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 testBinarySearch(self):
newFunctionAlgorithmObject = fa.functionAlgorithms(np.sin)
np.testing.assert_almost_equal(
newFunctionAlgorithmObject.searchArgWhereIncreasingFunctionTakesVal(0,
-np.pi/2.0, np.pi/2.0),0.0)
np.testing.assert_almost_equal(
newFunctionAlgorithmObject.searchArgWhereIncreasingFunctionTakesVal(-1,
-np.pi/2.0, np.pi/2.0), -1.57079632094)
np.testing.assert_almost_equal(
newFunctionAlgorithmObject.searchArgWhereIncreasingFunctionTakesVal(1,
-np.pi/2.0, np.pi/2.0), 1.57079632094)
def testBinarySearch(self):
newFunctionAlgorithmObject = fa.functionAlgorithms(np.sin)
np.testing.assert_almost_equal(
newFunctionAlgorithmObject.searchArgWhereIncreasingFunctionTakesVal(0, -np.pi / 2.0, np.pi / 2.0), 0.0
)
np.testing.assert_almost_equal(
newFunctionAlgorithmObject.searchArgWhereIncreasingFunctionTakesVal(-1, -np.pi / 2.0, np.pi / 2.0),
-1.57079632094,
)
np.testing.assert_almost_equal(
newFunctionAlgorithmObject.searchArgWhereIncreasingFunctionTakesVal(1, -np.pi / 2.0, np.pi / 2.0),
1.57079632094,
)
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 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)
)