def testScale(self):
"""
Look at the scales of the unnormalised gradients.
"""
m = 100
n = 400
k = 3
X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)
w = 0.1
eps = 0.001
learner = MaxAUCTanh(k, w)
learner.normalise = False
learner.lmbdaU = 1.0
learner.lmbdaV = 1.0
learner.rho = 1.0
learner.numAucSamples = 100
indPtr, colInds = SparseUtils.getOmegaListPtr(X)
r = numpy.random.rand(m)
U = numpy.random.rand(X.shape[0], k)
V = numpy.random.rand(X.shape[1], k)
gi = numpy.random.rand(m)
gi /= gi.sum()
gp = numpy.random.rand(n)
gp /= gp.sum()
gq = numpy.random.rand(n)
gq /= gq.sum()
permutedRowInds = numpy.array(numpy.random.permutation(m),
numpy.uint32)
permutedColInds = numpy.array(numpy.random.permutation(n),
numpy.uint32)
maxLocalAuc = MaxLocalAUC(k, w)
normGp, normGq = maxLocalAuc.computeNormGpq(indPtr, colInds, gp, gq, m)
normDui = 0
for i in range(m):
du = learner.derivativeUi(indPtr, colInds, U, V, r, gi, gp, gq, i)
normDui += numpy.linalg.norm(du)
normDui /= float(m)
print(normDui)
normDvi = 0
for i in range(n):
dv = learner.derivativeVi(indPtr, colInds, U, V, r, gi, gp, gq, i)
normDvi += numpy.linalg.norm(dv)
normDvi /= float(n)
print(normDvi)
def testScale(self):
"""
Look at the scales of the unnormalised gradients.
"""
m = 100
n = 400
k = 3
X = SparseUtils.generateSparseBinaryMatrix((m, n), k, csarray=True)
w = 0.1
eps = 0.001
learner = MaxAUCTanh(k, w)
learner.normalise = False
learner.lmbdaU = 1.0
learner.lmbdaV = 1.0
learner.rho = 1.0
learner.numAucSamples = 100
indPtr, colInds = SparseUtils.getOmegaListPtr(X)
r = numpy.random.rand(m)
U = numpy.random.rand(X.shape[0], k)
V = numpy.random.rand(X.shape[1], k)
gi = numpy.random.rand(m)
gi /= gi.sum()
gp = numpy.random.rand(n)
gp /= gp.sum()
gq = numpy.random.rand(n)
gq /= gq.sum()
permutedRowInds = numpy.array(numpy.random.permutation(m), numpy.uint32)
permutedColInds = numpy.array(numpy.random.permutation(n), numpy.uint32)
maxLocalAuc = MaxLocalAUC(k, w)
normGp, normGq = maxLocalAuc.computeNormGpq(indPtr, colInds, gp, gq, m)
normDui = 0
for i in range(m):
du = learner.derivativeUi(indPtr, colInds, U, V, r, gi, gp, gq, i)
normDui += numpy.linalg.norm(du)
normDui /= float(m)
print(normDui)
normDvi = 0
for i in range(n):
dv = learner.derivativeVi(indPtr, colInds, U, V, r, gi, gp, gq, i)
normDvi += numpy.linalg.norm(dv)
normDvi /= float(n)
print(normDvi)
def testDerivativeU(self):
m = 10
n = 20
nnzPerRow = 5
X = SparseUtils.generateSparseBinaryMatrix((m, n),
nnzPerRow,
csarray=True)
k = 5
u = 0.1
w = 1 - u
eps = 0.05
learner = MaxAUCTanh(k, w)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = n
numRuns = 20
r = numpy.zeros(m)
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 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 = MaxAUCTanh(k, w)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = 100
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)
permutedColInds = numpy.arange(n, dtype=numpy.uint32)
#Test with small number of AUC samples, but normalise
learner.numAucSamples = n
numRuns = 1000
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):
du1 += learner.derivativeUiApprox(indPtr, colInds, U, V, gp,
gq, permutedColInds, 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))
self.assertTrue(
numpy.linalg.norm(du1 - du2) / numpy.linalg.norm(du1) < 0.5)
#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):
du1 += learner.derivativeUiApprox(indPtr, colInds, U, V, gp,
gq, permutedColInds, 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
learner.rho = 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):
du1 += learner.derivativeUiApprox(indPtr, colInds, U, V, gp,
gq, permutedColInds, 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 testDerivativeU(self):
m = 10
n = 20
nnzPerRow = 5
X = SparseUtils.generateSparseBinaryMatrix((m, n), nnzPerRow, csarray=True)
k = 5
u = 0.1
w = 1-u
eps = 0.05
learner = MaxAUCTanh(k, w)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = n
numRuns = 20
r = numpy.zeros(m)
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 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 = MaxAUCTanh(k, w)
learner.normalise = False
learner.lmbdaU = 0
learner.lmbdaV = 0
learner.rho = 1.0
learner.numAucSamples = 100
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)
permutedColInds = numpy.arange(n, dtype=numpy.uint32)
#Test with small number of AUC samples, but normalise
learner.numAucSamples = n
numRuns = 1000
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):
du1 += learner.derivativeUiApprox(indPtr, colInds, U, V, gp, gq, permutedColInds, 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))
self.assertTrue(numpy.linalg.norm(du1 - du2)/numpy.linalg.norm(du1) < 0.5)
#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):
du1 += learner.derivativeUiApprox(indPtr, colInds, U, V, gp, gq, permutedColInds, 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
learner.rho = 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):
du1 += learner.derivativeUiApprox(indPtr, colInds, U, V, gp, gq, permutedColInds, 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))
