def constructIntegrandFunctionObject(marginalPair, eta, k, l, N):
"""
Input: marginalPair, e.g. [0.5,0.3]
eta, k,l, N
Output:
integrand function which object maps t to Estimated emission probability of p(baseMarginals)(t) from p^\eta
and which has some additional methods/properties, facilitating binary search, associated with it.
"""
#functionFromTwoMarginalsAndParameterToIntegrand(x,y,t) = Estimated emission probability of p(x,y,t) from p^\eta
functionFromTwoMarginalsAndParameterToIntegrand = epc.emissionProbabilityCalculator(
eta, k, l, N).RobbinsEstimateOfEmissionProbability
t = 0.001 #used for logger
logging.info("For marginals %s, Robbins function takes value %s at t=%s" %
(marginalPair,
functionFromTwoMarginalsAndParameterToIntegrand(
marginalPair[0], marginalPair[1], t), t))
functionFromParameterToIntegrandObject = fa.functionAlgorithms(
functionFromTwoMarginalsAndParameterToIntegrand)
functionFromParameterToIntegrandObject.setFixedArgumentList(marginalPair)
logging.info(
"Fixed argument list set to %s" %
(str(functionFromParameterToIntegrandObject.fixedArgumentList)))
#functionFromParameterToIntegrand(t) = Estimated emission probability of p(baseMarginals)(t) from p^\eta
functionFromParameterToIntegrand = functionFromParameterToIntegrandObject.functionOfOneVariable
logging.info("As func. of one variable, takes value %s at t=%s" %
(functionFromParameterToIntegrand(t), t))
return fa.functionAlgorithms(functionFromParameterToIntegrand)
def setUp(self):
k,l=2,2
N=100
gamma=1e-3
eta=1e-3
probabilityCalculatorAssociatedToEta = epc.emissionProbabilityCalculator(eta, k, l, N)
probabilityCalculatorAssociatedToEta.setGamma(gamma)
self.functionProbabilityOfEmissionByP_eta_Robbins = probabilityCalculatorAssociatedToEta.RobbinsEstimateOfEmissionProbabilityTimesCharFunctionOfTauMinusGamma
def testSearchArgWhereIncreasingFunctionTakesProportionOfMaxVal(self):
theProportion = stats.norm.pdf(1)/stats.norm.pdf(0)
N_list = list(10*np.array(range(1,10)))
N_list.extend((100*np.array(range(1,10))))
k,l=2,2
eta=0.01
gamma = 0.001
logger.debug("Set eta=%s, gamma=%s"%(eta,gamma))
#firstMarginalsDist = stats.uniform(loc = .4,scale = .2)
#secondMarginalsDist = stats.uniform(loc = .4,scale = .2)
for N in N_list:
for iteration in range(1):
#firstMarginal, secondMarginal = [firstMarginalsDist.rvs(), secondMarginalsDist.rvs()]
firstMarginal, secondMarginal = 1.0/l, 1.0/k #0.5, 0.5 for binary-binary
logger.debug("Randomly chosen marginals: (%s,%s)"%(firstMarginal, secondMarginal))
functionFromTwoMarginalsAndParameterToIntegrand = epc.emissionProbabilityCalculator(eta, k, l, N).RobbinsEstimateOfEmissionProbability
logger.debug("For marginals (%s,%s), Robbins function takes value %s at t=%s"%(firstMarginal, secondMarginal, functionFromTwoMarginalsAndParameterToIntegrand(firstMarginal, secondMarginal, 0.001), 0.001))
functionFromParameterToIntegrandObject = fa.functionAlgorithms(functionFromTwoMarginalsAndParameterToIntegrand)
functionFromParameterToIntegrandObject.setFixedArgumentList([firstMarginal, secondMarginal])
logger.debug("Fixed argument list set to %s"%(str(functionFromParameterToIntegrandObject.fixedArgumentList)))
functionFromParameterToIntegrand = functionFromParameterToIntegrandObject.functionOfOneVariable
logger.debug("As func. of one variable, takes value %s at t=%s"%(functionFromParameterToIntegrand(0.001), 0.001))
probDistPath = pdpf.probabilityDistributionPathFactory([firstMarginal, secondMarginal], k, l).construct()
t_gamma_plus = probDistPath.largestPos_t_atWhichKLDivergenceFromBaseIsLessThanEta(gamma)
t_gamma_minus = probDistPath.smallestNeg_t_atWhichKLDivergenceFromBaseIsLessThanEta(gamma)
logger.debug("Robbins function takes value %s at t_gamma_plus=%s"%(functionFromParameterToIntegrandObject.theFunction(firstMarginal, secondMarginal, t_gamma_plus), t_gamma_plus))
logger.debug("Robbins function takes value %s at t_gamma_minus=%s"%(functionFromParameterToIntegrandObject.theFunction(firstMarginal, secondMarginal, t_gamma_minus), t_gamma_minus))
integrandFunctionObject = fa.functionAlgorithms(functionFromParameterToIntegrand)
logger.info("Searching for where the function is proportion %s of the max between %s and %s"%(theProportion, t_gamma_minus, t_gamma_plus))
computedScale = integrandFunctionObject.searchArgWhereIncreasingFunctionTakesProportionOfMaxVal(theProportion, t_gamma_minus, t_gamma_plus)
logger.info("For marginals (%s,%s), N=%s, computed scale is %s"%(firstMarginal, secondMarginal, N, computedScale))
def constructIntegrandFunctionObject(marginalPair, eta, k,l,N):
"""
Input: marginalPair, e.g. [0.5,0.3]
eta, k,l, N
Output:
integrand function which object maps t to Estimated emission probability of p(baseMarginals)(t) from p^\eta
and which has some additional methods/properties, facilitating binary search, associated with it.
"""
#functionFromTwoMarginalsAndParameterToIntegrand(x,y,t) = Estimated emission probability of p(x,y,t) from p^\eta
functionFromTwoMarginalsAndParameterToIntegrand = epc.emissionProbabilityCalculator(eta, k, l, N).RobbinsEstimateOfEmissionProbability
t=0.001 #used for logger
logging.info("For marginals %s, Robbins function takes value %s at t=%s"%(
marginalPair, functionFromTwoMarginalsAndParameterToIntegrand(marginalPair[0], marginalPair[1], t), t))
functionFromParameterToIntegrandObject = fa.functionAlgorithms(functionFromTwoMarginalsAndParameterToIntegrand)
functionFromParameterToIntegrandObject.setFixedArgumentList(marginalPair)
logging.info("Fixed argument list set to %s"%(str(functionFromParameterToIntegrandObject.fixedArgumentList)))
#functionFromParameterToIntegrand(t) = Estimated emission probability of p(baseMarginals)(t) from p^\eta
functionFromParameterToIntegrand = functionFromParameterToIntegrandObject.functionOfOneVariable
logging.info("As func. of one variable, takes value %s at t=%s"%(functionFromParameterToIntegrand(t), t))
return fa.functionAlgorithms(functionFromParameterToIntegrand)
def functionProbabilityOfEmissionByP_eta_Robbins(eta,N,gamma,k,l):
probabilityCalculatorAssociatedToEta = epc.emissionProbabilityCalculator(eta, k, l, N)
probabilityCalculatorAssociatedToEta.setGamma(gamma)
return probabilityCalculatorAssociatedToEta.RobbinsEstimateOfEmissionProbabilityTimesCharFunctionOfTauMinusGamma
def functionProbabilityOfEmissionByP_eta_Robbins(eta, N, gamma, k, l):
probabilityCalculatorAssociatedToEta = epc.emissionProbabilityCalculator(
eta, k, l, N)
probabilityCalculatorAssociatedToEta.setGamma(gamma)
return probabilityCalculatorAssociatedToEta.RobbinsEstimateOfEmissionProbabilityTimesCharFunctionOfTauMinusGamma
def _testIntegratetoFlatFile(self):
#load in benchmark data
benchmarks = genfromtxt('cdf_for_valsets_of_variables_of_size2and2', delimiter=',', skip_header=4)
benchmarks_without_stepsize = benchmarks[:,1:]
lineInBenchMarkFileList = [0, 9]
#prepare the csv file
f=open('/home/eliot/Documents/sontag/benchmarkcomparisons/N@100_N@[email protected]', 'wt')
writer = csv.writer(f)
for lineInBenchMarkFile in lineInBenchMarkFileList:
benchmark_N = (lineInBenchMarkFile+1)*benchMarkInterval_N
benchmarksForThisN = benchmarks_without_stepsize[lineInBenchMarkFile]
stepSizeInBenchmarks = benchmarks[0,0]
numStepsInBenchmarks = len(benchmarks[0])
logging.info("Read in %s lines of benchmarks with stepsize=%s and %s steps"%(len(benchmarks_without_stepsize), stepSizeInBenchmarks, numStepsInBenchmarks))
#constants common to all of the runs
k, l = 2,2
eta = 0.01
N = benchmark_N
maxIterations = 10000
dictionaryFromNameOfMethodToResults = {}
#build the inputs to IntegrateWithStoppingCriterion
#the integrand, namely probability-of-emission calculator from p-eta, which is common to ALL methods
probabilityCalculatorAssociatedToEta = epc.emissionProbabilityCalculator(eta, k, l, N)
for gammaNumber in range(numStepsInBenchmarks-1):
gamma = (gammaNumber+1)*stepSizeInBenchmarks
benchMarkBeta = benchmarksForThisN[gammaNumber]
probabilityCalculatorAssociatedToEta.setGamma(gamma)
functionProbabilityOfEmissionByP_eta_Robbins = probabilityCalculatorAssociatedToEta.RobbinsEstimateOfEmissionProbabilityTimesCharFunctionOfTauMinusGamma
#the probability distribution used to choose marginals distribution, also common to ALL methods (except for completely-uniform, if implemented)
Gaussianscale = it.ChernoffRadius(CentralProbability, N)
normalDistLocUniformScaleDepOnChernoff = stats.norm(loc=0.5,scale=Gaussianscale)
#e.g. 5, .95 means "seeking 95 percent certainty answer is within 5 percent of truth , typically also common to all runs
accuracy_percent = 10
probability_accuracy_achieved = 0.95
#the method for picking the parameter-distribution based on the marginals, specific to this run
#
statsDistFactory = sdf.statsDistributionFactory(gamma)
dictionaryFromNameOfMethodToMethod = {}
dictionaryFromNameOfMethodToMethod['GaussianScaleAdaptiveTo_l_gamma']=statsDistFactory.GaussianCenteredAttGammaPlusfromMarginals
#dictionaryFromNameOfMethodToMethod['GaussianScaleAdaptiveTo_N']=statsDistFactory.GaussianCenteredAttGammaPlusfromMarginalsScaledFromScaleRatio
#functionFromMarginalsTo_t_Distribution = statsDistFactory.GaussianCenteredAttGammaPlusfromMarginals
uniformMarginals = [1.0/k, 1.0/l]
for nameOfMethod in dictionaryFromNameOfMethodToMethod.keys():
if dictionaryFromNameOfMethodToResults.has_key( nameOfMethod):
resultsDictionary = dictionaryFromNameOfMethodToResults[nameOfMethod]
else:
resultsDictionary = {}
statsDistFactory.set_eta(eta)
statsDistFactory.set_N(N)
statsDistFactory.CalculateAndSetScaleRatio(uniformMarginals)
#functionFromMarginalsTo_t_Distribution = statsDistFactory.GaussianCenteredAttGammaPlusfromMarginalsScaledFromScaleRatio
functionFromMarginalsTo_t_Distribution = dictionaryFromNameOfMethodToMethod[nameOfMethod]
#start the calculation proper
with Timer.Timer() as t:
iteration_values, rho_hat_values = iwsc.IntegrateWithStoppingCriterion(k,l,
functionProbabilityOfEmissionByP_eta_Robbins,
normalDistLocUniformScaleDepOnChernoff, functionFromMarginalsTo_t_Distribution, #!!!MAIN THING TO CHANGE!!!
maxIterations, 100, 100, #frequencyOfRecodingreslt, frequencyOfApplicationOfStoppingCriterion
accuracy_percent, probability_accuracy_achieved)
logging.info("Time elapsed is %.03f sec." % t.interval)
logging.info("Iteration_values for the method %s for eta=%s, gamma=%s, N=%s, accpercent=%s, prob_achieved=%s"%(nameOfMethod, eta,gamma,N,accuracy_percent, probability_accuracy_achieved))
logging.info(iteration_values)
logging.info("rho_hat_values for the method %s for eta=%s, gamma=%s, N=%s, accpercent=%s, prob_achieved=%s"%(nameOfMethod, eta,gamma,N,accuracy_percent, probability_accuracy_achieved))
logging.info( rho_hat_values)
betaResult = rho_hat_values[-1]*N**3
if resultsDictionary.has_key('time'):
resultsDictionary['time'].append(t.interval)
else:
resultsDictionary['time'] = [t.interval]
if resultsDictionary.has_key('CalculatedResult'):
resultsDictionary['CalculatedResult'].append(betaResult)
else:
resultsDictionary['CalculatedResult'] = [betaResult]
if resultsDictionary.has_key('BenchmarkBeta'):
resultsDictionary['BenchmarkBeta'].append(benchMarkBeta)
else:
resultsDictionary['BenchmarkBeta'] = [benchMarkBeta]
dictionaryFromNameOfMethodToResults[nameOfMethod] = resultsDictionary
fileNameForPickleDump = "/home/eliot/Documents/sontag/benchmarkcomparisons/testRun" + str(N)
pickle.dump( dictionaryFromNameOfMethodToResults, open( fileNameForPickleDump, "wb" ) )
#write to the CSV file
N_header = 'N=%s'%(N)
writer.writerow( [N_header])
for resultsDictionary in dictionaryFromNameOfMethodToResults.values():
for key in resultsDictionary.keys():
print key
print resultsDictionary[key]
rowList = resultsDictionary[key]
rowList.insert(0,key)
print rowList
writer.writerow(rowList)
f.close()
def testSearchArgWhereIncreasingFunctionTakesProportionOfMaxVal(self):
theProportion = stats.norm.pdf(1) / stats.norm.pdf(0)
N_list = list(10 * np.array(range(1, 10)))
N_list.extend((100 * np.array(range(1, 10))))
k, l = 2, 2
eta = 0.01
gamma = 0.001
logger.debug("Set eta=%s, gamma=%s" % (eta, gamma))
# firstMarginalsDist = stats.uniform(loc = .4,scale = .2)
# secondMarginalsDist = stats.uniform(loc = .4,scale = .2)
for N in N_list:
for iteration in range(1):
# firstMarginal, secondMarginal = [firstMarginalsDist.rvs(), secondMarginalsDist.rvs()]
firstMarginal, secondMarginal = 1.0 / l, 1.0 / k # 0.5, 0.5 for binary-binary
logger.debug("Randomly chosen marginals: (%s,%s)" % (firstMarginal, secondMarginal))
functionFromTwoMarginalsAndParameterToIntegrand = epc.emissionProbabilityCalculator(
eta, k, l, N
).RobbinsEstimateOfEmissionProbability
logger.debug(
"For marginals (%s,%s), Robbins function takes value %s at t=%s"
% (
firstMarginal,
secondMarginal,
functionFromTwoMarginalsAndParameterToIntegrand(firstMarginal, secondMarginal, 0.001),
0.001,
)
)
functionFromParameterToIntegrandObject = fa.functionAlgorithms(
functionFromTwoMarginalsAndParameterToIntegrand
)
functionFromParameterToIntegrandObject.setFixedArgumentList([firstMarginal, secondMarginal])
logger.debug(
"Fixed argument list set to %s" % (str(functionFromParameterToIntegrandObject.fixedArgumentList))
)
functionFromParameterToIntegrand = functionFromParameterToIntegrandObject.functionOfOneVariable
logger.debug(
"As func. of one variable, takes value %s at t=%s"
% (functionFromParameterToIntegrand(0.001), 0.001)
)
probDistPath = pdpf.probabilityDistributionPathFactory(
[firstMarginal, secondMarginal], k, l
).construct()
t_gamma_plus = probDistPath.largestPos_t_atWhichKLDivergenceFromBaseIsLessThanEta(gamma)
t_gamma_minus = probDistPath.smallestNeg_t_atWhichKLDivergenceFromBaseIsLessThanEta(gamma)
logger.debug(
"Robbins function takes value %s at t_gamma_plus=%s"
% (
functionFromParameterToIntegrandObject.theFunction(firstMarginal, secondMarginal, t_gamma_plus),
t_gamma_plus,
)
)
logger.debug(
"Robbins function takes value %s at t_gamma_minus=%s"
% (
functionFromParameterToIntegrandObject.theFunction(
firstMarginal, secondMarginal, t_gamma_minus
),
t_gamma_minus,
)
)
integrandFunctionObject = fa.functionAlgorithms(functionFromParameterToIntegrand)
logger.info(
"Searching for where the function is proportion %s of the max between %s and %s"
% (theProportion, t_gamma_minus, t_gamma_plus)
)
computedScale = integrandFunctionObject.searchArgWhereIncreasingFunctionTakesProportionOfMaxVal(
theProportion, t_gamma_minus, t_gamma_plus
)
logger.info(
"For marginals (%s,%s), N=%s, computed scale is %s"
% (firstMarginal, secondMarginal, N, computedScale)
)
