/
glad_naive.py
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/
glad_naive.py
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
import argparse
import logging
import math
import numpy as np
import scipy as sp
import scipy.stats
import scipy.optimize
import unittest
import warnings
THRESHOLD = 1e-5
verbose = False
debug = False
logger = None
warnings.filterwarnings('error')
class Label:
def __init__(self, taskIdx=-1, labelerId=-1, label=-1):
self.taskIdx = taskIdx
self.labelerId = labelerId
self.label = label
class Dataset:
def __init__(self, labels=[], numLabels=-1, numLabelers=-1, numTasks=-1,
priorAlpha=None, priorBeta=None, priorZ1=None,
alpha=None, beta=None, probZ1=None, probZ0=None):
self.labels = labels
self.numLabels = numLabels
self.numLabelers = numLabelers
self.numTasks = numTasks
self.priorAlpha = priorAlpha
self.priorBeta = priorBeta
self.priorZ1 = priorZ1
self.alpha = alpha
self.beta = beta
self.probZ1 = probZ1
self.probZ0 = probZ0
def init_logger():
global logger
logger = logging.getLogger('GLAD')
logger.setLevel(logging.DEBUG)
log_fmt = '%(asctime)s/%(name)s[%(levelname)s]: %(message)s'
logging.basicConfig(format=log_fmt)
def sigmoid(x):
return 1.0 / (1.0 + np.exp(-x))
def load_data(filename):
data = Dataset()
with open(filename) as f:
# Read parameters
header = f.readline().split()
data.numLabels = int(header[0])
data.numLabelers = int(header[1])
data.numTasks = int(header[2])
data.priorZ1 = float(header[3])
if verbose:
logger.info('Reading {} labels of {} labelers over {} tasks for prior P(Z=1) = {}'.format(data.numLabels, data.numLabelers, data.numTasks, data.priorZ1))
# Read Labels
for line in f:
task, labeler, label = map(int, line.split())
if verbose:
logger.info("Read: task({})={} by labeler {}".format(task, label, labeler))
item = Label(taskIdx=task, labelerId=labeler, label=label)
data.labels.append(item)
# Initialize Probs
data.priorAlpha = np.ones(data.numLabelers)
data.priorBeta = np.ones(data.numTasks)
data.probZ1 = np.empty(data.numTasks)
data.probZ0 = np.empty(data.numTasks)
data.priorZ1 = np.zeros(data.numTasks) + data.priorZ1
data.beta = np.empty(data.numTasks)
data.alpha = np.empty(data.numLabelers)
return data
def EM(data):
u"""Infer true labels, tasks' difficulty and workers' ability
"""
# Initialize parameters to starting values
data.alpha = data.priorAlpha.copy()
data.beta = data.priorBeta.copy()
EStep(data)
lastQ = computeQ(data)
MStep(data)
Q = computeQ(data)
counter = 1
while abs((Q - lastQ)/lastQ) > THRESHOLD:
if verbose: logger.info('EM: iter={}'.format(counter))
lastQ = Q
EStep(data)
MStep(data)
Q = computeQ(data)
counter += 1
def EStep(data):
u"""Evaluate the posterior probability of true labels given observed labels and parameters
"""
if verbose: logger.info('EStep')
data.probZ1 = np.log(data.priorZ1)
data.probZ0 = np.log(1 - data.priorZ1)
for item in data.labels:
i = item.labelerId
j = item.taskIdx
lij = item.label
data.probZ1[j] += logProbL(lij, 1, data.alpha[i], data.beta[j])
data.probZ0[j] += logProbL(lij, 0, data.alpha[i], data.beta[j])
# Exponentiate and renormalize
data.probZ1 = np.exp(data.probZ1)
data.probZ0 = np.exp(data.probZ0)
data.probZ1 = data.probZ1 / (data.probZ1 + data.probZ0)
data.probZ0 = 1 - data.probZ1
# TODO: nan -> abort
return data
def packX(data):
return np.r_[data.alpha.copy(), data.beta.copy()]
def unpackX(x, data):
data.alpha = x[:data.numLabelers]
data.beta = x[data.numLabelers:]
def getBoundsX(data, alpha=(-100, 100), beta=(-100, 100)):
alpha_bounds = np.array([[alpha[0], alpha[1]] for i in range(data.numLabelers)])
beta_bounds = np.array([[beta[0], beta[1]] for i in range(data.numLabelers)])
return np.r_[alpha_bounds, beta_bounds]
def f(x, *args):
u"""Return the value of the objective function
"""
data = args[0]
d = Dataset(labels=data.labels, numLabels=data.numLabels, numLabelers=data.numLabelers,
numTasks=data.numTasks,
priorAlpha=data.priorAlpha, priorBeta=data.priorBeta, priorZ1=data.priorZ1,
probZ1=data.probZ1, probZ0=data.probZ0)
unpackX(x, d)
return - computeQ(d)
def df(x, *args):
u"""Return gradient vector
"""
data = args[0]
d = Dataset(labels=data.labels, numLabels=data.numLabels, numLabelers=data.numLabelers,
numTasks=data.numTasks,
priorAlpha=data.priorAlpha, priorBeta=data.priorBeta, priorZ1=data.priorZ1,
probZ1=data.probZ1, probZ0=data.probZ0)
unpackX(x, d)
dQdAlpha, dQdBeta = gradientQ(d)
# Flip the sign since we want to minimize
return np.r_[-dQdAlpha, -dQdBeta]
def MStep(data):
if verbose: logger.info('MStep')
initial_params = packX(data)
params = sp.optimize.minimize(fun=f, x0=initial_params, args=(data,), method='CG',
jac=df, tol=0.01,
options={'maxiter': 25, 'disp': verbose})
if debug: logger.debug(params)
unpackX(params.x, data)
def computeQ(data):
u"""Calculate the expectation of the joint likelihood
"""
Q = 0
# Start with the expectation of the sum of priors over all tasks
Q += (data.probZ1 * np.log(data.priorZ1)).sum()
Q += (data.probZ0 * np.log(1 - data.priorZ1)).sum()
# the expectation of the sum of posteriors over all tasks
for item in data.labels:
i = item.labelerId
j = item.taskIdx
alpha = data.alpha[i]
beta = data.beta[j]
lij = item.label
try:
logSigma = - np.log(1 + np.exp(- np.exp(beta) * alpha))
except Warning:
# For large negative x, -log(1 + exp(-x)) = x
logSigma = np.exp(beta) * alpha;
try:
logOneMinusSigma = - np.log(1 + np.exp(np.exp(beta) * alpha))
except Warning:
# For large positive x, -log(1 + exp(x)) = x
logOneMinusSigma = - np.exp(beta) * alpha;
Q += data.probZ1[j] * (lij * logSigma + (1 - lij) * logOneMinusSigma) + data.probZ0[j] * ((1 - lij) * logSigma + lij * logOneMinusSigma)
# Add Gaussian (standard normal) prior for alpha
try:
Q += np.log(sp.stats.norm.pdf(data.alpha - data.priorAlpha)).sum()
except Warning:
logger.warning('an invalid value was assigned to np.log [computeQ]')
Q = np.nan
# Add Gaussian (standard normal) prior for beta
try:
Q += np.log(sp.stats.norm.pdf(data.beta - data.priorBeta)).sum()
except Warning:
logger.warning('an invalid value was assigned to np.log [computeQ]')
Q = np.nan
if debug:
logger.debug('a[0]={} a[1]={} a[2]={} b[0]={}'.format(data.alpha[0], data.alpha[1],
data.alpha[2], data.beta[0]))
logger.debug('Q={}'.format(Q))
return Q
def gradientQ(data):
dQdAlpha = - (data.alpha - data.priorAlpha)
dQdBeta = - (data.beta - data.priorBeta)
for item in data.labels:
i = item.labelerId
j = item.taskIdx
alpha = data.alpha[i]
beta = data.beta[j]
lij = item.label
try:
sigma = sigmoid(np.exp(beta) * alpha)
except Warning:
if alpha < 0:
sigma = 0
else:
raise
dQdAlpha[i] += (data.probZ1[j] * (lij - sigma) + data.probZ0[j] * (1 - lij - sigma)) * np.exp(beta)
dQdBeta[j] += (data.probZ1[j] * (lij - sigma) + data.probZ0[j] * (1 - lij - sigma)) * alpha * np.exp(beta)
if debug:
logger.debug('dQdAlpha[0]={} dQdAlpha[1]={} dQdAlpha[2]={} dQdBeta[0]={}'.format(dQdAlpha[0], dQdAlpha[1],
dQdAlpha[2], dQdBeta[0]))
return dQdAlpha, dQdBeta
def logProbL(l, z, alphaI, betaJ):
u"""Return log posterior probability of the label given true label, difficulity and ability
"""
if (z == l):
p = - np.log(1 + np.exp(- np.exp(betaJ) * alphaI))
else:
p = - np.log(1 + np.exp(np.exp(betaJ) * alphaI))
return p
def output(data):
alpha = np.c_[np.arange(1, data.numLabelers+1), data.alpha]
np.savetxt('alpha.csv', alpha, fmt=['%d', '%.5f'], delimiter=',', header='id,alpha')
beta = np.c_[np.arange(1, data.numTasks+1), data.beta]
np.savetxt('beta.csv', beta, fmt=['%d', '%.5f'], delimiter=',', header='id,beta')
label = np.c_[np.arange(1, data.numTasks+1), data.probZ0, data.probZ1]
np.savetxt('label.csv', label, fmt=['%d', '%.5f', '%.5f'], delimiter=',', header='id,z0,z1')
def outputResults(data):
for i in range(data.numLabelers):
print('Alpha[{idx}] = {val:.5f}'.format(idx=i, val=data.alpha[i]))
for j in range(data.numTasks):
print('Beta[{idx}] = {val:.5f}'.format(idx=j, val=np.exp(data.beta[j])))
for j in range(data.numTasks):
print('P(Z({idx})=1) = {val:.5f}'.format(idx=j, val=data.probZ1[j]))
def main(args=None):
global debug, verbose
debug = args.debug
if debug == True:
verbose = True
else:
verbose = args.verbose
data = load_data(args.filename)
EM(data)
output(data)
outputResults(data)
return 0
if __name__ == '__main__':
init_logger()
parser = argparse.ArgumentParser()
parser.add_argument('filename')
parser.add_argument('-v', '--verbose', action='store_true', default=False)
parser.add_argument('-d', '--debug', action='store_true', default=False)
args = parser.parse_args()
code = main(args)
exit(code)