def testOrdinalRegression(self):
m, n = 100, 300
for regparam in [0.00000001, 1, 100000000]:
#for regparam in [1000]:
Xtrain = np.mat(np.random.rand(n, m))
Y = np.mat(np.random.rand(m, 1))
rpool = {}
rpool['train_features'] = Xtrain.T
rpool['train_labels'] = Y
rpool['regparam'] = regparam
rpool["bias"] = 1.0
k = LinearKernel.createKernel(**rpool)
rpool['kernel_obj'] = k
rls = CGRankRLS.createLearner(**rpool)
rls.train()
model = rls.getModel()
W = model.W
In = np.mat(np.identity(n))
Im = np.mat(np.identity(m))
L = np.mat(Im-(1./m)*np.ones((m,m), dtype=np.float64))
G = Xtrain*L*Xtrain.T+regparam*In
W2 = np.squeeze(np.array(G.I*Xtrain*L*Y))
for i in range(W.shape[0]):
#for j in range(W.shape[1]):
# self.assertAlmostEqual(W[i,j],W2[i,j], places=5)
self.assertAlmostEqual(W[i], W2[i], places = 5)
def testOrdinalRegression(self):
m, n = 100, 300
for regparam in [0.00000001, 1, 100000000]:
#for regparam in [1000]:
Xtrain = np.mat(np.random.rand(n, m))
Y = np.mat(np.random.rand(m, 1))
rpool = {}
rpool['train_features'] = Xtrain.T
rpool['train_labels'] = Y
rpool['regparam'] = regparam
rpool["bias"] = 1.0
k = LinearKernel.createKernel(**rpool)
rpool['kernel_obj'] = k
rls = CGRankRLS.createLearner(**rpool)
rls.train()
model = rls.getModel()
W = model.W
In = np.mat(np.identity(n))
Im = np.mat(np.identity(m))
L = np.mat(Im - (1. / m) * np.ones((m, m), dtype=np.float64))
G = Xtrain * L * Xtrain.T + regparam * In
W2 = np.squeeze(np.array(G.I * Xtrain * L * Y))
for i in range(W.shape[0]):
#for j in range(W.shape[1]):
# self.assertAlmostEqual(W[i,j],W2[i,j], places=5)
self.assertAlmostEqual(W[i], W2[i], places=5)
def generate_xortask(self,
trainpos1 = 5,
trainneg1 = 5,
trainpos2 = 6,
trainneg2 = 7,
testpos1 = 26,
testneg1 = 27,
testpos2 = 25,
testneg2 = 25
):
np.random.seed(55)
X_train1, Y_train1 = self.generate_data(trainpos1, trainneg1, 5, 0, 1)
X_train2, Y_train2 = self.generate_data(trainpos2, trainneg2, 5, 4, 6)
X_test1, Y_test1 = self.generate_data(testpos1, testneg1, 5, 0, 1)
X_test2, Y_test2 = self.generate_data(testpos2, testneg2, 5, 4, 6)
#kernel1 = GaussianKernel.createKernel(gamma=0.01, train_features=X_train1)
kernel1 = LinearKernel.createKernel(train_features=X_train1)
K_train1 = kernel1.getKM(X_train1)
K_test1 = kernel1.getKM(X_test1)
#kernel2 = GaussianKernel.createKernel(gamma=0.01, train_features=X_train2)
kernel2 = LinearKernel.createKernel(train_features=X_train2)
K_train2 = kernel2.getKM(X_train2)
K_test2 = kernel2.getKM(X_test2)
#The function to be learned is a xor function on the class labels
#of the two classification problems
Y_train = -1.*np.ones((trainpos1+trainneg1, trainpos2+trainneg2))
for i in range(trainpos1+trainneg1):
for j in range(trainpos2+trainneg2):
if Y_train1[i,0] != Y_train2[j,0]:
Y_train[i, j] = 1.
Y_test = -1.*np.ones((testpos1+testneg1, testpos2+testneg2))
for i in range(testpos1+testneg1):
for j in range(testpos2+testneg2):
if Y_test1[i,0] != Y_test2[j,0]:
Y_test[i, j] = 1.
return K_train1, K_train2, Y_train, K_test1, K_test2, Y_test, X_train1, X_train2, X_test1, X_test2
def testPairwisePreferences(self):
m, n = 100, 300
for regparam in [0.00000001, 1, 100000000]:
Xtrain = np.mat(np.random.rand(n, m))
Y = np.mat(np.random.rand(m, 1))
pairs = []
for i in range(1000):
a = random.randint(0, m - 1)
b = random.randint(0, m - 1)
if Y[a] > Y[b]:
pairs.append((a, b))
else:
pairs.append((b, a))
pairs = np.array(pairs)
rpool = {}
rpool['train_features'] = Xtrain.T
#rpool['train_labels'] = Y
rpool['train_preferences'] = pairs
rpool['regparam'] = regparam
rpool["bias"] = 1.0
k = LinearKernel.createKernel(**rpool)
rpool['kernel_obj'] = k
rls = CGRankRLS.createLearner(**rpool)
rls.train()
model = rls.getModel()
W = model.W
In = np.mat(np.identity(n))
Im = np.mat(np.identity(m))
vals = np.concatenate([
np.ones((pairs.shape[0]), dtype=np.float64), -np.ones(
(pairs.shape[0]), dtype=np.float64)
])
row = np.concatenate(
[np.arange(pairs.shape[0]),
np.arange(pairs.shape[0])])
col = np.concatenate([pairs[:, 0], pairs[:, 1]])
coo = coo_matrix((vals, (row, col)),
shape=(pairs.shape[0], Xtrain.T.shape[0]))
L = (coo.T * coo).todense()
G = Xtrain * L * Xtrain.T + regparam * In
W2 = np.squeeze(
np.array(G.I * Xtrain * coo.T *
np.mat(np.ones((pairs.shape[0], 1)))))
for i in range(W.shape[0]):
#for j in range(W.shape[1]):
# self.assertAlmostEqual(W[i,j],W2[i,j], places=4)
self.assertAlmostEqual(W[i], W2[i], places=4)
def testPairwisePreferences(self):
m, n = 100, 300
Xtrain = np.mat(np.random.rand(m, n))
Xtest = np.mat(np.random.rand(5, n))
for regparam in [0.00000001, 1, 100000000]:
Y = np.mat(np.random.rand(m, 1))
pairs = []
for i in range(1000):
a = random.randint(0, m - 1)
b = random.randint(0, m - 1)
if Y[a] > Y[b]:
pairs.append((a, b))
else:
pairs.append((b, a))
pairs = np.array(pairs)
rpool = {}
rpool['train_features'] = Xtrain
#rpool['train_labels'] = Y
rpool['train_preferences'] = pairs
rpool['regparam'] = regparam
rpool["bias"] = 1.0
k = LinearKernel.createKernel(**rpool)
rpool['kernel_obj'] = k
rls = PPRankRLS.createLearner(**rpool)
rls.train()
model = rls.getModel()
W = model.W
In = np.mat(np.identity(n))
Im = np.mat(np.identity(m))
vals = np.concatenate([np.ones((pairs.shape[0]), dtype = np.float64), -np.ones((pairs.shape[0]), dtype = np.float64)])
row = np.concatenate([np.arange(pairs.shape[0]), np.arange(pairs.shape[0])])
col = np.concatenate([pairs[:, 0], pairs[:, 1]])
coo = coo_matrix((vals, (row, col)), shape = (pairs.shape[0], Xtrain.shape[0]))
L = (coo.T * coo).todense()
G = Xtrain.T * L * Xtrain + regparam * In
W2 = np.squeeze(np.array(G.I * Xtrain.T * coo.T * np.mat(np.ones((pairs.shape[0], 1)))))
P1 = model.predict(Xtest)
P2 = Xtest * np.mat(W2).T
#print P1
#print P2
for i in range(P1.shape[0]):
#self.assertAlmostEqual(W[i], W2[i], places = 4)
self.assertAlmostEqual(P1[i], P2[i,0], places = 3)
def testLabelRankRLS(self):
print
print
print
print
print "Testing the cross-validation routines of the LabelRankRLS module."
print
print
np.random.seed(100)
floattype = np.float64
m, n = 100, 400 #data, features
Xtrain = np.mat(np.random.rand(m, n))
K = Xtrain * Xtrain.T
ylen = 1
Y = np.mat(np.zeros((m, ylen), dtype=floattype))
Y[:, 0] = np.sum(Xtrain, 1)
objcount = 20
labelcount = 5
hoindices = range(labelcount)
hocompl = list(set(range(m)) - set(hoindices))
size = m
P = np.mat(np.zeros((m, objcount), dtype=np.float64))
Q = np.mat(np.zeros((objcount, m), dtype=np.float64))
qidlist = [0 for i in range(100)]
for h in range(5, 12):
qidlist[h] = 1
for h in range(12, 32):
qidlist[h] = 2
for h in range(32, 34):
qidlist[h] = 3
for h in range(34, 85):
qidlist[h] = 4
for h in range(85, 100):
qidlist[h] = 5
qidlist_cv = qidlist[5: len(qidlist)]
objcount = max(qidlist) + 1
P = np.mat(np.zeros((m, objcount), dtype=np.float64))
for i in range(m):
qid = qidlist[i]
P[i, qid] = 1.
labelcounts = np.sum(P, axis=0)
P = np.divide(P, np.sqrt(labelcounts))
D = np.mat(np.ones((1, m), dtype=np.float64))
L = np.multiply(np.eye(m), D) - P * P.T
Kcv = K[np.ix_(hocompl, hocompl)]
Ycv = Y[hocompl]
Ktest = K[np.ix_(hoindices, hocompl)]
Lcv = L[np.ix_(hocompl, hocompl)]
Xcv = Xtrain[hocompl]
#Pcv = P[hocompl]#KLUDGE!!!!!
Pcv = P[np.ix_(hocompl, range(1, P.shape[1]))]#KLUDGE!!!!!
Xtest = Xtrain[hoindices]
Yho = Y[hocompl]
rpool = {}
rpool["train_features"] = Xtrain
rpool["train_labels"] = Y
rpool["train_qids"] = mapQids(qidlist)
primalrls = LabelRankRLS.createLearner(**rpool)
rpool = {}
rpool["kernel_matrix"] = K
rpool["train_labels"] = Y
rpool["train_qids"] = mapQids(qidlist)
dualrls = LabelRankRLS.createLearner(**rpool)
rpool = {}
rpool['train_features'] = Xcv
rpool['train_labels'] = Yho
rpool['kernel_obj'] = LinearKernel.createKernel(**rpool)
rpool['train_qids'] = mapQids(qidlist_cv)
primalrls_naive = LabelRankRLS.createLearner(**rpool)
rpool = {}
rpool['kernel_matrix'] = Kcv
rpool['train_labels'] = Yho
rpool['train_features'] = Xcv
rpool['kernel_obj'] = LinearKernel.createKernel(**rpool)
rpool['train_qids'] = mapQids(qidlist_cv)
dualrls_naive = LabelRankRLS.createLearner(**rpool)
testkm = K[np.ix_(hocompl, hoindices)]
loglambdas = range(-5, 5)
for j in range(0, len(loglambdas)):
regparam = 2. ** loglambdas[j]
print
print "Regparam 2^%1d" % loglambdas[j]
print np.squeeze(np.array((testkm.T * la.inv(Lcv * Kcv + regparam * np.eye(Lcv.shape[0])) * Lcv * Yho).T)), 'Dumb HO'
predhos = []
primalrls_naive.solve(regparam)
predho = primalrls_naive.getModel().predict(Xtest)
print predho.T, 'Naive HO (primal)'
predhos.append(predho)
dualrls_naive.solve(regparam)
predho = dualrls_naive.getModel().predict(testkm.T)
print predho.T, 'Naive HO (dual)'
predhos.append(predho)
primalrls.solve(regparam)
predho = np.squeeze(primalrls.computeHO(hoindices))
print predho.T, 'Fast HO (primal)'
predhos.append(predho)
dualrls.solve(regparam)
predho = np.squeeze(dualrls.computeHO(hoindices))
print predho.T, 'Fast HO (dual)'
predhos.append(predho)
predho0 = predhos.pop(0)
for predho in predhos:
self.assertEqual(predho0.shape, predho.shape)
for row in range(predho.shape[0]):
#for col in range(predho.shape[1]):
# self.assertAlmostEqual(predho0[row,col],predho[row,col], places=5)
self.assertAlmostEqual(predho0[row],predho[row], places=5)
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
primal_rls = RLS(X, Y, regparam=1.0, bias=0.)
W = primal_rls.predictor.W
d = X.shape[1]
W2 = np.linalg.solve(np.dot(X.T, X) + np.eye(d), np.dot(X.T, Y))
assert_allclose(W, W2)
#Fast regularization algorithm
primal_rls.solve(10.)
W = primal_rls.predictor.W
W2 = np.linalg.solve(np.dot(X.T, X) + 10.*np.eye(d), np.dot(X.T, Y))
assert_allclose(W, W2)
#Bias term included
primal_rls = RLS(X, Y, regparam=1.0, bias=2.)
O = np.sqrt(2.) * np.ones((X.shape[0],1))
X_new = np.hstack((X, O))
W = primal_rls.predictor.W
W2 = np.linalg.solve(np.dot(X_new.T, X_new) + np.eye(d+1), np.dot(X_new.T, Y))
b = primal_rls.predictor.b
b2 = W2[-1]
W2 = W2[:-1]
assert_allclose(W, W2)
assert_allclose(b, np.sqrt(2) * b2)
#reduced set approximation
primal_rls = RLS(X, Y, basis_vectors = X[self.bvectors], regparam=5.0, bias=2.)
W = primal_rls.predictor.W
b = primal_rls.predictor.b
K = np.dot(X_new, X_new.T)
Kr = K[:, self.bvectors]
Krr = K[np.ix_(self.bvectors, self.bvectors)]
A = np.linalg.solve(np.dot(Kr.T, Kr)+ 5.0 * Krr, np.dot(Kr.T, Y))
W2 = np.dot(X_new[self.bvectors].T, A)
b2 = W2[-1]
W2 = W2[:-1]
assert_allclose(W, W2)
assert_allclose(b, np.sqrt(2) * b2)
#Using pre-computed linear kernel matrix
kernel = LinearKernel(X, bias = 2.)
K = kernel.getKM(X)
dual_rls = RLS(K, Y, kernel = "PrecomputedKernel", regparam=0.01)
W = np.dot(X_new.T, dual_rls.predictor.W)
b = W[-1]
W = W[:-1]
W2 = np.linalg.solve(np.dot(X_new.T, X_new) + 0.01 * np.eye(d+1), np.dot(X_new.T, Y))
b2 = W2[-1]
W2 = W2[:-1]
assert_allclose(W, W2)
assert_allclose(b, b2)
#Pre-computed linear kernel, reduced set approximation
kernel = LinearKernel(X[self.bvectors], bias = 2.)
dual_rls = RLS(kernel.getKM(X), Y, kernel="PrecomputedKernel", basis_vectors = kernel.getKM(X[self.bvectors]), regparam=5.0)
W = np.dot(X_new[self.bvectors].T, dual_rls.predictor.W)
b = W[-1]
W = W[:-1]
K = np.dot(X_new, X_new.T)
Kr = K[:, self.bvectors]
Krr = K[np.ix_(self.bvectors, self.bvectors)]
A = np.linalg.solve(np.dot(Kr.T, Kr)+ 5.0 * Krr, np.dot(Kr.T, Y))
W2 = np.dot(X_new[self.bvectors].T, A)
b2 = W2[-1]
W2 = W2[:-1]
assert_allclose(W, W2)
assert_allclose(b, b2)
def testLabelRankRLS(self):
print
print
print
print
print "Testing the cross-validation routines of the LabelRankRLS module."
print
print
np.random.seed(100)
floattype = np.float64
m, n = 100, 400 #data, features
Xtrain = np.mat(np.random.rand(m, n))
K = Xtrain * Xtrain.T
ylen = 1
Y = np.mat(np.zeros((m, ylen), dtype=floattype))
Y[:, 0] = np.sum(Xtrain, 1)
objcount = 20
labelcount = 5
hoindices = range(labelcount)
hocompl = list(set(range(m)) - set(hoindices))
size = m
P = np.mat(np.zeros((m, objcount), dtype=np.float64))
Q = np.mat(np.zeros((objcount, m), dtype=np.float64))
qidlist = [0 for i in range(100)]
for h in range(5, 12):
qidlist[h] = 1
for h in range(12, 32):
qidlist[h] = 2
for h in range(32, 34):
qidlist[h] = 3
for h in range(34, 85):
qidlist[h] = 4
for h in range(85, 100):
qidlist[h] = 5
qidlist_cv = qidlist[5:len(qidlist)]
objcount = max(qidlist) + 1
P = np.mat(np.zeros((m, objcount), dtype=np.float64))
for i in range(m):
qid = qidlist[i]
P[i, qid] = 1.
labelcounts = np.sum(P, axis=0)
P = np.divide(P, np.sqrt(labelcounts))
D = np.mat(np.ones((1, m), dtype=np.float64))
L = np.multiply(np.eye(m), D) - P * P.T
Kcv = K[np.ix_(hocompl, hocompl)]
Ycv = Y[hocompl]
Ktest = K[np.ix_(hoindices, hocompl)]
Lcv = L[np.ix_(hocompl, hocompl)]
Xcv = Xtrain[hocompl]
#Pcv = P[hocompl]#KLUDGE!!!!!
Pcv = P[np.ix_(hocompl, range(1, P.shape[1]))] #KLUDGE!!!!!
Xtest = Xtrain[hoindices]
Yho = Y[hocompl]
rpool = {}
rpool["train_features"] = Xtrain
rpool["train_labels"] = Y
rpool["train_qids"] = mapQids(qidlist)
primalrls = LabelRankRLS.createLearner(**rpool)
rpool = {}
rpool["kernel_matrix"] = K
rpool["train_labels"] = Y
rpool["train_qids"] = mapQids(qidlist)
dualrls = LabelRankRLS.createLearner(**rpool)
rpool = {}
rpool['train_features'] = Xcv
rpool['train_labels'] = Yho
rpool['kernel_obj'] = LinearKernel.createKernel(**rpool)
rpool['train_qids'] = mapQids(qidlist_cv)
primalrls_naive = LabelRankRLS.createLearner(**rpool)
rpool = {}
rpool['kernel_matrix'] = Kcv
rpool['train_labels'] = Yho
rpool['train_features'] = Xcv
rpool['kernel_obj'] = LinearKernel.createKernel(**rpool)
rpool['train_qids'] = mapQids(qidlist_cv)
dualrls_naive = LabelRankRLS.createLearner(**rpool)
testkm = K[np.ix_(hocompl, hoindices)]
loglambdas = range(-5, 5)
for j in range(0, len(loglambdas)):
regparam = 2.**loglambdas[j]
print
print "Regparam 2^%1d" % loglambdas[j]
print np.squeeze(
np.array((testkm.T *
la.inv(Lcv * Kcv + regparam * np.eye(Lcv.shape[0])) *
Lcv * Yho).T)), 'Dumb HO'
predhos = []
primalrls_naive.solve(regparam)
predho = primalrls_naive.getModel().predict(Xtest)
print predho.T, 'Naive HO (primal)'
predhos.append(predho)
dualrls_naive.solve(regparam)
predho = dualrls_naive.getModel().predict(testkm.T)
print predho.T, 'Naive HO (dual)'
predhos.append(predho)
primalrls.solve(regparam)
predho = np.squeeze(primalrls.computeHO(hoindices))
print predho.T, 'Fast HO (primal)'
predhos.append(predho)
dualrls.solve(regparam)
predho = np.squeeze(dualrls.computeHO(hoindices))
print predho.T, 'Fast HO (dual)'
predhos.append(predho)
predho0 = predhos.pop(0)
for predho in predhos:
self.assertEqual(predho0.shape, predho.shape)
for row in range(predho.shape[0]):
#for col in range(predho.shape[1]):
# self.assertAlmostEqual(predho0[row,col],predho[row,col], places=5)
self.assertAlmostEqual(predho0[row], predho[row], places=5)
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
primal_rls = RLS(X, Y, regparam=1.0, bias=0.)
W = primal_rls.predictor.W
d = X.shape[1]
W2 = np.linalg.solve(
np.dot(X.T, X) + np.eye(d), np.dot(X.T, Y))
assert_allclose(W, W2)
#Fast regularization algorithm
primal_rls.solve(10.)
W = primal_rls.predictor.W
W2 = np.linalg.solve(
np.dot(X.T, X) + 10. * np.eye(d), np.dot(X.T, Y))
assert_allclose(W, W2)
#Bias term included
primal_rls = RLS(X, Y, regparam=1.0, bias=2.)
O = np.sqrt(2.) * np.ones((X.shape[0], 1))
X_new = np.hstack((X, O))
W = primal_rls.predictor.W
W2 = np.linalg.solve(
np.dot(X_new.T, X_new) + np.eye(d + 1), np.dot(X_new.T, Y))
b = primal_rls.predictor.b
b2 = W2[-1]
W2 = W2[:-1]
assert_allclose(W, W2)
assert_allclose(b, np.sqrt(2) * b2)
#reduced set approximation
primal_rls = RLS(X,
Y,
basis_vectors=X[self.bvectors],
regparam=5.0,
bias=2.)
W = primal_rls.predictor.W
b = primal_rls.predictor.b
K = np.dot(X_new, X_new.T)
Kr = K[:, self.bvectors]
Krr = K[np.ix_(self.bvectors, self.bvectors)]
A = np.linalg.solve(
np.dot(Kr.T, Kr) + 5.0 * Krr, np.dot(Kr.T, Y))
W2 = np.dot(X_new[self.bvectors].T, A)
b2 = W2[-1]
W2 = W2[:-1]
assert_allclose(W, W2)
assert_allclose(b, np.sqrt(2) * b2)
#Using pre-computed linear kernel matrix
kernel = LinearKernel(X, bias=2.)
K = kernel.getKM(X)
dual_rls = RLS(K, Y, kernel="PrecomputedKernel", regparam=0.01)
W = np.dot(X_new.T, dual_rls.predictor.W)
b = W[-1]
W = W[:-1]
W2 = np.linalg.solve(
np.dot(X_new.T, X_new) + 0.01 * np.eye(d + 1),
np.dot(X_new.T, Y))
b2 = W2[-1]
W2 = W2[:-1]
assert_allclose(W, W2)
assert_allclose(b, b2)
#Pre-computed linear kernel, reduced set approximation
kernel = LinearKernel(X[self.bvectors], bias=2.)
dual_rls = RLS(kernel.getKM(X),
Y,
kernel="PrecomputedKernel",
basis_vectors=kernel.getKM(X[self.bvectors]),
regparam=5.0)
W = np.dot(X_new[self.bvectors].T, dual_rls.predictor.W)
b = W[-1]
W = W[:-1]
K = np.dot(X_new, X_new.T)
Kr = K[:, self.bvectors]
Krr = K[np.ix_(self.bvectors, self.bvectors)]
A = np.linalg.solve(
np.dot(Kr.T, Kr) + 5.0 * Krr, np.dot(Kr.T, Y))
W2 = np.dot(X_new[self.bvectors].T, A)
b2 = W2[-1]
W2 = W2[:-1]
assert_allclose(W, W2)
assert_allclose(b, b2)