def testObjectiveApprox(self):
"""
We'll test the case in which we apprormate using a large number of samples
for the AUC and see if we get close to the exact objective
"""
m = 20
n = 30
k = 3
X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)
learner = MaxAUCSquare(k)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = n
indPtr, colInds = SparseUtils.getOmegaListPtr(X)
U = numpy.random.rand(X.shape[0], k)
V = numpy.random.rand(X.shape[1], k)
numRuns = 100
numTests = 5
gi = numpy.random.rand(m)
gi /= gi.sum()
gp = numpy.random.rand(n)
gp /= gp.sum()
gq = numpy.random.rand(n)
gq /= gq.sum()
#gi = numpy.ones(m)
#gp = numpy.ones(n)
#gq = numpy.ones(n)
#Let's compare against using the exact derivative
for i in range(numTests):
obj = 0
for j in range(numRuns):
obj += learner.objectiveApprox(indPtr, colInds, indPtr, colInds, U, V, gp, gq)
obj /= numRuns
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp, gq)
self.assertAlmostEquals(obj, obj2, 2)
learner.rho = 0.2
for i in range(numTests):
obj = 0
for j in range(numRuns):
obj += learner.objectiveApprox(indPtr, colInds, indPtr, colInds, U, V, gp, gq)
obj /= numRuns
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp, gq)
self.assertAlmostEquals(obj, obj2, 2)
learner.lmbdaV = 0.2
for i in range(numTests):
obj = 0
for j in range(numRuns):
obj += learner.objectiveApprox(indPtr, colInds, indPtr, colInds, U, V, gp, gq)
obj /= numRuns
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp, gq)
self.assertAlmostEquals(obj, obj2, 2)
#Check full and summary versions are the same
obj = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp, gq)
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp, gq)
self.assertAlmostEquals(obj, obj2, 2)
def testDerivativeUiApprox(self):
"""
We'll test the case in which we apprormate using a large number of samples
for the AUC and see if we get close to the exact derivative
"""
m = 20
n = 30
k = 3
X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)
w = 0.1
learner = MaxAUCSquare(k, w)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = 10
U = numpy.random.rand(X.shape[0], k)
V = numpy.random.rand(X.shape[1], k)
gp = numpy.random.rand(n)
gp /= gp.sum()
gq = numpy.random.rand(n)
gq /= gq.sum()
numRuns = 200
numTests = 5
indPtr, colInds = SparseUtils.getOmegaListPtr(X)
permutedRowInds = numpy.arange(m, dtype=numpy.uint32)
permutedColInds = numpy.arange(n, dtype=numpy.uint32)
#Test with small number of AUC samples, but normalise
learner.numAucSamples = 50
numRuns = 200
for i in numpy.random.permutation(m)[0:numTests]:
U = numpy.random.rand(X.shape[0], k)
V = numpy.random.rand(X.shape[1], k)
du1 = numpy.zeros(k)
for j in range(numRuns):
VDot, VDotDot, WDot, WDotDot = learner.computeMeansVW(indPtr, colInds, U, V, permutedRowInds, permutedColInds, gp, gq)
du1 += learner.derivativeUiApprox(U, V, VDot, VDotDot, WDot, WDotDot, i)
du1 /= numRuns
du2 = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)
#print(du1, du2)
print(du1/numpy.linalg.norm(du1), du2/numpy.linalg.norm(du2))
#print(numpy.linalg.norm(du1 - du2)/numpy.linalg.norm(du1))
nptst.assert_array_almost_equal(du1, du2, 2)
#Let's compare against using the exact derivative
for i in numpy.random.permutation(m)[0:numTests]:
U = numpy.random.rand(X.shape[0], k)
V = numpy.random.rand(X.shape[1], k)
du1 = numpy.zeros(k)
for j in range(numRuns):
VDot, VDotDot, WDot, WDotDot = learner.computeMeansVW(indPtr, colInds, U, V, permutedRowInds, permutedColInds, gp, gq)
du1 += learner.derivativeUiApprox(U, V, VDot, VDotDot, WDot, WDotDot, i)
du1 /= numRuns
du2 = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)
print(du1/numpy.linalg.norm(du1), du2/numpy.linalg.norm(du2))
nptst.assert_array_almost_equal(du1, du2, 2)
learner.lmbdaV = 0.5
for i in numpy.random.permutation(m)[0:numTests]:
U = numpy.random.rand(X.shape[0], k)
V = numpy.random.rand(X.shape[1], k)
du1 = numpy.zeros(k)
for j in range(numRuns):
VDot, VDotDot, WDot, WDotDot = learner.computeMeansVW(indPtr, colInds, U, V, permutedRowInds, permutedColInds, gp, gq)
du1 += learner.derivativeUiApprox(U, V, VDot, VDotDot, WDot, WDotDot, i)
du1 /= numRuns
du2 = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)
nptst.assert_array_almost_equal(du1, du2, 2)
print(du1/numpy.linalg.norm(du1), du2/numpy.linalg.norm(du2))
def testDerivativeV(self):
m = 10
n = 20
nnzPerRow = 5
X = SparseUtils.generateSparseBinaryMatrix((m, n), nnzPerRow, csarray=True)
for i in range(m):
X[i, 0] = 1
X[i, 1] = 0
k = 5
u = 0.1
w = 1-u
eps = 0.05
learner = MaxAUCSquare(k, w)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = 100
numRuns = 20
indPtr, colInds = SparseUtils.getOmegaListPtr(X)
gp = numpy.random.rand(n)
gp /= gp.sum()
gq = numpy.random.rand(n)
gq /= gq.sum()
for s in range(numRuns):
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
deltaV = numpy.zeros(V.shape)
for j in range(n):
deltaV[j, :] = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, j)
deltaV2 = numpy.zeros(V.shape)
eps = 0.00001
for i in range(n):
for j in range(k):
tempV = V.copy()
tempV[i,j] += eps
obj1 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV, gp, gq)
tempV = V.copy()
tempV[i,j] -= eps
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV, gp, gq)
deltaV2[i,j] = (obj1-obj2)/(2*eps)
#deltaV2[i,:] = deltaV2[i,:]/numpy.linalg.norm(deltaV2[i,:])
nptst.assert_almost_equal(deltaV, deltaV2, 3)
#Try r != 0 and rho > 0
for s in range(numRuns):
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
learner.rho = 1.0
deltaV = numpy.zeros(V.shape)
for j in range(n):
deltaV[j, :] = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, j)
deltaV2 = numpy.zeros(V.shape)
for i in range(n):
for j in range(k):
tempV = V.copy()
tempV[i,j] += eps
obj1 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV, gp, gq)
tempV = V.copy()
tempV[i,j] -= eps
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV, gp, gq)
deltaV2[i,j] = (obj1-obj2)/(2*eps)
#deltaV2[i,:] = deltaV2[i,:]/numpy.linalg.norm(deltaV2[i,:])
nptst.assert_almost_equal(deltaV, deltaV2, 3)
#Try r != 0 and rho > 0
for s in range(numRuns):
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
learner.lmbdaV = 100
deltaV = numpy.zeros(V.shape)
for j in range(n):
deltaV[j, :] = learner.derivativeVi(indPtr, colInds, U, V, gp, gq, j)
deltaV2 = numpy.zeros(V.shape)
for i in range(n):
for j in range(k):
tempV = V.copy()
tempV[i,j] += eps
obj1 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV, gp, gq)
tempV = V.copy()
tempV[i,j] -= eps
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, tempV, gp, gq)
deltaV2[i,j] = (obj1-obj2)/(2*eps)
#deltaV2[i,:] = deltaV2[i,:]/numpy.linalg.norm(deltaV2[i,:])
nptst.assert_almost_equal(deltaV, deltaV2, 3)
def testDerivativeU(self):
m = 10
n = 20
nnzPerRow = 5
X = SparseUtils.generateSparseBinaryMatrix((m, n), nnzPerRow, csarray=True)
k = 5
u = 0.1
eps = 0.05
learner = MaxAUCSquare(k)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = n
numRuns = 20
gi = numpy.random.rand(m)
gi /= gi.sum()
gp = numpy.random.rand(n)
gp /= gp.sum()
gq = numpy.random.rand(n)
gq /= gq.sum()
indPtr, colInds = SparseUtils.getOmegaListPtr(X)
for s in range(numRuns):
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
deltaU = numpy.zeros(U.shape)
for i in range(X.shape[0]):
deltaU[i, :] = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)
deltaU2 = numpy.zeros(U.shape)
eps = 10**-8
for i in range(m):
for j in range(k):
tempU = U.copy()
tempU[i,j] += eps
obj1 = learner.objective(indPtr, colInds, indPtr, colInds, tempU, V, gp, gq)
tempU = U.copy()
tempU[i,j] -= eps
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, tempU, V, gp, gq)
deltaU2[i,j] = (obj1-obj2)/(2*eps)
#deltaU2[i,:] = deltaU2[i,:]/numpy.linalg.norm(deltaU2[i,:])
#print(deltaU*100)
#print(deltaU2*100)
nptst.assert_almost_equal(deltaU, deltaU2, 3)
#Try r != 0 and rho > 0
for s in range(numRuns):
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
learner.rho = 0.1
deltaU = numpy.zeros(U.shape)
for i in range(X.shape[0]):
deltaU[i, :] = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)
deltaU2 = numpy.zeros(U.shape)
eps = 10**-9
for i in range(m):
for j in range(k):
tempU = U.copy()
tempU[i,j] += eps
obj1 = learner.objective(indPtr, colInds, indPtr, colInds, tempU, V, gp, gq)
tempU = U.copy()
tempU[i,j] -= eps
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, tempU, V, gp, gq)
deltaU2[i,j] = (obj1-obj2)/(2*eps)
nptst.assert_almost_equal(deltaU, deltaU2, 3)
#Try lmbda > 0
for s in range(numRuns):
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
learner.lmbdaU = 0.5
deltaU = numpy.zeros(U.shape)
for i in range(X.shape[0]):
deltaU[i, :] = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)
deltaU2 = numpy.zeros(U.shape)
eps = 10**-9
for i in range(m):
for j in range(k):
tempU = U.copy()
tempU[i,j] += eps
obj1 = learner.objective(indPtr, colInds, indPtr, colInds, tempU, V, gp, gq)
tempU = U.copy()
tempU[i,j] -= eps
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, tempU, V, gp, gq)
deltaU2[i,j] = (obj1-obj2)/(2*eps)
nptst.assert_almost_equal(deltaU, deltaU2, 3)
def testComputeV1V2(self):
m = 10
n = 20
nnzPerRow = 5
X = SparseUtils.generateSparseBinaryMatrix((m, n), nnzPerRow, csarray=True)
k = 5
learner = MaxAUCSquare(k)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = 20
numRuns = 500
gp = numpy.random.rand(n)
gp /= gp.sum()
gq = numpy.random.rand(n)
gq /= gq.sum()
permutedRowInds = numpy.arange(m, dtype=numpy.uint32)
permutedColInds = numpy.arange(n, dtype=numpy.uint32)
indPtr, colInds = SparseUtils.getOmegaListPtr(X)
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
V11 = numpy.zeros((m, k))
V21 = numpy.zeros((m, k))
W11 = numpy.zeros((m, k))
W21 = numpy.zeros((m, k))
for i in range(numRuns):
tempV1, tempV2, tempW1, tempW2 = learner.computeMeansVW(indPtr, colInds, U, V, permutedRowInds, permutedColInds, gp, gq)
V11 += tempV1
V21 += tempV2
W11 += tempW1
W21 += tempW2
V11 /= numRuns
V21 /= numRuns
W11 /= numRuns
W21 /= numRuns
#print(V11)
#print(V21)
#Now compute real solution
V12 = numpy.zeros((m, k))
V22 = numpy.zeros((m, k))
W12 = numpy.zeros((m, k))
W22 = numpy.zeros((m, k))
#The bootstrap sampling causes slight errors
for i in range(m):
normGp = 0
omegai = colInds[indPtr[i]:indPtr[i+1]]
for j in omegai:
V12[i, :] += V[j, :]*gp[j]
W12[i, :] += V[j, :]*gp[j]*(U[i, :].dot(V[j, :]))
normGp += gp[j]
V12[i, :] /= normGp
W12[i, :] /= normGp
normGq = 0
omegaBari = numpy.setdiff1d(numpy.arange(n, dtype=numpy.uint32), omegai, assume_unique=True)
for j in omegaBari:
V22[i, :] += V[j, :]*gq[j]
W22[i, :] += V[j, :]*gq[j]*(U[i, :].dot(V[j, :]))
normGq += gq[j]
V22[i, :] /= normGq
W22[i, :] /= normGq
#print(W21)
#print(W22)
nptst.assert_array_almost_equal(V11, V12, 1)
nptst.assert_array_almost_equal(V21, V22, 1)
nptst.assert_array_almost_equal(W11, W12, 1)
nptst.assert_array_almost_equal(W21, W22, 1)
def testObjectiveApprox(self):
"""
We'll test the case in which we apprormate using a large number of samples
for the AUC and see if we get close to the exact objective
"""
m = 20
n = 30
k = 3
X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)
learner = MaxAUCSquare(k)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = n
indPtr, colInds = SparseUtils.getOmegaListPtr(X)
U = numpy.random.rand(X.shape[0], k)
V = numpy.random.rand(X.shape[1], k)
numRuns = 100
numTests = 5
gi = numpy.random.rand(m)
gi /= gi.sum()
gp = numpy.random.rand(n)
gp /= gp.sum()
gq = numpy.random.rand(n)
gq /= gq.sum()
#gi = numpy.ones(m)
#gp = numpy.ones(n)
#gq = numpy.ones(n)
#Let's compare against using the exact derivative
for i in range(numTests):
obj = 0
for j in range(numRuns):
obj += learner.objectiveApprox(indPtr, colInds, indPtr,
colInds, U, V, gp, gq)
obj /= numRuns
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V,
gp, gq)
self.assertAlmostEquals(obj, obj2, 2)
learner.rho = 0.2
for i in range(numTests):
obj = 0
for j in range(numRuns):
obj += learner.objectiveApprox(indPtr, colInds, indPtr,
colInds, U, V, gp, gq)
obj /= numRuns
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V,
gp, gq)
self.assertAlmostEquals(obj, obj2, 2)
learner.lmbdaV = 0.2
for i in range(numTests):
obj = 0
for j in range(numRuns):
obj += learner.objectiveApprox(indPtr, colInds, indPtr,
colInds, U, V, gp, gq)
obj /= numRuns
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V,
gp, gq)
self.assertAlmostEquals(obj, obj2, 2)
#Check full and summary versions are the same
obj = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp, gq)
obj2 = learner.objective(indPtr, colInds, indPtr, colInds, U, V, gp,
gq)
self.assertAlmostEquals(obj, obj2, 2)
def testDerivativeV(self):
m = 10
n = 20
nnzPerRow = 5
X = SparseUtils.generateSparseBinaryMatrix((m, n),
nnzPerRow,
csarray=True)
for i in range(m):
X[i, 0] = 1
X[i, 1] = 0
k = 5
u = 0.1
w = 1 - u
eps = 0.05
learner = MaxAUCSquare(k, w)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = 100
numRuns = 20
indPtr, colInds = SparseUtils.getOmegaListPtr(X)
gp = numpy.random.rand(n)
gp /= gp.sum()
gq = numpy.random.rand(n)
gq /= gq.sum()
for s in range(numRuns):
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
deltaV = numpy.zeros(V.shape)
for j in range(n):
deltaV[j, :] = learner.derivativeVi(indPtr, colInds, U, V, gp,
gq, j)
deltaV2 = numpy.zeros(V.shape)
eps = 0.00001
for i in range(n):
for j in range(k):
tempV = V.copy()
tempV[i, j] += eps
obj1 = learner.objective(indPtr, colInds, indPtr, colInds,
U, tempV, gp, gq)
tempV = V.copy()
tempV[i, j] -= eps
obj2 = learner.objective(indPtr, colInds, indPtr, colInds,
U, tempV, gp, gq)
deltaV2[i, j] = (obj1 - obj2) / (2 * eps)
#deltaV2[i,:] = deltaV2[i,:]/numpy.linalg.norm(deltaV2[i,:])
nptst.assert_almost_equal(deltaV, deltaV2, 3)
#Try r != 0 and rho > 0
for s in range(numRuns):
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
learner.rho = 1.0
deltaV = numpy.zeros(V.shape)
for j in range(n):
deltaV[j, :] = learner.derivativeVi(indPtr, colInds, U, V, gp,
gq, j)
deltaV2 = numpy.zeros(V.shape)
for i in range(n):
for j in range(k):
tempV = V.copy()
tempV[i, j] += eps
obj1 = learner.objective(indPtr, colInds, indPtr, colInds,
U, tempV, gp, gq)
tempV = V.copy()
tempV[i, j] -= eps
obj2 = learner.objective(indPtr, colInds, indPtr, colInds,
U, tempV, gp, gq)
deltaV2[i, j] = (obj1 - obj2) / (2 * eps)
#deltaV2[i,:] = deltaV2[i,:]/numpy.linalg.norm(deltaV2[i,:])
nptst.assert_almost_equal(deltaV, deltaV2, 3)
#Try r != 0 and rho > 0
for s in range(numRuns):
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
learner.lmbdaV = 100
deltaV = numpy.zeros(V.shape)
for j in range(n):
deltaV[j, :] = learner.derivativeVi(indPtr, colInds, U, V, gp,
gq, j)
deltaV2 = numpy.zeros(V.shape)
for i in range(n):
for j in range(k):
tempV = V.copy()
tempV[i, j] += eps
obj1 = learner.objective(indPtr, colInds, indPtr, colInds,
U, tempV, gp, gq)
tempV = V.copy()
tempV[i, j] -= eps
obj2 = learner.objective(indPtr, colInds, indPtr, colInds,
U, tempV, gp, gq)
deltaV2[i, j] = (obj1 - obj2) / (2 * eps)
#deltaV2[i,:] = deltaV2[i,:]/numpy.linalg.norm(deltaV2[i,:])
nptst.assert_almost_equal(deltaV, deltaV2, 3)
def testDerivativeUiApprox(self):
"""
We'll test the case in which we apprormate using a large number of samples
for the AUC and see if we get close to the exact derivative
"""
m = 20
n = 30
k = 3
X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)
w = 0.1
learner = MaxAUCSquare(k, w)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = 10
U = numpy.random.rand(X.shape[0], k)
V = numpy.random.rand(X.shape[1], k)
gp = numpy.random.rand(n)
gp /= gp.sum()
gq = numpy.random.rand(n)
gq /= gq.sum()
numRuns = 200
numTests = 5
indPtr, colInds = SparseUtils.getOmegaListPtr(X)
permutedRowInds = numpy.arange(m, dtype=numpy.uint32)
permutedColInds = numpy.arange(n, dtype=numpy.uint32)
#Test with small number of AUC samples, but normalise
learner.numAucSamples = 50
numRuns = 200
for i in numpy.random.permutation(m)[0:numTests]:
U = numpy.random.rand(X.shape[0], k)
V = numpy.random.rand(X.shape[1], k)
du1 = numpy.zeros(k)
for j in range(numRuns):
VDot, VDotDot, WDot, WDotDot = learner.computeMeansVW(
indPtr, colInds, U, V, permutedRowInds, permutedColInds,
gp, gq)
du1 += learner.derivativeUiApprox(U, V, VDot, VDotDot, WDot,
WDotDot, i)
du1 /= numRuns
du2 = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)
#print(du1, du2)
print(du1 / numpy.linalg.norm(du1), du2 / numpy.linalg.norm(du2))
#print(numpy.linalg.norm(du1 - du2)/numpy.linalg.norm(du1))
nptst.assert_array_almost_equal(du1, du2, 2)
#Let's compare against using the exact derivative
for i in numpy.random.permutation(m)[0:numTests]:
U = numpy.random.rand(X.shape[0], k)
V = numpy.random.rand(X.shape[1], k)
du1 = numpy.zeros(k)
for j in range(numRuns):
VDot, VDotDot, WDot, WDotDot = learner.computeMeansVW(
indPtr, colInds, U, V, permutedRowInds, permutedColInds,
gp, gq)
du1 += learner.derivativeUiApprox(U, V, VDot, VDotDot, WDot,
WDotDot, i)
du1 /= numRuns
du2 = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)
print(du1 / numpy.linalg.norm(du1), du2 / numpy.linalg.norm(du2))
nptst.assert_array_almost_equal(du1, du2, 2)
learner.lmbdaV = 0.5
for i in numpy.random.permutation(m)[0:numTests]:
U = numpy.random.rand(X.shape[0], k)
V = numpy.random.rand(X.shape[1], k)
du1 = numpy.zeros(k)
for j in range(numRuns):
VDot, VDotDot, WDot, WDotDot = learner.computeMeansVW(
indPtr, colInds, U, V, permutedRowInds, permutedColInds,
gp, gq)
du1 += learner.derivativeUiApprox(U, V, VDot, VDotDot, WDot,
WDotDot, i)
du1 /= numRuns
du2 = learner.derivativeUi(indPtr, colInds, U, V, gp, gq, i)
nptst.assert_array_almost_equal(du1, du2, 2)
print(du1 / numpy.linalg.norm(du1), du2 / numpy.linalg.norm(du2))
def testComputeV1V2(self):
m = 10
n = 20
nnzPerRow = 5
X = SparseUtils.generateSparseBinaryMatrix((m, n),
nnzPerRow,
csarray=True)
k = 5
learner = MaxAUCSquare(k)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = 20
numRuns = 500
gp = numpy.random.rand(n)
gp /= gp.sum()
gq = numpy.random.rand(n)
gq /= gq.sum()
permutedRowInds = numpy.arange(m, dtype=numpy.uint32)
permutedColInds = numpy.arange(n, dtype=numpy.uint32)
indPtr, colInds = SparseUtils.getOmegaListPtr(X)
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
V11 = numpy.zeros((m, k))
V21 = numpy.zeros((m, k))
W11 = numpy.zeros((m, k))
W21 = numpy.zeros((m, k))
for i in range(numRuns):
tempV1, tempV2, tempW1, tempW2 = learner.computeMeansVW(
indPtr, colInds, U, V, permutedRowInds, permutedColInds, gp,
gq)
V11 += tempV1
V21 += tempV2
W11 += tempW1
W21 += tempW2
V11 /= numRuns
V21 /= numRuns
W11 /= numRuns
W21 /= numRuns
#print(V11)
#print(V21)
#Now compute real solution
V12 = numpy.zeros((m, k))
V22 = numpy.zeros((m, k))
W12 = numpy.zeros((m, k))
W22 = numpy.zeros((m, k))
#The bootstrap sampling causes slight errors
for i in range(m):
normGp = 0
omegai = colInds[indPtr[i]:indPtr[i + 1]]
for j in omegai:
V12[i, :] += V[j, :] * gp[j]
W12[i, :] += V[j, :] * gp[j] * (U[i, :].dot(V[j, :]))
normGp += gp[j]
V12[i, :] /= normGp
W12[i, :] /= normGp
normGq = 0
omegaBari = numpy.setdiff1d(numpy.arange(n, dtype=numpy.uint32),
omegai,
assume_unique=True)
for j in omegaBari:
V22[i, :] += V[j, :] * gq[j]
W22[i, :] += V[j, :] * gq[j] * (U[i, :].dot(V[j, :]))
normGq += gq[j]
V22[i, :] /= normGq
W22[i, :] /= normGq
#print(W21)
#print(W22)
nptst.assert_array_almost_equal(V11, V12, 1)
nptst.assert_array_almost_equal(V21, V22, 1)
nptst.assert_array_almost_equal(W11, W12, 1)
nptst.assert_array_almost_equal(W21, W22, 1)
def testDerivativeU(self):
m = 10
n = 20
nnzPerRow = 5
X = SparseUtils.generateSparseBinaryMatrix((m, n),
nnzPerRow,
csarray=True)
k = 5
u = 0.1
eps = 0.05
learner = MaxAUCSquare(k)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = n
numRuns = 20
gi = numpy.random.rand(m)
gi /= gi.sum()
gp = numpy.random.rand(n)
gp /= gp.sum()
gq = numpy.random.rand(n)
gq /= gq.sum()
indPtr, colInds = SparseUtils.getOmegaListPtr(X)
for s in range(numRuns):
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
deltaU = numpy.zeros(U.shape)
for i in range(X.shape[0]):
deltaU[i, :] = learner.derivativeUi(indPtr, colInds, U, V, gp,
gq, i)
deltaU2 = numpy.zeros(U.shape)
eps = 10**-8
for i in range(m):
for j in range(k):
tempU = U.copy()
tempU[i, j] += eps
obj1 = learner.objective(indPtr, colInds, indPtr, colInds,
tempU, V, gp, gq)
tempU = U.copy()
tempU[i, j] -= eps
obj2 = learner.objective(indPtr, colInds, indPtr, colInds,
tempU, V, gp, gq)
deltaU2[i, j] = (obj1 - obj2) / (2 * eps)
#deltaU2[i,:] = deltaU2[i,:]/numpy.linalg.norm(deltaU2[i,:])
#print(deltaU*100)
#print(deltaU2*100)
nptst.assert_almost_equal(deltaU, deltaU2, 3)
#Try r != 0 and rho > 0
for s in range(numRuns):
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
learner.rho = 0.1
deltaU = numpy.zeros(U.shape)
for i in range(X.shape[0]):
deltaU[i, :] = learner.derivativeUi(indPtr, colInds, U, V, gp,
gq, i)
deltaU2 = numpy.zeros(U.shape)
eps = 10**-9
for i in range(m):
for j in range(k):
tempU = U.copy()
tempU[i, j] += eps
obj1 = learner.objective(indPtr, colInds, indPtr, colInds,
tempU, V, gp, gq)
tempU = U.copy()
tempU[i, j] -= eps
obj2 = learner.objective(indPtr, colInds, indPtr, colInds,
tempU, V, gp, gq)
deltaU2[i, j] = (obj1 - obj2) / (2 * eps)
nptst.assert_almost_equal(deltaU, deltaU2, 3)
#Try lmbda > 0
for s in range(numRuns):
U = numpy.random.randn(m, k)
V = numpy.random.randn(n, k)
learner.lmbdaU = 0.5
deltaU = numpy.zeros(U.shape)
for i in range(X.shape[0]):
deltaU[i, :] = learner.derivativeUi(indPtr, colInds, U, V, gp,
gq, i)
deltaU2 = numpy.zeros(U.shape)
eps = 10**-9
for i in range(m):
for j in range(k):
tempU = U.copy()
tempU[i, j] += eps
obj1 = learner.objective(indPtr, colInds, indPtr, colInds,
tempU, V, gp, gq)
tempU = U.copy()
tempU[i, j] -= eps
obj2 = learner.objective(indPtr, colInds, indPtr, colInds,
tempU, V, gp, gq)
deltaU2[i, j] = (obj1 - obj2) / (2 * eps)
nptst.assert_almost_equal(deltaU, deltaU2, 3)