def generateGaussianCenters(self, referenceSamples=None):
"""
Choose Gaussian centers based on a strategy
"""
gaussianCenters = self.generateAllGaussianCenters(referenceSamples)
Matrix.show("Gaussian Centers", gaussianCenters, self.settings)
return gaussianCenters
def generateGaussianCenters(self, referenceSamples=None) :
"""
Choose Gaussian centers based on a strategy
"""
gaussianCenters = self.generateAllGaussianCenters(referenceSamples)
Matrix.show("Gaussian Centers", gaussianCenters, self.settings)
return gaussianCenters
def computeModelParameters(self,
referenceSamples=None,
testSamples=None,
gaussianCenters=None):
"""
Computes model parameters via k-fold cross validation process
"""
(refRows, refCols) = referenceSamples.shape
(testRows, testCols) = testSamples.shape
sigmaWidths = self.computeGaussianWidthCandidates(
referenceSamples, testSamples)
lambdaCandidates = self.generateRegularizationParams()
Vector.show("Sigma Candidates", sigmaWidths, self.settings)
Vector.show("Lambda Candidates", lambdaCandidates, self.settings)
# Initialize cross validation scoring matrix
crossValidationScores = numpy.zeros(
(numpy.size(sigmaWidths), numpy.size(lambdaCandidates)))
# Initialize a cross validation index assignment list
referenceSamplesCVIdxs = numpy.random.permutation(refCols)
referenceSamplesCVSplit = numpy.floor(numpy.r_[0:refCols] *
self.crossFolds / refCols)
testSamplesCVIdxs = numpy.random.permutation(testCols)
testSamplesCVSplit = numpy.floor(numpy.r_[0:testCols] *
self.crossFolds / testCols)
# Initiate k-fold cross-validation procedure. Using variable
# notation similar to the RULSIF formulas.
for sigmaIdx in numpy.r_[0:numpy.size(sigmaWidths)]:
# (re-)Calculate the kernel matrix using the candidate sigma width
sigma = sigmaWidths[sigmaIdx]
K_ref = GaussianKernel(sigma).apply(referenceSamples,
gaussianCenters).T
K_test = GaussianKernel(sigma).apply(testSamples,
gaussianCenters).T
# Initialize a new result matrix for the current sigma candidate
foldResult = numpy.zeros(
(self.crossFolds, numpy.size(lambdaCandidates)))
for foldIdx in numpy.r_[0:self.crossFolds]:
K_ref_trainingSet = K_ref[:, referenceSamplesCVIdxs[
referenceSamplesCVSplit != foldIdx]]
K_test_trainingSet = K_test[:, testSamplesCVIdxs[
testSamplesCVSplit != foldIdx]]
H_h_KthFold = AlphaRelativeDensityRatioEstimator.H_hat(
self.alphaConstraint, K_ref_trainingSet,
K_test_trainingSet)
h_h_KthFold = AlphaRelativeDensityRatioEstimator.h_hat(
K_ref_trainingSet)
for lambdaIdx in numpy.r_[0:numpy.size(lambdaCandidates)]:
lambdaCandidate = lambdaCandidates[lambdaIdx]
theta_h_KthFold = AlphaRelativeDensityRatioEstimator.theta_hat(
H_h_KthFold, h_h_KthFold, lambdaCandidate,
self.kernelBasis)
# Select the subset of the kernel matrix not used in the training set
# for use as the test set to validate against
K_ref_testSet = K_ref[:, referenceSamplesCVIdxs[
referenceSamplesCVSplit == foldIdx]]
K_test_testSet = K_test[:, testSamplesCVIdxs[
testSamplesCVSplit == foldIdx]]
r_alpha_Xref = AlphaRelativeDensityRatioEstimator.g_of_X_theta(
K_ref_testSet, theta_h_KthFold)
r_alpha_Xtest = AlphaRelativeDensityRatioEstimator.g_of_X_theta(
K_test_testSet, theta_h_KthFold)
# Calculate the objective function J(theta) under the current parameters
J = AlphaRelativeDensityRatioEstimator.J_of_theta(
self.alphaConstraint, r_alpha_Xref, r_alpha_Xtest)
foldResult[foldIdx, lambdaIdx] = J
crossValidationScores[sigmaIdx, :] = numpy.mean(foldResult, 0)
Matrix.show("Cross-Validation Scores", crossValidationScores,
self.settings)
crossValidationMinScores = crossValidationScores.min(1)
crossValidationMinIdxForLambda = crossValidationScores.argmin(1)
crossValidationMinIdxForSigma = crossValidationMinScores.argmin()
optimalSigma = sigmaWidths[crossValidationMinIdxForSigma]
optimalLambda = lambdaCandidates[
crossValidationMinIdxForLambda[crossValidationMinIdxForSigma]]
return (optimalSigma, optimalLambda)
def computeModelParameters(self, referenceSamples=None, testSamples=None, gaussianCenters=None) :
"""
Computes model parameters via k-fold cross validation process
"""
(refRows , refCols ) = referenceSamples.shape
(testRows, testCols) = testSamples.shape
sigmaWidths = self.computeGaussianWidthCandidates(referenceSamples, testSamples)
lambdaCandidates = self.generateRegularizationParams()
Vector.show("Sigma Candidates", sigmaWidths, self.settings)
Vector.show("Lambda Candidates", lambdaCandidates, self.settings)
# Initialize cross validation scoring matrix
crossValidationScores = numpy.zeros( (numpy.size(sigmaWidths), numpy.size(lambdaCandidates)) )
# Initialize a cross validation index assignment list
referenceSamplesCVIdxs = numpy.random.permutation(refCols)
referenceSamplesCVSplit = numpy.floor(numpy.r_[0:refCols] * self.crossFolds / refCols)
testSamplesCVIdxs = numpy.random.permutation(testCols)
testSamplesCVSplit = numpy.floor(numpy.r_[0:testCols] * self.crossFolds / testCols)
# Initiate k-fold cross-validation procedure. Using variable
# notation similar to the RULSIF formulas.
for sigmaIdx in numpy.r_[0:numpy.size(sigmaWidths)] :
# (re-)Calculate the kernel matrix using the candidate sigma width
sigma = sigmaWidths[sigmaIdx]
K_ref = GaussianKernel(sigma).apply(referenceSamples, gaussianCenters).T
K_test = GaussianKernel(sigma).apply(testSamples, gaussianCenters).T
# Initialize a new result matrix for the current sigma candidate
foldResult = numpy.zeros( (self.crossFolds, numpy.size(lambdaCandidates)) )
for foldIdx in numpy.r_[0:self.crossFolds] :
K_ref_trainingSet = K_ref[:, referenceSamplesCVIdxs[referenceSamplesCVSplit != foldIdx]]
K_test_trainingSet = K_test[:, testSamplesCVIdxs[testSamplesCVSplit != foldIdx]]
H_h_KthFold = AlphaRelativeDensityRatioEstimator.H_hat(self.alphaConstraint, K_ref_trainingSet, K_test_trainingSet)
h_h_KthFold = AlphaRelativeDensityRatioEstimator.h_hat(K_ref_trainingSet)
for lambdaIdx in numpy.r_[0:numpy.size(numpy.lambdaCandidates)] :
lambdaCandidate = lambdaCandidates[lambdaIdx]
theta_h_KthFold = AlphaRelativeDensityRatioEstimator.theta_hat(H_h_KthFold, h_h_KthFold, lambdaCandidate, self.kernelBasis)
# Select the subset of the kernel matrix not used in the training set
# for use as the test set to validate against
K_ref_testSet = K_ref[:, referenceSamplesCVIdxs[referenceSamplesCVSplit == foldIdx]]
K_test_testSet = K_test[:, testSamplesCVIdxs[testSamplesCVSplit == foldIdx]]
r_alpha_Xref = AlphaRelativeDensityRatioEstimator.g_of_X_theta(K_ref_testSet , theta_h_KthFold)
r_alpha_Xtest = AlphaRelativeDensityRatioEstimator.g_of_X_theta(K_test_testSet, theta_h_KthFold)
# Calculate the objective function J(theta) under the current parameters
J = AlphaRelativeDensityRatioEstimator.J_of_theta(self.alphaConstraint, r_alpha_Xref, r_alpha_Xtest)
foldResult[foldIdx, lambdaIdx] = J
crossValidationScores[sigmaIdx, :] = numpy.mean(foldResult, 0)
Matrix.show("Cross-Validation Scores", crossValidationScores, self.settings)
crossValidationMinScores = crossValidationScores.min(1)
crossValidationMinIdxForLambda = crossValidationScores.argmin(1)
crossValidationMinIdxForSigma = crossValidationMinScores.argmin()
optimalSigma = sigmaWidths[crossValidationMinIdxForSigma]
optimalLambda = lambdaCandidates[crossValidationMinIdxForLambda[crossValidationMinIdxForSigma]]
return (optimalSigma, optimalLambda)
