamma):
k = ibeta.shape[0]-1
quasi_oracle_matrix = np.zeros((k,k))
for i in range(k):
for j in range(k):
if self.transition_matrix[i,j] == 0:
quasi_oracle_matrix[i,j] = 0
else:
for l in range(int(self.transition_matrix[i,j])):
quasi_oracle_matrix[i,j] += (random.random() < ((self.alpha0 * self.beta[j])/(self.alpha0 * self.beta[j] + l)))
# print "DEBUG HYPER SAMPLE"
# print self.beta
# print self.beta.shape
# print self.transition_matrix
# print np.sum(quasi_oracle_matrix, axis=0)
self.beta = np.asarray(map(lambda x: np.random.gamma(max(x,1),1), np.sum(quasi_oracle_matrix, axis=0)))
self.beta = np.append(self.beta, np.random.gamma(self.gamma,1))
# print self.beta
# print self.beta.shape
for i in range(self.hyper_resampling_num):
w = np.random.beta(ialpha + 1, map(lambda x: max(1,x), np.sum(self.transition_matrix, axis=1)))
p = np.asarray(map(lambda x: max(1,x), np.sum(self.transition_matrix, axis=1)))/ialpha
p = np.divide(p,p+1)
s = np.random.binomial(1,p)
self.alpha0 = np.random.gamma(self.alpha0_a + np.sum(np.sum(quasi_oracle_matrix)) - np.sum(s), (1.0/(self.alpha0_b - np.sum(np.log(w)))))
k = len(self.beta)
m = np.sum(np.sum(quasi_oracle_matrix))
for i in range(self.hyper_resampling_num):
mu = np.random.beta(igamma + 1, m)
pi_mu = 1.0 / ((1.0 + (m * (self.gamma_b - np.log(mu)))) / (self.gamma_a + k - 1))
# print "DEBUG GAMMA INFERENCE"
# print 1.0/(self.gamma_b - np.log(mu))
if random.random() < pi_mu:
self.gamma = np.random.gamma(self.gamma_a + k, 1.0/(self.gamma_b - np.log(mu)))
else:
self.gamma = np.random.gamma(self.gamma_a + k - 1, 1.0/(self.gamma_b - np.log(mu)))
def sample(self,t):
# print "DEBUG COUNTS"
# print self.transition_matrix
# print self.emission_matrix
# print self.observation_array
t = t%self.observation_array.shape[0]-1
if t < self.observation_array.shape[0]:
ip1 = self.state_array[t+1]
if t > 0:
im1 = self.state_array[t-1]
et = self.observation_array[t]
self.emission_matrix[self.state_array[t],self.observation_array[t]] -= 1
if t > 0:
self.transition_matrix[self.state_array[t],self.state_array[t+1]] -= 1
if t < self.observation_array.shape[0]:
self.transition_matrix[self.state_array[t-1],self.state_array[t]] -= 1
augmented_probabilities = np.zeros(len(self.state_list)+1)
for _, state in enumerate(self.state_list):
i = state.index
if t > 0:
# print "AUG PROB DEBUG"
# print i
# print _
# print augmented_probabilities[i]
# print self.transition_matrix[0,i]
# print self.beta.shape
# print self.beta[i]
augmented_probabilities[i] = self.transition_matrix[im1,i] + self.alpha0 * self.beta[i]
else:
# print "AUG PROB DEBUG"
# print i
# print _
# print augmented_probabilities[i]
# print self.transition_matrix[0,i]
# print self.beta.shape
# print self.beta[i]
augmented_probabilities[i] = self.transition_matrix[0,i] + self.alpha0 * self.beta[i]
if t < self.observation_array.shape[0]:
if t > 0:
if i != self.state_array[t-1]:
augmented_probabilities[i] = augmented_probabilities[i] * ((self.transition_matrix[i,ip1] + self.alpha0 * self.beta[self.state_array[t+1]])/(np.sum(self.transition_matrix[i,:])+self.alpha0))
elif i == self.state_array[t-1] and i != self.state_array[t+1]:
augmented_probabilities[i] = augmented_probabilities[i] * ((self.transition_matrix[i,ip1] + self.alpha0 * self.beta[self.state_array[t+1]])/(np.sum(self.transition_matrix[i,:])+self.alpha0 + 1))
elif i == self.state_array[t-1] and i == self.state_array[t+1]:
augmented_probabilities[i] = augmented_probabilities[i] * ((self.transition_matrix[i,ip1] + 1 + self.alpha0 * self.beta[self.state_array[t+1]])/(np.sum(self.transition_matrix[i,:])+self.alpha0 + 1))
elif t == 0:
if i != 0:
augmented_probabilities[i] = augmented_probabilities[i] * ((self.transition_matrix[i,ip1] + self.alpha0 * self.beta[self.state_array[t+1]])/(np.sum(self.transition_matrix[i,:])+self.alpha0))
elif i == 0 and i != self.state_array[t+1]:
augmented_probabilities[i] = augmented_probabilities[i] * ((self.transition_matrix[i,ip1] + self.alpha0 * self.beta[self.state_array[t+1]])/(np.sum(self.transition_matrix[i,:]) + 1 + self.alpha0))
elif i == 0 and i == self.state_array[t+1]:
augmented_probabilities[i] = augmented_probabilities[i] * ((self.transition_matrix[i,ip1] + 1 + self.alpha0 * self.beta[self.state_array[t+1]])/(np.sum(self.transition_matrix[i,:]) + 1 + self.alpha0))
augmented_probabilities[i] = augmented_probabilities[i] * ((self.emission_matrix[i,et] + self.emission_priors[et]) / (np.sum(self.emission_matrix[i,:]) + np.sum(self.emission_priors)))
augmented_probabilities[-1] = ((self.emission_priors[et]/np.sum(self.emission_priors)) * self.alpha0 * self.beta[-1])
if t < self.observation_array.shape[0]:
augmented_probabilities[-1] = augmented_probabilities[-1] * self.beta[ip1]
norm_probabilities = augmented_probabilities / np.sum(augmented_probabilities)
new_state = 0
nw_st_tmp = random.random()*float(np.sum(augmented_probabilities))
for i, tmp in enumerate(augmented_probabilities):
if np.sum(augmented_probabilities[:i+1]) > nw_st_tmp:
new_state = i
break
if new_state == len(self.state_list):
self.add_state()
self.state_array[t] = new_state
self.state_assignments[t] = self.state_list[new_state]
self.count_state_emissions()
self.count_state_transitions()
i = 0
while i < len(self.state_list):
# print "EMPTY STATE MONITOR DEBUG"
# print len(self.state_list)
# print self.transition_matrix.shape
# print i
if (np.sum(self.transition_matrix[i,:]) + np.sum(self.transition_matrix[:,i])) < 1:
# print "REMOVED STATE\n\n\n"
self.remove_state(i)
i = 0
i += 1
self.sample_hypers(self.alpha0,self.beta, self.gamma)
# print "DEBUG SAMPLE"
# print "transition matrix"
# print self.transition_matrix
# print "emission matrix"
# print self.emission_matrix
# print "observation array"
# print self.observation_array
# print "state array"
# print self.state_array
#
# print "============================================================="
#
# print "aug prob, betas, new state"
# print augmented_probabilities
# print self.beta
# print new_state
class hiddenState:
def __init__(self, index, parent_model):
self.index = index
self.model = parent_model
self.emission_vector = np.zeros(len(self.model.observation_set))
log = []
input_seq = sys.argv[1]
output_tag = sys.argv[2]
model = hiddenModel(list(input_seq),alpha_a=4.0 ,alpha_b = 2.0, gamma_a = 3, gamma_b = 6)
animation_history_trans = []
animation_history_em = []
model.initialize_random(states=20)
for large in range(100000):
model.sample(large)
log.append(len(model.state_list))
if large%100 == 0:
animation_history_trans.append(model.transition_matrix)
animation_history_em.append(model.emission_matrix)
transition_output = open(output_tag + "transitions.txt",mode='w')
emission_output = open(output_tag + "emissions.txt", mode='w')
transition_output.write(str(model.transition_matrix))
emission_output.write(str(model.emission_matrix))
# fig = plt.figure()
# ax = plt.axes()
# im = ax.imshow([])
# def plot_movie(frame):
# im.set_data(transition_output[frame])
# return im
#
# anim = FuncAnimation(fig,plot_movie,frames=10000)
# writer = ImageMagickFileWriter()
# anim.save("heatmap_animation.gif", writer=writer fps=100)
plt.figure()
plt.plot(range(100000),log)
plt.savefig(output_tag + "number_of_states.png")
plt.figure()
plt.imshow(self.transition_matrix)
plt.savefig("transition_matrix.png")
plt.figure()
plt.imshow(self.emission_matrix)
plt.savefig("emission_matrix.png")