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hardEM_sage.bak.py
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hardEM_sage.bak.py
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import networkx as nx
from datetime import datetime
from sage import *
from sage.numerical.mip import MixedIntegerLinearProgram
import sage.numerical.backends.glpk_backend as backend
from sage.numerical.backends.generic_backend import get_solver
from numpy import log, pi
from random import randint
import multiprocessing as mp
from multiprocessing import Pool
import random
import os
EPS = 0.001
EM_RESTARTS = 8
EM_ITERATION_LIMIT = 5
LP_TIME_LIMIT = 60
LP_ITERATION_LIMIT = 5 * (10 ** 3)
log_2pi = log(2 * pi)
def slog(msg):
print('%s\t%s: %s' % (os.getpid(), datetime.now().strftime('%I:%M:%S %p'), msg))
class hard_EM:
def __init__(self, author_graph, TAU=0.5001, nparts=5, init_partition=None):
self.parts = range(nparts)
self.TAU = TAU
self.author_graph = nx.convert_node_labels_to_integers(author_graph, discard_old_labels=False)
self._lp_init = False
# init hidden vars
if init_partition:
self.partition = init_partition
else:
self._rand_init_partition()
self.m_step()
def _rand_init_partition(self):
slog('Random partitioning with seed: %s' % os.getpid())
random.seed(os.getpid())
self.partition = {}
nparts = len(self.parts)
for a in self.author_graph:
self.partition[a] = randint(0, nparts - 1)
def _init_LP(self):
if self._lp_init:
return
slog('Init LP')
self.lp = MixedIntegerLinearProgram(solver='GLPK', maximization=False)
#self.lp.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only) # LP relaxation
self.lp.solver_parameter("iteration_limit", LP_ITERATION_LIMIT)
# self.lp.solver_parameter("timelimit", LP_TIME_LIMIT)
# add constraints once here
# constraints
self.alpha = self.lp.new_variable(dim=2)
beta2 = self.lp.new_variable(dim=2)
beta3 = self.lp.new_variable(dim=3)
# alphas are indicator vars
for a in self.author_graph:
self.lp.add_constraint(sum(self.alpha[a][p] for p in self.parts) == 1)
# beta2 is the sum of beta3s
slog('Init LP - pair constraints')
for a, b in self.author_graph.edges():
if self.author_graph[a][b]['denom'] <= 2:
continue
self.lp.add_constraint(0.5 * sum(beta3[a][b][p] for p in self.parts) - beta2[a][b], min=0, max=0)
for p in self.parts:
self.lp.add_constraint(self.alpha[a][p] - self.alpha[b][p] - beta3[a][b][p], max=0)
self.lp.add_constraint(self.alpha[b][p] - self.alpha[a][p] - beta3[a][b][p], max=0)
# store indiv potential linear function as a dict to improve performance
self.objF_indiv_dict = {}
self.alpha_dict = {}
for a in self.author_graph:
self.alpha_dict[a] = {}
for p in self.parts:
var_id = self.alpha_dict[a][p] = self.alpha[a][p].dict().keys()[0]
self.objF_indiv_dict[var_id] = 0 # init variables coeffs to zero
# pairwise potentials
slog('Obj func - pair potentials')
objF_pair_dict = {}
s = log(1 - self.TAU) - log(self.TAU)
for a, b in self.author_graph.edges():
if self.author_graph[a][b]['denom'] <= 2:
continue
var_id = beta2[a][b].dict().keys()[0]
objF_pair_dict[var_id] = -self.author_graph[a][b]['weight'] * s
self.objF_pair = self.lp(objF_pair_dict)
self._lp_init = True
slog('Init LP Done')
def log_phi(self, a, p):
author = self.author_graph.node[a]
th = self.theta[p]
res = th['logPr']
if author['hlpful_fav_unfav']:
res += th['logPrH']
else:
res += th['log1-PrH']
if author['isRealName']:
res += th['logPrR']
else:
res += th['log1-PrR']
res += -((author['revLen'] - th['muL']) ** 2) / (2 * th['sigma2L'] + EPS) - (log_2pi + log(th['sigma2L'])) / 2.0
return res
def log_likelihood(self):
ll = sum(self.log_phi(a, self.partition[a]) for a in self.author_graph.nodes())
log_TAU, log_1_TAU = log(self.TAU), log(1 - self.TAU)
for a, b in self.author_graph.edges():
if self.partition[a] == self.partition[b]:
ll += log_TAU * self.author_graph[a][b]['weight']
else:
ll += log_1_TAU * self.author_graph[a][b]['weight']
return ll
def e_step(self):
slog('E-Step')
if not self._lp_init:
self._init_LP()
slog('Obj func - indiv potentials')
# individual potentials
for a in self.author_graph:
for p in self.parts:
self.objF_indiv_dict[self.alpha_dict[a][p]] = -self.log_phi(a, p)
objF_indiv = self.lp(self.objF_indiv_dict)
self.lp.set_objective(self.lp.sum([objF_indiv, self.objF_pair]))
# solve the LP
slog('Solving the LP')
self.lp.solve(log=3)
slog('Solving the LP Done')
# hard partitions for nodes (authors)
self.partition = {}
for a in self.author_graph:
membship = self.lp.get_values(self.alpha[a])
self.partition[a] = max(membship, key=membship.get)
slog('E-Step Done')
def m_step(self):
slog('M-Step')
stat = {p: [0.0] * len(self.parts) for p in ['freq', 'hlpful', 'realNm', 'muL', 'M2']}
for a in self.author_graph:
p = self.partition[a]
author = self.author_graph.node[a]
stat['freq'][p] += 1
if author['hlpful_fav_unfav']: stat['hlpful'][p] += 1
if author['isRealName']: stat['realNm'][p] += 1
delta = author['revLen'] - stat['muL'][p]
stat['muL'][p] += delta / stat['freq'][p]
stat['M2'][p] += delta * (author['revLen'] - stat['muL'][p])
self.theta = [{p: 0.0 for p in ['logPr', 'logPrH', 'log1-PrH', 'logPrR', 'log1-PrR', 'sigma2L', 'muL']}
for p in self.parts]
sum_freq = sum(stat['freq'][p] for p in self.parts)
for p in self.parts:
self.theta[p]['logPr'] = log(stat['freq'][p] / (sum_freq + EPS) + EPS)
self.theta[p]['logPrH'] = log(stat['hlpful'][p] / (stat['freq'][p] + EPS) + EPS)
self.theta[p]['log1-PrH'] = log(1 - stat['hlpful'][p] / (stat['freq'][p] + EPS) + EPS)
self.theta[p]['logPrR'] = log(stat['realNm'][p] / (stat['freq'][p] + EPS) + EPS)
self.theta[p]['log1-PrR'] = log(1 - stat['realNm'][p] / (stat['freq'][p] + EPS) + EPS)
self.theta[p]['muL'] = stat['muL'][p]
self.theta[p]['sigma2L'] = stat['M2'][p] / (stat['freq'][p] - 1 + EPS) + EPS
slog('M-Step Done')
def iterate(self, MAX_ITER=20):
past_ll = -float('inf')
ll = self.log_likelihood()
EPS = 0.1
itr = 0
while abs(ll - past_ll) > EPS and itr < MAX_ITER:
if ll < past_ll:
slog('ll decreased')
itr += 1
self.e_step()
self.m_step()
past_ll = ll
ll = self.log_likelihood()
slog('itr #%s\tlog_l: %s\tdelta: %s' % (itr, ll, ll - past_ll))
if itr == MAX_ITER:
slog('Hit max iteration: %d' % MAX_ITER)
return ll, self.partition
def run_EM_pool(self, nprocs=mp.cpu_count()):
pool = Pool(processes=nprocs)
ll_partitions = pool.map(em_parallel_mapper, [self] * EM_RESTARTS)
ll, partition = reduce(ll_partition_reducer, ll_partitions)
pool.terminate()
int_to_orig_node_label = {v: k for k, v in self.author_graph.node_labels.items()}
node_to_partition = {int_to_orig_node_label[n]: partition[n] for n in partition}
return ll, node_to_partition
def em_parallel_mapper(em_instance):
if not em_instance._lp_init:
em_instance._init_LP()
em_instance._rand_init_partition()
return em_instance.iterate(MAX_ITER=EM_ITERATION_LIMIT)
def ll_partition_reducer(t1, t2):
if t1[0] >= t2[0]:
return t1
else:
return t2