def test_kernel(self):
#tests that learning with kernels works
for X in [self.Xtrain1, self.Xtrain2]:
for Y in [self.Ytrain1, self.Ytrain2]:
m = X.shape[0]
L = m * np.eye(m) - np.ones((m,m))
#Basic case
dual_rls = GlobalRankRLS(X, Y, kernel= "GaussianKernel", regparam=5.0, gamma=0.01)
kernel = GaussianKernel(X, gamma = 0.01)
K = kernel.getKM(X)
m = K.shape[0]
A = dual_rls.predictor.A
A2 = np.linalg.solve(np.dot(L, K) +5.0*np.eye(m), np.dot(L, Y) )
assert_allclose(A, A2)
#Fast regularization
dual_rls.solve(1000)
A = dual_rls.predictor.A
A2 = np.linalg.solve(np.dot(L, K) + 1000 * np.eye(m), np.dot(L, Y))
assert_allclose(A, A2)
#Precomputed kernel
dual_rls = GlobalRankRLS(K, Y, kernel="PrecomputedKernel", regparam = 1000)
assert_allclose(dual_rls.predictor.W, A2)
#Reduced set approximation
kernel = PolynomialKernel(X[self.bvectors], gamma=0.5, coef0 = 1.2, degree = 2)
Kr = kernel.getKM(X)
Krr = kernel.getKM(X[self.bvectors])
dual_rls = GlobalRankRLS(X, Y, kernel="PolynomialKernel", basis_vectors = X[self.bvectors], regparam = 200, gamma=0.5, coef0=1.2, degree = 2)
A = dual_rls.predictor.A
A2 = np.linalg.solve(np.dot(Kr.T, np.dot(L, Kr))+ 200 * Krr, np.dot(Kr.T, np.dot(L, Y)))
assert_allclose(A, A2)
dual_rls = GlobalRankRLS(Kr, Y, kernel="PrecomputedKernel", basis_vectors = Krr, regparam=200)
A = dual_rls.predictor.W
assert_allclose(A, A2)
def test_kernel(self):
#tests that learning with kernels works
for X in [self.Xtrain1, self.Xtrain2]:
for Y in [self.Ytrain1, self.Ytrain2]:
m = X.shape[0]
L = m * np.eye(m) - np.ones((m, m))
#Basic case
dual_rls = GlobalRankRLS(X,
Y,
kernel="GaussianKernel",
regparam=5.0,
gamma=0.01)
kernel = GaussianKernel(X, gamma=0.01)
K = kernel.getKM(X)
m = K.shape[0]
A = dual_rls.predictor.A
A2 = np.linalg.solve(
np.dot(L, K) + 5.0 * np.eye(m), np.dot(L, Y))
assert_allclose(A, A2)
#Fast regularization
dual_rls.solve(1000)
A = dual_rls.predictor.A
A2 = np.linalg.solve(
np.dot(L, K) + 1000 * np.eye(m), np.dot(L, Y))
assert_allclose(A, A2)
#Precomputed kernel
dual_rls = GlobalRankRLS(K,
Y,
kernel="PrecomputedKernel",
regparam=1000)
assert_allclose(dual_rls.predictor.W, A2)
#Reduced set approximation
kernel = PolynomialKernel(X[self.bvectors],
gamma=0.5,
coef0=1.2,
degree=2)
Kr = kernel.getKM(X)
Krr = kernel.getKM(X[self.bvectors])
dual_rls = GlobalRankRLS(X,
Y,
kernel="PolynomialKernel",
basis_vectors=X[self.bvectors],
regparam=200,
gamma=0.5,
coef0=1.2,
degree=2)
A = dual_rls.predictor.A
A2 = np.linalg.solve(
np.dot(Kr.T, np.dot(L, Kr)) + 200 * Krr,
np.dot(Kr.T, np.dot(L, Y)))
assert_allclose(A, A2)
dual_rls = GlobalRankRLS(Kr,
Y,
kernel="PrecomputedKernel",
basis_vectors=Krr,
regparam=200)
A = dual_rls.predictor.W
assert_allclose(A, A2)
def test_linear(self):
#Test that learning with linear kernel works correctly both
#with low and high-dimensional data
for X in [self.Xtrain1, self.Xtrain2]:
for Y in [self.Ytrain1, self.Ytrain2]:
#Basic case
m = X.shape[0]
L = m * np.eye(m) - np.ones((m, m))
primal_rls = GlobalRankRLS(X, Y, regparam=1.0, bias=0.)
W = primal_rls.predictor.W
d = X.shape[1]
W2 = np.linalg.solve(
np.dot(X.T, np.dot(L, X)) + np.eye(d),
np.dot(X.T, np.dot(L, Y)))
assert_allclose(W, W2)
#For RankRLS, bias should have no effect
primal_rls = GlobalRankRLS(X, Y, regparam=1.0, bias=5.)
W2 = primal_rls.predictor.W
assert_allclose(W, W2)
#Fast regularization
primal_rls.solve(10)
W = primal_rls.predictor.W
W2 = np.linalg.solve(
np.dot(X.T, np.dot(L, X)) + 10 * np.eye(d),
np.dot(X.T, np.dot(L, Y)))
assert_allclose(W, W2)
#reduced set approximation
#primal_rls = GlobalRankRLS(X, Y, basis_vectors = X[self.bvectors], regparam=5.0)
#W = primal_rls.predictor.W
K = np.dot(X, X.T)
Kr = K[:, self.bvectors]
Krr = K[np.ix_(self.bvectors, self.bvectors)]
A = np.linalg.solve(
np.dot(Kr.T, np.dot(L, Kr)) + 5.0 * Krr,
np.dot(Kr.T, np.dot(L, Y)))
W_reduced = np.dot(X[self.bvectors].T, A)
#assert_allclose(W, W_reduced)
#Pre-computed linear kernel, reduced set approximation
dual_rls = GlobalRankRLS(Kr,
Y,
kernel="PrecomputedKernel",
basis_vectors=Krr,
regparam=5.0)
W = np.dot(X[self.bvectors].T, dual_rls.predictor.W)
assert_allclose(W, W_reduced)
#Precomputed kernel matrix
dual_rls = GlobalRankRLS(K,
Y,
kernel="PrecomputedKernel",
regparam=0.01)
W = np.dot(X.T, dual_rls.predictor.W)
W2 = np.linalg.solve(
np.dot(X.T, np.dot(L, X)) + 0.01 * np.eye(d),
np.dot(X.T, np.dot(L, Y)))
assert_allclose(W, W2)
def test_linear(self):
#Test that learning with linear kernel works correctly both
#with low and high-dimensional data
for X in [self.Xtrain1, self.Xtrain2]:
for Y in [self.Ytrain1, self.Ytrain2]:
#Basic case
m = X.shape[0]
L = m * np.eye(m) - np.ones((m,m))
primal_rls = GlobalRankRLS(X, Y, regparam=1.0, bias=0.)
W = primal_rls.predictor.W
d = X.shape[1]
W2 = np.linalg.solve(np.dot(X.T, np.dot(L, X)) + np.eye(d), np.dot(X.T, np.dot(L, Y)))
assert_allclose(W, W2)
#For RankRLS, bias should have no effect
primal_rls = GlobalRankRLS(X, Y, regparam=1.0, bias=5.)
W2 = primal_rls.predictor.W
assert_allclose(W, W2)
#Fast regularization
primal_rls.solve(10)
W = primal_rls.predictor.W
W2 = np.linalg.solve(np.dot(X.T, np.dot(L, X)) + 10 * np.eye(d), np.dot(X.T, np.dot(L, Y)))
assert_allclose(W, W2)
#reduced set approximation
#primal_rls = GlobalRankRLS(X, Y, basis_vectors = X[self.bvectors], regparam=5.0)
#W = primal_rls.predictor.W
K = np.dot(X, X.T)
Kr = K[:, self.bvectors]
Krr = K[np.ix_(self.bvectors, self.bvectors)]
A = np.linalg.solve(np.dot(Kr.T, np.dot(L, Kr))+ 5.0 * Krr, np.dot(Kr.T, np.dot(L, Y)))
W_reduced = np.dot(X[self.bvectors].T, A)
#assert_allclose(W, W_reduced)
#Pre-computed linear kernel, reduced set approximation
dual_rls = GlobalRankRLS(Kr, Y, kernel="PrecomputedKernel", basis_vectors = Krr, regparam=5.0)
W = np.dot(X[self.bvectors].T, dual_rls.predictor.W)
assert_allclose(W, W_reduced)
#Precomputed kernel matrix
dual_rls = GlobalRankRLS(K, Y, kernel = "PrecomputedKernel", regparam=0.01)
W = np.dot(X.T, dual_rls.predictor.W)
W2 = np.linalg.solve(np.dot(X.T, np.dot(L, X)) + 0.01 * np.eye(d), np.dot(X.T, np.dot(L, Y)))
assert_allclose(W, W2)
def test_holdout(self):
for X in [self.Xtrain1, self.Xtrain2]:
for Y in [self.Ytrain1, self.Ytrain2]:
m = X.shape[0]
hoindices = [3, 5, 8, 10, 17, 21]
hocompl = list(set(range(m)) - set(hoindices))
#Holdout with linear kernel
rls1 = GlobalRankRLS(X, Y)
rls2 = GlobalRankRLS(X[hocompl], Y[hocompl])
P1 = rls1.holdout(hoindices)
P2 = rls2.predict(X[hoindices])
assert_allclose(P1, P2)
#Holdout with bias
rls1 = GlobalRankRLS(X, Y, bias=3.0)
rls2 = GlobalRankRLS(X[hocompl], Y[hocompl], bias=3.0)
P1 = rls1.holdout(hoindices)
P2 = rls2.predict(X[hoindices])
assert_allclose(P1, P2)
#Fast regularization
for i in range(-5, 5):
rls1.solve(2**i)
rls2.solve(2**i)
P1 = rls1.holdout(hoindices)
P2 = rls2.predict(X[hoindices])
assert_allclose(P1, P2)
#Kernel holdout
rls1 = GlobalRankRLS(X, Y, kernel="GaussianKernel", gamma=0.01)
rls2 = GlobalRankRLS(X[hocompl],
Y[hocompl],
kernel="GaussianKernel",
gamma=0.01)
P1 = rls1.holdout(hoindices)
P2 = rls2.predict(X[hoindices])
assert_allclose(P1, P2)
for i in range(-15, 15):
rls1.solve(2**i)
rls2.solve(2**i)
P1 = rls1.holdout(hoindices)
P2 = rls2.predict(X[hoindices])
assert_allclose(P1, P2)
#Incorrect indices
I = [0, 3, 100]
self.assertRaises(IndexError, rls1.holdout, I)
I = [-1, 0, 2]
self.assertRaises(IndexError, rls1.holdout, I)
I = [1, 1, 2]
self.assertRaises(IndexError, rls1.holdout, I)
def test_holdout(self):
for X in [self.Xtrain1, self.Xtrain2]:
for Y in [self.Ytrain1, self.Ytrain2]:
m = X.shape[0]
hoindices = [3, 5, 8, 10, 17, 21]
hocompl = list(set(range(m)) - set(hoindices))
#Holdout with linear kernel
rls1 = GlobalRankRLS(X, Y)
rls2 = GlobalRankRLS(X[hocompl], Y[hocompl])
P1 = rls1.holdout(hoindices)
P2 = rls2.predict(X[hoindices])
assert_allclose(P1, P2)
#Holdout with bias
rls1 = GlobalRankRLS(X, Y, bias = 3.0)
rls2 = GlobalRankRLS(X[hocompl], Y[hocompl], bias = 3.0)
P1 = rls1.holdout(hoindices)
P2 = rls2.predict(X[hoindices])
assert_allclose(P1, P2)
#Fast regularization
for i in range(-5, 5):
rls1.solve(2**i)
rls2.solve(2**i)
P1 = rls1.holdout(hoindices)
P2 = rls2.predict(X[hoindices])
assert_allclose(P1, P2)
#Kernel holdout
rls1 = GlobalRankRLS(X, Y, kernel = "GaussianKernel", gamma = 0.01)
rls2 = GlobalRankRLS(X[hocompl], Y[hocompl], kernel = "GaussianKernel", gamma = 0.01)
P1 = rls1.holdout(hoindices)
P2 = rls2.predict(X[hoindices])
assert_allclose(P1, P2)
for i in range(-15, 15):
rls1.solve(2**i)
rls2.solve(2**i)
P1 = rls1.holdout(hoindices)
P2 = rls2.predict(X[hoindices])
assert_allclose(P1, P2)
#Incorrect indices
I = [0, 3, 100]
self.assertRaises(IndexError, rls1.holdout, I)
I = [-1, 0, 2]
self.assertRaises(IndexError, rls1.holdout, I)
I = [1,1,2]
self.assertRaises(IndexError, rls1.holdout, I)
def testAllPairsRankRLS(self):
print(
"Testing the cross-validation routines of the GlobalRankRLS module.\n\n"
)
np.random.seed(100)
floattype = np.float64
m, n, h = 30, 200, 10
Xtrain = np.random.rand(m, n)
trainlabels = np.random.rand(m, h)
trainkm = np.dot(Xtrain, Xtrain.T)
ylen = 1
L = np.mat(m * np.eye(m) - np.ones((m, m), dtype=floattype))
hoindices = [5, 7]
hoindices3 = [5, 7, 9]
hocompl = list(set(range(m)) - set(hoindices))
hocompl3 = list(set(range(m)) - set(hoindices3))
loglambdas = range(-5, 5)
for j in range(0, len(loglambdas)):
regparam = 2.**loglambdas[j]
print("\nRegparam 2^%1d" % loglambdas[j])
Kcv = trainkm[np.ix_(hocompl, hocompl)]
Ycv = trainlabels[hocompl]
Ktest = trainkm[np.ix_(hocompl, hoindices)]
Xcv = Xtrain[hocompl]
Xtest = Xtrain[hoindices]
Lcv = np.mat((m - 2) * np.eye(m - 2) -
np.ones((m - 2, m - 2), dtype=floattype))
oind = 1
rpool = {}
rpool['Y'] = Ycv
rpool['X'] = Xcv
rpool['regparam'] = regparam
naivedualrls = GlobalRankRLS(**rpool)
naivedualrls.solve(regparam)
hopreds = []
hopred = naivedualrls.predictor.predict(Xtest)
print(str(hopred[0, oind]) + ' ' + str(hopred[1, oind]) + ' Naive')
hopreds.append((hopred[0, oind], hopred[1, oind]))
rpool = {}
rpool['Y'] = trainlabels
rpool['X'] = Xtrain
rpool['regparam'] = regparam
hodualrls = GlobalRankRLS(**rpool)
hodualrls.solve(regparam)
hopred_start, hopred_end = hodualrls.leave_pair_out(
np.array([hoindices[0], 1, 1, 2]),
np.array([hoindices[1], 2, 3, 3]))
print(
str(hopred_start[0][1]) + ' ' + str(hopred_end[0][1]) +
' Fast')
hopreds.append((hopred_start[0][1], hopred_end[0][1]))
self.assertAlmostEqual(hopreds[0][0], hopreds[1][0])
self.assertAlmostEqual(hopreds[0][1], hopreds[1][1])
#Test with single output just in case.
rpool = {}
rpool['Y'] = trainlabels[:, 1]
rpool['X'] = Xtrain
rpool['regparam'] = regparam
hodualrls = GlobalRankRLS(**rpool)
hodualrls.solve(regparam)
hopred_start, hopred_end = hodualrls.leave_pair_out(
np.array([hoindices[0], 1, 1, 2]),
np.array([hoindices[1], 2, 3, 3]))
#print(str(hopred_start[0]) + ' ' + str(hopred_end[0]) + ' Fast')
#Test with single output just in case.
rpool = {}
rpool['Y'] = trainlabels[:, 1]
rpool['X'] = Xtrain
rpool['regparam'] = regparam
hodualrls = GlobalRankRLS(**rpool)
hodualrls.solve(regparam)
hopred_start, hopred_end = hodualrls.leave_pair_out(
np.array([hoindices[0]]), np.array([hoindices[1]]))
#print(str(hopred_start) + ' ' + str(hopred_end) + ' Fast')
hopreds = []
rpool = {}
rpool['Y'] = trainlabels
rpool['X'] = Xtrain
rpool['regparam'] = regparam
hoprimalrls = GlobalRankRLS(**rpool)
hoprimalrls.solve(regparam)
hopred = hoprimalrls.holdout(hoindices)
print(str(hopred[0, oind]) + ' ' + str(hopred[1, oind]) + ' HO')
hopreds.append((hopred[0, oind], hopred[1, oind]))
hopred = Xtest * la.inv(Xcv.T * Lcv * Xcv + regparam *
np.mat(np.eye(n))) * Xcv.T * Lcv * Ycv
print(
str(hopred[0, oind]) + ' ' + str(hopred[1, oind]) +
' Dumb (primal)')
hopreds.append((hopred[0, oind], hopred[1, oind]))
hopred0 = hopreds.pop(0)
for hopred in hopreds:
self.assertAlmostEqual(hopred0[0], hopred[0])
self.assertAlmostEqual(hopred0[1], hopred[1])
def testAllPairsRankRLS(self):
print("Testing the cross-validation routines of the GlobalRankRLS module.\n\n")
np.random.seed(100)
floattype = np.float64
m, n, h = 30, 200, 10
Xtrain = np.random.rand(m, n)
trainlabels = np.random.rand(m, h)
trainkm = np.dot(Xtrain, Xtrain.T)
ylen = 1
L = np.mat(m * np.eye(m) - np.ones((m, m), dtype=floattype))
hoindices = [5, 7]
hoindices3 = [5, 7, 9]
hocompl = list(set(range(m)) - set(hoindices))
hocompl3 = list(set(range(m)) - set(hoindices3))
loglambdas = range(-5, 5)
for j in range(0, len(loglambdas)):
regparam = 2. ** loglambdas[j]
print("\nRegparam 2^%1d" % loglambdas[j])
Kcv = trainkm[np.ix_(hocompl, hocompl)]
Ycv = trainlabels[hocompl]
Ktest = trainkm[np.ix_(hocompl, hoindices)]
Xcv = Xtrain[hocompl]
Xtest = Xtrain[hoindices]
Lcv = np.mat((m - 2) * np.eye(m - 2) - np.ones((m - 2, m - 2), dtype=floattype))
oind = 1
rpool = {}
rpool['Y'] = Ycv
rpool['X'] = Xcv
rpool['regparam'] = regparam
naivedualrls = GlobalRankRLS(**rpool)
naivedualrls.solve(regparam)
hopreds = []
hopred = naivedualrls.predictor.predict(Xtest)
print(str(hopred[0, oind]) + ' ' + str(hopred[1, oind]) + ' Naive')
hopreds.append((hopred[0, oind], hopred[1, oind]))
rpool = {}
rpool['Y'] = trainlabels
rpool['X'] = Xtrain
rpool['regparam'] = regparam
hodualrls = GlobalRankRLS(**rpool)
hodualrls.solve(regparam)
hopred_start, hopred_end = hodualrls.leave_pair_out(np.array([hoindices[0], 1, 1, 2]), np.array([hoindices[1], 2, 3, 3]))
print(str(hopred_start[0][1]) + ' ' + str(hopred_end[0][1]) + ' Fast')
hopreds.append((hopred_start[0][1], hopred_end[0][1]))
self.assertAlmostEqual(hopreds[0][0], hopreds[1][0])
self.assertAlmostEqual(hopreds[0][1], hopreds[1][1])
#Test with single output just in case.
rpool = {}
rpool['Y'] = trainlabels[:, 1]
rpool['X'] = Xtrain
rpool['regparam'] = regparam
hodualrls = GlobalRankRLS(**rpool)
hodualrls.solve(regparam)
hopred_start, hopred_end = hodualrls.leave_pair_out(np.array([hoindices[0], 1, 1, 2]), np.array([hoindices[1], 2, 3, 3]))
#print(str(hopred_start[0]) + ' ' + str(hopred_end[0]) + ' Fast')
#Test with single output just in case.
rpool = {}
rpool['Y'] = trainlabels[:, 1]
rpool['X'] = Xtrain
rpool['regparam'] = regparam
hodualrls = GlobalRankRLS(**rpool)
hodualrls.solve(regparam)
hopred_start, hopred_end = hodualrls.leave_pair_out(np.array([hoindices[0]]), np.array([hoindices[1]]))
#print(str(hopred_start) + ' ' + str(hopred_end) + ' Fast')
hopreds = []
rpool = {}
rpool['Y'] = trainlabels
rpool['X'] = Xtrain
rpool['regparam'] = regparam
hoprimalrls = GlobalRankRLS(**rpool)
hoprimalrls.solve(regparam)
hopred = hoprimalrls.holdout(hoindices)
print(str(hopred[0, oind]) + ' ' + str(hopred[1, oind]) + ' HO')
hopreds.append((hopred[0, oind], hopred[1, oind]))
hopred = Xtest * la.inv(Xcv.T * Lcv * Xcv + regparam * np.mat(np.eye(n))) * Xcv.T * Lcv * Ycv
print(str(hopred[0, oind]) + ' ' + str(hopred[1, oind]) + ' Dumb (primal)')
hopreds.append((hopred[0, oind], hopred[1, oind]))
hopred0 = hopreds.pop(0)
for hopred in hopreds:
self.assertAlmostEqual(hopred0[0],hopred[0])
self.assertAlmostEqual(hopred0[1],hopred[1])