def leave_x1_out(self):
"""
Computes the leave-row-out cross-validation predictions. Here, all instances
related to a single object from domain 1 are left out together at a time.
Returns
-------
F : array, shape = [n_samples1*n_samples2]
Training set labels. Label for (X1[i], X2[j]) maps to
F[i + j*n_samples1] (column order).
"""
YU = self.Y * self.U
filteredevals2 = self.evals2 / (self.evals2 + self.regparam2)
foo = np.multiply(YU, filteredevals2.T)
foo = foo * self.U.T
foo = np.array(foo)
rlsparams = {}
rlsparams["regparam"] = self.regparam1
rlsparams["Y"] = foo
rlsparams["bias"] = 0.
if self.kernelmode:
rlsparams["X"] = np.array(self.K1)
rlsparams['kernel'] = 'PrecomputedKernel'
else:
rlsparams["X"] = np.array(self.X1)
ordinary_rls_for_rows = RLS(**rlsparams)
lro = ordinary_rls_for_rows.leave_one_out().ravel(order = 'F')
return lro
def leave_x2_out(self):
"""
Computes the leave-column-out cross-validation predictions. Here, all instances
related to a single object from domain 2 are left out together at a time.
Returns
-------
F : array, shape = [n_samples1*n_samples2]
Training set labels. Label for (X1[i], X2[j]) maps to
F[i + j*n_samples1] (column order).
"""
VTY = self.V.T * self.Y
filteredevals1 = self.evals1 / (self.evals1 + self.regparam1)
foo = np.multiply(VTY, filteredevals1)
foo = self.V * foo
foo = np.array(foo)
rlsparams = {}
rlsparams["regparam"] = self.regparam2
rlsparams["Y"] = foo.T
rlsparams["bias"] = 0.
if self.kernelmode:
rlsparams["X"] = np.array(self.K2)
rlsparams['kernel'] = 'PrecomputedKernel'
else:
rlsparams["X"] = np.array(self.X2)
ordinary_rls_for_columns = RLS(**rlsparams)
lco = ordinary_rls_for_columns.leave_one_out().T.ravel(order = 'F')
return lco
def leave_x2_out(self):
"""
Computes the leave-column-out cross-validation predictions. Here, all instances
related to a single object from domain 2 are left out together at a time.
Returns
-------
F : array, shape = [n_samples1*n_samples2]
Training set labels. Label for (X1[i], X2[j]) maps to
F[i + j*n_samples1] (column order).
"""
VTY = self.V.T * self.Y
filteredevals1 = self.evals1 / (self.evals1 + self.regparam1)
foo = np.multiply(VTY, filteredevals1)
foo = self.V * foo
foo = np.array(foo)
rlsparams = {}
rlsparams["regparam"] = self.regparam2
rlsparams["Y"] = foo.T
rlsparams["bias"] = 0.
if self.kernelmode:
rlsparams["X"] = np.array(self.K2)
rlsparams['kernel'] = 'PrecomputedKernel'
else:
rlsparams["X"] = np.array(self.X2)
ordinary_rls_for_columns = RLS(**rlsparams)
lco = ordinary_rls_for_columns.leave_one_out().T.ravel(order = 'F')
return lco
def leave_x1_out(self):
"""
Computes the leave-row-out cross-validation predictions. Here, all instances
related to a single object from domain 1 are left out together at a time.
Returns
-------
F : array, shape = [n_samples1*n_samples2]
Training set labels. Label for (X1[i], X2[j]) maps to
F[i + j*n_samples1] (column order).
"""
YU = self.Y * self.U
filteredevals2 = self.evals2 / (self.evals2 + self.regparam2)
foo = np.multiply(YU, filteredevals2.T)
foo = foo * self.U.T
foo = np.array(foo)
rlsparams = {}
rlsparams["regparam"] = self.regparam1
rlsparams["Y"] = foo
rlsparams["bias"] = 0.
if self.kernelmode:
rlsparams["X"] = np.array(self.K1)
rlsparams['kernel'] = 'PrecomputedKernel'
else:
rlsparams["X"] = np.array(self.X1)
ordinary_rls_for_rows = RLS(**rlsparams)
lro = ordinary_rls_for_rows.leave_one_out().ravel(order='F')
return lro
def train_rls():
X_train, Y_train, X_test, Y_test = load_housing()
#select randomly 100 basis vectors
indices = range(X_train.shape[0])
indices = random.sample(indices, 100)
basis_vectors = X_train[indices]
kernel = GaussianKernel(basis_vectors, gamma=0.00003)
K_train = kernel.getKM(X_train)
K_rr = kernel.getKM(basis_vectors)
K_test = kernel.getKM(X_test)
learner = RLS(K_train,
Y_train,
basis_vectors=K_rr,
kernel="PrecomputedKernel",
regparam=0.0003)
#Leave-one-out cross-validation predictions, this is fast due to
#computational short-cut
P_loo = learner.leave_one_out()
#Test set predictions
P_test = learner.predict(K_test)
print("leave-one-out error %f" % sqerror(Y_train, P_loo))
print("test error %f" % sqerror(Y_test, P_test))
#Sanity check, can we do better than predicting mean of training labels?
print("mean predictor %f" %
sqerror(Y_test,
np.ones(Y_test.shape) * np.mean(Y_train)))
def train_rls():
X_train, Y_train, X_test, Y_test = load_housing()
#select randomly 100 basis vectors
indices = range(X_train.shape[0])
indices = random.sample(indices, 100)
basis_vectors = X_train[indices]
kernel = GaussianKernel(basis_vectors, gamma=0.00003)
K_train = kernel.getKM(X_train)
K_rr = kernel.getKM(basis_vectors)
K_test = kernel.getKM(X_test)
learner = RLS(K_train, Y_train, basis_vectors = K_rr, kernel="PrecomputedKernel", regparam=0.0003)
#Leave-one-out cross-validation predictions, this is fast due to
#computational short-cut
P_loo = learner.leave_one_out()
#Test set predictions
P_test = learner.predict(K_test)
print("leave-one-out error %f" %sqerror(Y_train, P_loo))
print("test error %f" %sqerror(Y_test, P_test))
#Sanity check, can we do better than predicting mean of training labels?
print("mean predictor %f" %sqerror(Y_test, np.ones(Y_test.shape)*np.mean(Y_train)))
def test_two_step_rls(self):
regparam1 = 0.001
regparam2 = 10
#regparam1 = 1
#regparam2 = 1
K_train1, K_train2, Y_train, K_test1, K_test2, Y_test, X_train1, X_train2, X_test1, X_test2 \
= self.generate_xortask()
Y_train = Y_train.ravel(order = 'F')
Y_test = Y_test.ravel(order = 'F')
train_rows, train_columns = K_train1.shape[0], K_train2.shape[0]
#print K_train1.shape, K_train2.shape, K_test1.shape, K_test2.shape, train_rows, train_columns
trainlabelcount = train_rows * train_columns
#Train linear two-step RLS with data-matrices
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["X1"] = X_train1
params["X2"] = X_train2
params["Y"] = Y_train
linear_two_step_learner = TwoStepRLS(**params)
linear_twostepoutofsampleloo = linear_two_step_learner.out_of_sample_loo().reshape((train_rows, train_columns), order = 'F')
linear_lro = linear_two_step_learner.leave_x1_out()
linear_lco = linear_two_step_learner.leave_x2_out()
#Train kernel two-step RLS with pre-computed kernel matrices
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1
params["K2"] = K_train2
params["Y"] = Y_train
kernel_two_step_learner = TwoStepRLS(**params)
kernel_twostepoutofsampleloo = kernel_two_step_learner.out_of_sample_loo().reshape((train_rows, train_columns), order = 'F')
kernel_lro = kernel_two_step_learner.leave_x1_out()
kernel_lco = kernel_two_step_learner.leave_x2_out()
tspred = kernel_two_step_learner.predict(K_train1, K_train2)
#Train ordinary linear RLS in two steps for a reference
params = {}
params["regparam"] = regparam2
params["X"] = X_train2
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F').T
params['bias'] = 0
ordinary_linear_rls_first_step = RLS(**params)
firststeploo = ordinary_linear_rls_first_step.leave_one_out().T
params = {}
params["regparam"] = regparam1
params["X"] = X_train1
params["Y"] = firststeploo.reshape((train_rows, train_columns), order = 'F')
params['bias'] = 0
ordinary_linear_rls_second_step = RLS(**params)
secondsteploo_linear_rls = ordinary_linear_rls_second_step.leave_one_out()
#Train ordinary kernel RLS in two steps for a reference
params = {}
params["regparam"] = regparam2
params["X"] = K_train2
params['kernel'] = 'PrecomputedKernel'
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F').T
ordinary_kernel_rls_first_step = RLS(**params)
firststeploo = ordinary_kernel_rls_first_step.leave_one_out().T
params = {}
params["regparam"] = regparam1
params["X"] = K_train1
params["kernel"] = "PrecomputedKernel"
params["Y"] = firststeploo.reshape((train_rows, train_columns), order = 'F')
ordinary_kernel_rls_second_step = RLS(**params)
secondsteploo_kernel_rls = ordinary_kernel_rls_second_step.leave_one_out()
#Train ordinary kernel RLS in one step with the crazy kernel for a reference
params = {}
params["regparam"] = 1.
crazykernel = la.inv(regparam1 * regparam2 * np.kron(la.inv(K_train2), la.inv(K_train1))
+ regparam1 * np.kron(np.eye(K_train2.shape[0]), la.inv(K_train1))
+ regparam2 * np.kron(la.inv(K_train2), np.eye(K_train1.shape[0])))
params["X"] = crazykernel
params['kernel'] = 'PrecomputedKernel'
params["Y"] = Y_train
ordinary_one_step_kernel_rls_with_crazy_kernel = RLS(**params)
fooloo = ordinary_one_step_kernel_rls_with_crazy_kernel.leave_one_out()[0]
allinds = np.arange(trainlabelcount)
allinds_fortran_shaped = allinds.reshape((train_rows, train_columns), order = 'F')
hoinds = sorted(allinds_fortran_shaped[0].tolist() + allinds_fortran_shaped[1:, 0].tolist())
hocompl = sorted(list(set(allinds)-set(hoinds)))
fooholdout = ordinary_one_step_kernel_rls_with_crazy_kernel.holdout(hoinds)[0]
params = {}
params["regparam"] = 1.
params["X"] = crazykernel[np.ix_(hocompl, hocompl)]
params['kernel'] = 'PrecomputedKernel'
params["Y"] = Y_train[hocompl]
ordinary_one_step_kernel_rls_with_crazy_kernel = RLS(**params)
barholdout = ordinary_one_step_kernel_rls_with_crazy_kernel.predict(crazykernel[np.ix_([0], hocompl)])
params = {}
params["regparam"] = 1.
K_train1_cut = K_train1[np.ix_(range(1, K_train1.shape[0]), range(1, K_train1.shape[1]))]
K_train2_cut = K_train2[np.ix_(range(1, K_train2.shape[0]), range(1, K_train2.shape[1]))]
crazykernel_cut = la.inv(regparam1 * regparam2 * np.kron(la.inv(K_train2_cut), la.inv(K_train1_cut))
+ regparam1 * np.kron(np.eye(K_train2_cut.shape[0]), la.inv(K_train1_cut))
+ regparam2 * np.kron(la.inv(K_train2_cut), np.eye(K_train1_cut.shape[0])))
params["X"] = crazykernel_cut
params['kernel'] = 'PrecomputedKernel'
#params["Y"] = Y_train[hocompl]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[np.ix_(range(1, train_rows), range(1, train_columns))].ravel(order = 'F')
ordinary_one_step_kernel_rls_with_crazy_kernel = RLS(**params)
bazholdout = ordinary_one_step_kernel_rls_with_crazy_kernel.predict(
np.dot(np.dot(np.kron(K_train2[np.ix_([0], range(1, K_train2.shape[1]))], K_train1[np.ix_([0], range(1, K_train1.shape[1]))]),
la.inv(np.kron(K_train2_cut, K_train1_cut))),
crazykernel_cut))
#print fooholdout, 'fooholdout', barholdout, bazholdout
#Train linear two-step RLS without out-of-sample rows or columns for [0,0]
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["X1"] = X_train1[range(1, X_train1.shape[0])]
params["X2"] = X_train2[range(1, X_train2.shape[0])]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[np.ix_(range(1, train_rows), range(1, train_columns))].ravel(order = 'F')
linear_two_step_learner_00 = TwoStepRLS(**params)
linear_two_step_testpred_00 = linear_two_step_learner_00.predict(X_train1[0], X_train2[0])
#Train linear two-step RLS without out-of-sample rows or columns for [2,4]
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["X1"] = X_train1[[0, 1] + range(3, K_train1.shape[0])]
params["X2"] = X_train2[[0, 1, 2, 3] + range(5, K_train2.shape[0])]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[np.ix_([0, 1] + range(3, train_rows), [0, 1, 2, 3] + range(5, train_columns))].ravel(order = 'F')
linear_two_step_learner_24 = TwoStepRLS(**params)
linear_two_step_testpred_24 = linear_two_step_learner_24.predict(X_train1[2], X_train2[4])
#Train kernel two-step RLS without out-of-sample rows or columns for [0,0]
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1[np.ix_(range(1, K_train1.shape[0]), range(1, K_train1.shape[1]))]
params["K2"] = K_train2[np.ix_(range(1, K_train2.shape[0]), range(1, K_train2.shape[1]))]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[np.ix_(range(1, train_rows), range(1, train_columns))].ravel(order = 'F')
kernel_two_step_learner_00 = TwoStepRLS(**params)
kernel_two_step_testpred_00 = kernel_two_step_learner_00.predict(K_train1[range(1, K_train1.shape[0]), 0], K_train2[0, range(1, K_train2.shape[0])])
#Train kernel two-step RLS without out-of-sample rows or columns for [2,4]
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1[np.ix_([0, 1] + range(3, K_train1.shape[0]), [0, 1] + range(3, K_train1.shape[0]))]
params["K2"] = K_train2[np.ix_([0, 1, 2, 3] + range(5, K_train2.shape[0]), [0, 1, 2, 3] + range(5, K_train2.shape[0]))]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[np.ix_([0, 1] + range(3, train_rows), [0, 1, 2, 3] + range(5, train_columns))].ravel(order = 'F')
kernel_two_step_learner_24 = TwoStepRLS(**params)
kernel_two_step_testpred_24 = kernel_two_step_learner_24.predict(K_train1[[0, 1] + range(3, K_train1.shape[0]), 2], K_train2[4, [0, 1, 2, 3] + range(5, K_train2.shape[0])])
#Train kernel two-step RLS without out-of-sample row 0
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1[np.ix_(range(1, K_train1.shape[0]), range(1, K_train1.shape[1]))]
params["K2"] = K_train2
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[range(1, train_rows)].ravel(order = 'F')
kernel_two_step_learner_lro_0 = TwoStepRLS(**params)
kernel_two_step_testpred_lro_0 = kernel_two_step_learner_lro_0.predict(K_train1[range(1, K_train1.shape[0]), 0], K_train2)
print('')
print('Leave-row-out with linear two-step RLS:')
print(linear_lro.reshape((train_rows, train_columns), order = 'F')[0])
print('Leave-row-out with kernel two-step RLS:')
print(kernel_lro.reshape((train_rows, train_columns), order = 'F')[0])
print('Two-step RLS trained without the held-out row predictions for the row:')
print(kernel_two_step_testpred_lro_0)
np.testing.assert_almost_equal(linear_lro.reshape((train_rows, train_columns), order = 'F')[0], kernel_two_step_testpred_lro_0)
np.testing.assert_almost_equal(kernel_lro.reshape((train_rows, train_columns), order = 'F')[0], kernel_two_step_testpred_lro_0)
#Train kernel two-step RLS without out-of-sample column 0
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1
params["K2"] = K_train2[np.ix_(range(1, K_train2.shape[0]), range(1, K_train2.shape[1]))]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[:, range(1, train_columns)].ravel(order = 'F')
kernel_two_step_learner_lco_0 = TwoStepRLS(**params)
kernel_two_step_testpred_lco_0 = kernel_two_step_learner_lco_0.predict(K_train1, K_train2[range(1, K_train2.shape[0]), 0])
print('')
print('Leave-column-out with linear two-step RLS:')
print(linear_lco[range(train_rows)])
print('Leave-column-out with kernel two-step RLS:')
print(kernel_lco[range(train_rows)])
print('Two-step RLS trained without the held-out column predictions for the column:')
print(kernel_two_step_testpred_lco_0)
np.testing.assert_almost_equal(linear_lco[range(train_rows)], kernel_two_step_testpred_lco_0)
np.testing.assert_almost_equal(kernel_lco[range(train_rows)], kernel_two_step_testpred_lco_0)
print('')
print('Out-of-sample LOO: Stacked ordinary linear RLS LOO, Stacked ordinary kernel RLS LOO, linear two-step RLS OOSLOO, kernel two-step RLS OOSLOO, linear two-step RLS OOS-pred, kernel two-step RLS OOS-pred')
print('[0, 0]: ' + str(secondsteploo_linear_rls[0, 0])
+ ' ' + str(secondsteploo_kernel_rls[0, 0])
+ ' ' + str(linear_two_step_testpred_00)
+ ' ' + str(kernel_two_step_testpred_00)
+ ' ' + str(linear_twostepoutofsampleloo[0, 0])
+ ' ' + str(kernel_twostepoutofsampleloo[0, 0]))
print('[2, 4]: ' + str(secondsteploo_linear_rls[2, 4])
+ ' ' + str(secondsteploo_kernel_rls[2, 4])
+ ' ' + str(linear_two_step_testpred_24)
+ ' ' + str(kernel_two_step_testpred_24)
+ ' ' + str(linear_twostepoutofsampleloo[2, 4])
+ ' ' + str(kernel_twostepoutofsampleloo[2, 4]))
np.testing.assert_almost_equal(secondsteploo_linear_rls, secondsteploo_kernel_rls)
np.testing.assert_almost_equal(secondsteploo_linear_rls, linear_twostepoutofsampleloo)
np.testing.assert_almost_equal(secondsteploo_linear_rls, kernel_twostepoutofsampleloo)
np.testing.assert_almost_equal(secondsteploo_linear_rls[0, 0], linear_two_step_testpred_00)
np.testing.assert_almost_equal(secondsteploo_linear_rls[0, 0], kernel_two_step_testpred_00)
#Train kernel two-step RLS with pre-computed kernel matrices and with output at position [2, 4] changed
Y_24 = Y_train.copy()
Y_24 = Y_24.reshape((train_rows, train_columns), order = 'F')
Y_24[2, 4] = 55.
Y_24 = Y_24.ravel(order = 'F')
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1
params["K2"] = K_train2
params["Y"] = Y_24
kernel_two_step_learner_Y_24 = TwoStepRLS(**params)
kernel_two_step_testpred_Y_24 = kernel_two_step_learner_Y_24.predict(K_test1, K_test2)
kernel_two_step_learner_inSampleLOO_24a = kernel_two_step_learner.in_sample_loo().reshape((train_rows, train_columns), order = 'F')[2, 4]
kernel_two_step_learner_inSampleLOO_24b = kernel_two_step_learner_Y_24.in_sample_loo().reshape((train_rows, train_columns), order = 'F')[2, 4]
print('')
print('In-sample LOO: Kernel two-step RLS ISLOO with original outputs, Kernel two-step RLS ISLOO with modified output at [2, 4]')
print('[2, 4] ' + str(kernel_two_step_learner_inSampleLOO_24a) + ' ' + str(kernel_two_step_learner_inSampleLOO_24b))
np.testing.assert_almost_equal(kernel_two_step_learner_inSampleLOO_24a, kernel_two_step_learner_inSampleLOO_24b)
#Train kernel two-step RLS with pre-computed kernel matrices and with output at position [1, 1] changed
Y_00 = Y_train.copy()
Y_00 = Y_00.reshape((train_rows, train_columns), order = 'F')
Y_00[0, 0] = 55.
Y_00 = Y_00.ravel(order = 'F')
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1
params["K2"] = K_train2
params["Y"] = Y_00
kernel_two_step_learner_Y_00 = TwoStepRLS(**params)
kernel_two_step_testpred_Y_00 = kernel_two_step_learner_Y_00.predict(K_test1, K_test2)
kernel_two_step_learner_inSampleLOO_00a = kernel_two_step_learner.in_sample_loo()[0]
kernel_two_step_learner_inSampleLOO_00b = kernel_two_step_learner_Y_00.in_sample_loo()[0]
print('')
print('In-sample LOO: Kernel two-step RLS ISLOO with original outputs, Kernel two-step RLS ISLOO with modified output at [0, 0]')
print('[0, 0] ' + str(kernel_two_step_learner_inSampleLOO_00a) + ' ' + str(kernel_two_step_learner_inSampleLOO_00b))
np.testing.assert_almost_equal(kernel_two_step_learner_inSampleLOO_00a, kernel_two_step_learner_inSampleLOO_00b)
#Create symmetric data
K_train1, K_train2, Y_train, K_test1, K_test2, Y_test, X_train1, X_train2, X_test1, X_test2 \
= self.generate_xortask(
trainpos1 = 6,
trainneg1 = 7,
trainpos2 = 6,
trainneg2 = 7,
testpos1 = 26,
testneg1 = 27,
testpos2 = 25,
testneg2 = 25
)
K_train1 = K_train2
K_test1 = K_test2
Y_train = 0.5 * (Y_train + Y_train.T)
Y_train = Y_train.ravel(order = 'F')
Y_test = Y_test.ravel(order = 'F')
train_rows, train_columns = K_train1.shape[0], K_train2.shape[0]
test_rows, test_columns = K_test1.shape[0], K_test2.shape[0]
trainlabelcount = train_rows * train_columns
#Train symmetric kernel two-step RLS with pre-computed kernel matrices
params = {}
params["regparam1"] = regparam2
params["regparam2"] = regparam2
params["K1"] = K_train1
params["K2"] = K_train2
params["Y"] = Y_train
kernel_two_step_learner = TwoStepRLS(**params)
kernel_two_step_testpred = kernel_two_step_learner.predict(K_test1, K_test2).reshape((test_rows, test_columns), order = 'F')
#Train two-step RLS without out-of-sample rows or columns
rowind, colind = 2, 4
trainrowinds = range(K_train1.shape[0])
trainrowinds.remove(rowind)
trainrowinds.remove(colind)
traincolinds = range(K_train2.shape[0])
traincolinds.remove(rowind)
traincolinds.remove(colind)
params = {}
params["regparam1"] = regparam2
params["regparam2"] = regparam2
params["K1"] = K_train1[np.ix_(trainrowinds, trainrowinds)]
params["K2"] = K_train2[np.ix_(traincolinds, traincolinds)]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[np.ix_(trainrowinds, traincolinds)].ravel(order = 'F')
kernel_kron_learner = TwoStepRLS(**params)
kernel_kron_testpred = kernel_kron_learner.predict(K_train1[np.ix_([rowind], trainrowinds)], K_train2[np.ix_([colind], traincolinds)]).reshape((1, 1), order = 'F')
fcsho = kernel_two_step_learner.out_of_sample_loo_symmetric().reshape((train_rows, train_columns), order = 'F')
print('')
print('Symmetric double out-of-sample LOO: Test prediction, LOO')
print('[2, 4]: ' + str(kernel_kron_testpred[0, 0]) + ' ' + str(fcsho[2, 4]))
np.testing.assert_almost_equal(kernel_kron_testpred[0, 0], fcsho[2, 4])
def test_kron_rls(self):
regparam = 0.001
K_train1, K_train2, Y_train, K_test1, K_test2, Y_test, X_train1, X_train2, X_test1, X_test2 = self.generate_xortask()
Y_train = Y_train.ravel(order = 'F')
Y_test = Y_test.ravel(order = 'F')
train_rows, train_columns = K_train1.shape[0], K_train2.shape[0]
test_rows, test_columns = K_test1.shape[0], K_test2.shape[0]
trainlabelcount = train_rows * train_columns
#Train linear Kronecker RLS with data-matrices
params = {}
params["regparam"] = regparam
params["X1"] = X_train1
params["X2"] = X_train2
params["Y"] = Y_train
linear_kron_learner = KronRLS(**params)
linear_kron_testpred = linear_kron_learner.predict(X_test1, X_test2).reshape((test_rows, test_columns), order = 'F')
#Train kernel Kronecker RLS with pre-computed kernel matrices
params = {}
params["regparam"] = regparam
params["K1"] = K_train1
params["K2"] = K_train2
params["Y"] = Y_train
kernel_kron_learner = KronRLS(**params)
kernel_kron_testpred = kernel_kron_learner.predict(K_test1, K_test2).reshape((test_rows, test_columns), order = 'F')
#Train an ordinary RLS regressor for reference
K_Kron_train_x = np.kron(K_train2, K_train1)
params = {}
params["X"] = K_Kron_train_x
params["kernel"] = "PrecomputedKernel"
params["Y"] = Y_train.reshape(trainlabelcount, 1, order = 'F')
ordrls_learner = RLS(**params)
ordrls_learner.solve(regparam)
K_Kron_test_x = np.kron(K_test2, K_test1)
ordrls_testpred = ordrls_learner.predict(K_Kron_test_x)
ordrls_testpred = ordrls_testpred.reshape((test_rows, test_columns), order = 'F')
print('')
print('Prediction: linear KronRLS, kernel KronRLS, ordinary RLS')
print('[0, 0] ' + str(linear_kron_testpred[0, 0]) + ' ' + str(kernel_kron_testpred[0, 0]) + ' ' + str(ordrls_testpred[0, 0]))
print('[0, 1] ' + str(linear_kron_testpred[0, 1]) + ' ' + str(kernel_kron_testpred[0, 1]) + ' ' + str(ordrls_testpred[0, 1]))
print('[1, 0] ' + str(linear_kron_testpred[1, 0]) + ' ' + str(kernel_kron_testpred[1, 0]) + ' ' + str(ordrls_testpred[1, 0]))
print('Meanabsdiff: linear KronRLS - ordinary RLS, kernel KronRLS - ordinary RLS')
print(str(np.mean(np.abs(linear_kron_testpred - ordrls_testpred))) + ' ' + str(np.mean(np.abs(kernel_kron_testpred - ordrls_testpred))))
np.testing.assert_almost_equal(linear_kron_testpred, ordrls_testpred)
np.testing.assert_almost_equal(kernel_kron_testpred, ordrls_testpred)
print('')
ordrls_loopred = ordrls_learner.leave_one_out().reshape((train_rows, train_columns), order = 'F')
linear_kron_loopred = linear_kron_learner.in_sample_loo().reshape((train_rows, train_columns), order = 'F')
kernel_kron_loopred = kernel_kron_learner.in_sample_loo().reshape((train_rows, train_columns), order = 'F')
print('In-sample LOO: linear KronRLS, kernel KronRLS, ordinary RLS')
print('[0, 0] ' + str(linear_kron_loopred[0, 0]) + ' ' + str(kernel_kron_loopred[0, 0]) + ' ' + str(ordrls_loopred[0, 0]))
print('[0, 1] ' + str(linear_kron_loopred[0, 1]) + ' ' + str(kernel_kron_loopred[0, 1]) + ' ' + str(ordrls_loopred[0, 1]))
print('[1, 0] ' + str(linear_kron_loopred[1, 0]) + ' ' + str(kernel_kron_loopred[1, 0]) + ' ' + str(ordrls_loopred[1, 0]))
print('Meanabsdiff: linear KronRLS - ordinary RLS, kernel KronRLS - ordinary RLS')
print(str(np.mean(np.abs(linear_kron_loopred - ordrls_loopred))) + ' ' + str(np.mean(np.abs(kernel_kron_loopred - ordrls_loopred))))
np.testing.assert_almost_equal(linear_kron_loopred, ordrls_loopred)
np.testing.assert_almost_equal(kernel_kron_loopred, ordrls_loopred)
def test_two_step_rls(self):
regparam1 = 0.001
regparam2 = 10
#regparam1 = 1
#regparam2 = 1
K_train1, K_train2, Y_train, K_test1, K_test2, Y_test, X_train1, X_train2, X_test1, X_test2 \
= self.generate_xortask()
Y_train = Y_train.ravel(order = 'F')
Y_test = Y_test.ravel(order = 'F')
train_rows, train_columns = K_train1.shape[0], K_train2.shape[0]
#print K_train1.shape, K_train2.shape, K_test1.shape, K_test2.shape, train_rows, train_columns
trainlabelcount = train_rows * train_columns
row_hoinds = [1,2,4]
row_hocompl = sorted(list(set(range(train_rows))-set(row_hoinds)))
col_hoinds = [1,3,4,5]
col_hocompl = sorted(list(set(range(train_columns))-set(col_hoinds)))
hoinds = [1,2,4]
#Train linear two-step RLS with data-matrices
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["X1"] = X_train1
params["X2"] = X_train2
params["Y"] = Y_train
linear_two_step_learner = TwoStepRLS(**params)
linear_twostepoutofsampleloo = linear_two_step_learner.out_of_sample_loo().reshape((train_rows, train_columns), order = 'F')
linear_lro = linear_two_step_learner.leave_x1_out()
linear_lco = linear_two_step_learner.leave_x2_out()
linear_lmro = linear_two_step_learner.x1_kfold_cv([row_hoinds])
linear_lmco = linear_two_step_learner.x2_kfold_cv([col_hoinds])
linear_lmrco = linear_two_step_learner.out_of_sample_kfold_cv([row_hoinds], [col_hoinds])
#Train kernel two-step RLS with pre-computed kernel matrices
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1
params["K2"] = K_train2
params["Y"] = Y_train
kernel_two_step_learner = TwoStepRLS(**params)
kernel_twostepoutofsampleloo = kernel_two_step_learner.out_of_sample_loo().reshape((train_rows, train_columns), order = 'F')
kernel_lro = kernel_two_step_learner.leave_x1_out()
kernel_lco = kernel_two_step_learner.leave_x2_out()
kernel_lmro = linear_two_step_learner.x1_kfold_cv([row_hoinds])
kernel_lmco = kernel_two_step_learner.x2_kfold_cv([col_hoinds])
kernel_lmrco = kernel_two_step_learner.out_of_sample_kfold_cv([row_hoinds], [col_hoinds])
tspred = kernel_two_step_learner.predict(K_train1, K_train2)
#Train ordinary linear RLS in two steps for a reference
params = {}
params["regparam"] = regparam2
params["X"] = X_train2
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F').T
params['bias'] = 0
ordinary_linear_rls_first_step = RLS(**params)
firststeploo = ordinary_linear_rls_first_step.leave_one_out().T
params = {}
params["regparam"] = regparam1
params["X"] = X_train1
params["Y"] = firststeploo.reshape((train_rows, train_columns), order = 'F')
params['bias'] = 0
ordinary_linear_rls_second_step = RLS(**params)
secondsteploo_linear_rls = ordinary_linear_rls_second_step.leave_one_out()
#Train ordinary kernel RLS in two steps for a reference
params = {}
params["regparam"] = regparam2
params["X"] = K_train2
params['kernel'] = 'PrecomputedKernel'
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F').T
ordinary_kernel_rls_first_step = RLS(**params)
firststeploo = ordinary_kernel_rls_first_step.leave_one_out().T
params = {}
params["regparam"] = regparam1
params["X"] = K_train1
params["kernel"] = "PrecomputedKernel"
params["Y"] = firststeploo.reshape((train_rows, train_columns), order = 'F')
ordinary_kernel_rls_second_step = RLS(**params)
secondsteploo_kernel_rls = ordinary_kernel_rls_second_step.leave_one_out()
#Train ordinary kernel RLS in one step with the crazy kernel for a reference
params = {}
params["regparam"] = 1.
crazykernel = la.inv(regparam1 * regparam2 * np.kron(la.inv(K_train2), la.inv(K_train1))
+ regparam1 * np.kron(np.eye(K_train2.shape[0]), la.inv(K_train1))
+ regparam2 * np.kron(la.inv(K_train2), np.eye(K_train1.shape[0])))
params["X"] = crazykernel
params['kernel'] = 'PrecomputedKernel'
params["Y"] = Y_train
ordinary_one_step_kernel_rls_with_crazy_kernel_whole_data = RLS(**params)
crazyloo = ordinary_one_step_kernel_rls_with_crazy_kernel_whole_data.leave_one_out()
allinds = np.arange(trainlabelcount)
allinds_fortran_shaped = allinds.reshape((train_rows, train_columns), order = 'F')
#hoinds = sorted(allinds_fortran_shaped[0].tolist() + allinds_fortran_shaped[1:, 0].tolist())
hoinds = [1, 20, 90]
imp_row_hoinds, imp_col_hoinds = np.unravel_index(hoinds, (train_rows, train_columns), order = 'F')
#print(hoinds, imp_row_hoinds, imp_col_hoinds)
kernel_iscv = kernel_two_step_learner.in_sample_kfoldcv([(imp_row_hoinds, imp_col_hoinds)])
hocompl = sorted(list(set(allinds) - set(hoinds)))
crazy_ho = ordinary_one_step_kernel_rls_with_crazy_kernel_whole_data.holdout(hoinds)
params = {}
params["regparam"] = 1.
params["X"] = crazykernel[np.ix_(hocompl, hocompl)]
params['kernel'] = 'PrecomputedKernel'
params["Y"] = Y_train[hocompl]
ordinary_one_step_kernel_rls_with_crazy_kernel_without_ho_data = RLS(**params)
prediction_with_crazy_kernel = ordinary_one_step_kernel_rls_with_crazy_kernel_without_ho_data.predict(crazykernel[np.ix_(hoinds, hocompl)])
'''params = {}
params["regparam"] = 1.
K_train1_cut = K_train1[np.ix_(range(1, K_train1.shape[0]), range(1, K_train1.shape[1]))]
K_train2_cut = K_train2[np.ix_(range(1, K_train2.shape[0]), range(1, K_train2.shape[1]))]
crazykernel_cut = la.inv(regparam1 * regparam2 * np.kron(la.inv(K_train2_cut), la.inv(K_train1_cut))
+ regparam1 * np.kron(np.eye(K_train2_cut.shape[0]), la.inv(K_train1_cut))
+ regparam2 * np.kron(la.inv(K_train2_cut), np.eye(K_train1_cut.shape[0])))
params["X"] = crazykernel_cut
params['kernel'] = 'PrecomputedKernel'
#params["Y"] = Y_train[hocompl]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[np.ix_(range(1, train_rows), range(1, train_columns))].ravel(order = 'F')
ordinary_one_step_kernel_rls_with_crazy_kernel = RLS(**params)'''
print('In-sample hold-out, ordinary RLS with crazy kernel hold-out, ordinary RLS with crazy kernel prediction:\n', kernel_iscv[hoinds], crazy_ho, prediction_with_crazy_kernel)
np.testing.assert_almost_equal(kernel_iscv[hoinds], crazy_ho)
np.testing.assert_almost_equal(prediction_with_crazy_kernel, crazy_ho)
kernel_two_step_learner_inSampleLOO = kernel_two_step_learner.in_sample_loo()#.reshape((train_rows, train_columns), order = 'F')
print('')
print('In-sample LOO, ordinary RLS with crazy kernel LOO:\n', kernel_two_step_learner_inSampleLOO[5], crazyloo[5])
np.testing.assert_almost_equal( kernel_two_step_learner_inSampleLOO, crazyloo)
#Train linear two-step RLS without out-of-sample rows or columns for [0,0]
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["X1"] = X_train1[range(1, X_train1.shape[0])]
params["X2"] = X_train2[range(1, X_train2.shape[0])]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[np.ix_(range(1, train_rows), range(1, train_columns))].ravel(order = 'F')
linear_two_step_learner_00 = TwoStepRLS(**params)
linear_two_step_testpred_00 = linear_two_step_learner_00.predict(X_train1[0], X_train2[0])
#Train linear two-step RLS without out-of-sample rows or columns for [2,4]
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["X1"] = X_train1[[0, 1] + list(range(3, K_train1.shape[0]))]
params["X2"] = X_train2[[0, 1, 2, 3] + list(range(5, K_train2.shape[0]))]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[np.ix_([0, 1] + list(range(3, train_rows)), [0, 1, 2, 3] + list(range(5, train_columns)))].ravel(order = 'F')
linear_two_step_learner_24 = TwoStepRLS(**params)
linear_two_step_testpred_24 = linear_two_step_learner_24.predict(X_train1[2], X_train2[4])
#Train kernel two-step RLS without out-of-sample rows or columns for [0,0]
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1[np.ix_(range(1, K_train1.shape[0]), range(1, K_train1.shape[1]))]
params["K2"] = K_train2[np.ix_(range(1, K_train2.shape[0]), range(1, K_train2.shape[1]))]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[np.ix_(range(1, train_rows), range(1, train_columns))].ravel(order = 'F')
kernel_two_step_learner_00 = TwoStepRLS(**params)
kernel_two_step_testpred_00 = kernel_two_step_learner_00.predict(K_train1[range(1, K_train1.shape[0]), 0], K_train2[0, range(1, K_train2.shape[0])])
#Train kernel two-step RLS without out-of-sample rows or columns for [2,4]
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1[np.ix_([0, 1] + list(range(3, K_train1.shape[0])), [0, 1] + list(range(3, K_train1.shape[0])))]
params["K2"] = K_train2[np.ix_([0, 1, 2, 3] + list(range(5, K_train2.shape[0])), [0, 1, 2, 3] + list(range(5, K_train2.shape[0])))]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[np.ix_([0, 1] + list(range(3, train_rows)), [0, 1, 2, 3] + list(range(5, train_columns)))].ravel(order = 'F')
kernel_two_step_learner_24 = TwoStepRLS(**params)
kernel_two_step_testpred_24 = kernel_two_step_learner_24.predict(K_train1[2, [0, 1] + list(range(3, K_train1.shape[0]))], K_train2[4, [0, 1, 2, 3] + list(range(5, K_train2.shape[0]))])
#Train kernel two-step RLS without out-of-sample row 0
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1[np.ix_(range(1, K_train1.shape[0]), range(1, K_train1.shape[1]))]
params["K2"] = K_train2
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[range(1, train_rows)].ravel(order = 'F')
kernel_two_step_learner_lro_0 = TwoStepRLS(**params)
kernel_two_step_testpred_lro_0 = kernel_two_step_learner_lro_0.predict(K_train1[0, range(1, K_train1.shape[0])], K_train2)
print('')
print('Leave-row-out with linear two-step RLS:')
print(linear_lro.reshape((train_rows, train_columns), order = 'F')[0])
print('Leave-row-out with kernel two-step RLS:')
print(kernel_lro.reshape((train_rows, train_columns), order = 'F')[0])
print('Two-step RLS trained without the held-out row predictions for the row:')
print(kernel_two_step_testpred_lro_0)
np.testing.assert_almost_equal(linear_lro.reshape((train_rows, train_columns), order = 'F')[0], kernel_two_step_testpred_lro_0)
np.testing.assert_almost_equal(kernel_lro.reshape((train_rows, train_columns), order = 'F')[0], kernel_two_step_testpred_lro_0)
#Train kernel two-step RLS without out-of-sample rows 1,2 and 4
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1[np.ix_(row_hocompl, row_hocompl)]
params["K2"] = K_train2
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[row_hocompl].ravel(order = 'F')
kernel_two_step_learner_lmro = TwoStepRLS(**params)
kernel_two_step_testpred_lmro = kernel_two_step_learner_lmro.predict(K_train1[np.ix_(row_hoinds, row_hocompl)], K_train2)
print('')
print('Leave-multiple-rows-out with linear two-step RLS:')
print(linear_lmro.reshape((train_rows, train_columns), order = 'F')[row_hoinds])
print('Leave-multiple-rows-out with kernel two-step RLS:')
print(kernel_lmro.reshape((train_rows, train_columns), order = 'F')[row_hoinds])
print('Two-step RLS trained without the held-out rows predictions for the rows:')
print(kernel_two_step_testpred_lmro.reshape((len(row_hoinds), train_columns), order = 'F'))
np.testing.assert_almost_equal(linear_lmro.reshape((train_rows, train_columns), order = 'F')[row_hoinds], kernel_two_step_testpred_lmro.reshape((len(row_hoinds), train_columns), order = 'F'))
np.testing.assert_almost_equal(kernel_lmro.reshape((train_rows, train_columns), order = 'F')[row_hoinds], kernel_two_step_testpred_lmro.reshape((len(row_hoinds), train_columns), order = 'F'))
#Train kernel two-step RLS without out-of-sample column 0
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1
params["K2"] = K_train2[np.ix_(range(1, K_train2.shape[0]), range(1, K_train2.shape[1]))]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[:, range(1, train_columns)].ravel(order = 'F')
kernel_two_step_learner_lco_0 = TwoStepRLS(**params)
kernel_two_step_testpred_lco_0 = kernel_two_step_learner_lco_0.predict(K_train1, K_train2[0, range(1, K_train2.shape[0])])
print('')
print('Leave-column-out with linear two-step RLS:')
print(linear_lco[range(train_rows)])
print('Leave-column-out with kernel two-step RLS:')
print(kernel_lco[range(train_rows)])
print('Two-step RLS trained without the held-out column predictions for the column:')
print(kernel_two_step_testpred_lco_0)
np.testing.assert_almost_equal(linear_lco[range(train_rows)], kernel_two_step_testpred_lco_0)
np.testing.assert_almost_equal(kernel_lco[range(train_rows)], kernel_two_step_testpred_lco_0)
#Train kernel two-step RLS without out-of-sample columns 1, 3, 4 and 5
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1
params["K2"] = K_train2[np.ix_(col_hocompl, col_hocompl)]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[:, col_hocompl].ravel(order = 'F')
kernel_two_step_learner_lmco = TwoStepRLS(**params)
kernel_two_step_testpred_lmco = kernel_two_step_learner_lmco.predict(K_train1, K_train2[np.ix_(col_hoinds, col_hocompl)])
print('')
print('Leave-multiple-columns-out with linear two-step RLS:')
print(linear_lmco.reshape((train_rows, train_columns), order = 'F')[:, col_hoinds])
print('Leave-multiple-columns-out with kernel two-step RLS:')
print(kernel_lmco.reshape((train_rows, train_columns), order = 'F')[:, col_hoinds])
print('Two-step RLS trained without the held-out columns predictions for the columns:')
print(kernel_two_step_testpred_lmco.reshape((train_rows, len(col_hoinds)), order = 'F'))
np.testing.assert_almost_equal(linear_lmco.reshape((train_rows, train_columns), order = 'F')[:, col_hoinds], kernel_two_step_testpred_lmco.reshape((train_rows, len(col_hoinds)), order = 'F'))
np.testing.assert_almost_equal(kernel_lmco.reshape((train_rows, train_columns), order = 'F')[:, col_hoinds], kernel_two_step_testpred_lmco.reshape((train_rows, len(col_hoinds)), order = 'F'))
#np.testing.assert_almost_equal(linear_lmco[range(train_rows)], kernel_two_step_testpred_lmco)
#np.testing.assert_almost_equal(kernel_lmco[range(train_rows)], kernel_two_step_testpred_lmco)
print('')
print('Out-of-sample LOO: Stacked ordinary linear RLS LOO, Stacked ordinary kernel RLS LOO, linear two-step RLS OOSLOO, kernel two-step RLS OOSLOO, linear two-step RLS OOS-pred, kernel two-step RLS OOS-pred')
print('[0, 0]: ' + str(secondsteploo_linear_rls[0, 0])
+ ' ' + str(secondsteploo_kernel_rls[0, 0])
+ ' ' + str(linear_two_step_testpred_00)
+ ' ' + str(kernel_two_step_testpred_00)
+ ' ' + str(linear_twostepoutofsampleloo[0, 0])
+ ' ' + str(kernel_twostepoutofsampleloo[0, 0]))
print('[2, 4]: ' + str(secondsteploo_linear_rls[2, 4])
+ ' ' + str(secondsteploo_kernel_rls[2, 4])
+ ' ' + str(linear_two_step_testpred_24)
+ ' ' + str(kernel_two_step_testpred_24)
+ ' ' + str(linear_twostepoutofsampleloo[2, 4])
+ ' ' + str(kernel_twostepoutofsampleloo[2, 4]))
np.testing.assert_almost_equal(secondsteploo_linear_rls, secondsteploo_kernel_rls)
np.testing.assert_almost_equal(secondsteploo_linear_rls, linear_twostepoutofsampleloo)
np.testing.assert_almost_equal(secondsteploo_linear_rls, kernel_twostepoutofsampleloo)
np.testing.assert_almost_equal(secondsteploo_linear_rls[0, 0], linear_two_step_testpred_00)
np.testing.assert_almost_equal(secondsteploo_linear_rls[0, 0], kernel_two_step_testpred_00)
np.testing.assert_almost_equal(secondsteploo_linear_rls[2, 4], linear_two_step_testpred_24)
np.testing.assert_almost_equal(secondsteploo_linear_rls[2, 4], kernel_two_step_testpred_24)
#Train kernel two-step RLS without out-of-sample rows 1,2 and 4 as well as without out-of-sample columns 1, 3, 4 and 5
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1[np.ix_(row_hocompl, row_hocompl)]
params["K2"] = K_train2[np.ix_(col_hocompl, col_hocompl)]
params["Y"] = Y_train.reshape((train_rows, train_columns), order = 'F')[np.ix_(row_hocompl, col_hocompl)].ravel(order = 'F')
kernel_two_step_learner_lmrco = TwoStepRLS(**params)
kernel_two_step_testpred_lmrco = kernel_two_step_learner_lmrco.predict(K_train1[np.ix_(row_hoinds, row_hocompl)],
K_train2[np.ix_(col_hoinds, col_hocompl)])
print('')
print('Leave-multiple-rows-and-columns-out with linear two-step RLS:')
print(linear_lmrco.reshape((train_rows, train_columns), order = 'F')[np.ix_(row_hoinds, col_hoinds)])
print('Leave-multiple-rows-and-columns-out with kernel two-step RLS:')
print(kernel_lmrco.reshape((train_rows, train_columns), order = 'F')[np.ix_(row_hoinds, col_hoinds)])
print('Two-step RLS trained without the held-out rows and columns predictions for the held out block:')
print(kernel_two_step_testpred_lmrco.reshape((len(row_hoinds), len(col_hoinds)), order = 'F'))
#np.testing.assert_almost_equal(linear_lmro.reshape((train_rows, train_columns), order = 'F')[row_hoinds], kernel_two_step_testpred_lmrco.reshape((len(row_hoinds), train_columns), order = 'F'))
np.testing.assert_almost_equal(kernel_lmrco.reshape((train_rows, train_columns), order = 'F')[np.ix_(row_hoinds, col_hoinds)],
kernel_two_step_testpred_lmrco.reshape((len(row_hoinds), len(col_hoinds)), order = 'F'))
#Train kernel two-step RLS with pre-computed kernel matrices and with output at position [2, 4] changed
Y_24 = Y_train.copy()
Y_24 = Y_24.reshape((train_rows, train_columns), order = 'F')
Y_24[2, 4] = 55.
Y_24 = Y_24.ravel(order = 'F')
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1
params["K2"] = K_train2
params["Y"] = Y_24
kernel_two_step_learner_Y_24 = TwoStepRLS(**params)
kernel_two_step_testpred_Y_24 = kernel_two_step_learner_Y_24.predict(K_test1, K_test2)
kernel_two_step_learner_inSampleLOO_24a = kernel_two_step_learner.in_sample_loo().reshape((train_rows, train_columns), order = 'F')[2, 4]
kernel_two_step_learner_inSampleLOO_24b = kernel_two_step_learner_Y_24.in_sample_loo().reshape((train_rows, train_columns), order = 'F')[2, 4]
print('')
print('In-sample LOO: Kernel two-step RLS ISLOO with original outputs, Kernel two-step RLS ISLOO with modified output at [2, 4]')
print('[2, 4] ' + str(kernel_two_step_learner_inSampleLOO_24a) + ' ' + str(kernel_two_step_learner_inSampleLOO_24b))
np.testing.assert_almost_equal(kernel_two_step_learner_inSampleLOO_24a, kernel_two_step_learner_inSampleLOO_24b)
#Train kernel two-step RLS with pre-computed kernel matrices and with output at position [1, 1] changed
Y_00 = Y_train.copy()
Y_00 = Y_00.reshape((train_rows, train_columns), order = 'F')
Y_00[0, 0] = 55.
Y_00 = Y_00.ravel(order = 'F')
params = {}
params["regparam1"] = regparam1
params["regparam2"] = regparam2
params["K1"] = K_train1
params["K2"] = K_train2
params["Y"] = Y_00
kernel_two_step_learner_Y_00 = TwoStepRLS(**params)
kernel_two_step_testpred_Y_00 = kernel_two_step_learner_Y_00.predict(K_test1, K_test2)
kernel_two_step_learner_inSampleLOO_00a = kernel_two_step_learner.in_sample_loo()[0]
kernel_two_step_learner_inSampleLOO_00b = kernel_two_step_learner_Y_00.in_sample_loo()[0]
print('')
print('In-sample LOO: Kernel two-step RLS ISLOO with original outputs, Kernel two-step RLS ISLOO with modified output at [0, 0]')
print('[0, 0] ' + str(kernel_two_step_learner_inSampleLOO_00a) + ' ' + str(kernel_two_step_learner_inSampleLOO_00b))
np.testing.assert_almost_equal(kernel_two_step_learner_inSampleLOO_00a, kernel_two_step_learner_inSampleLOO_00b)
#Create symmetric data
K_train1, K_train2, Y_train, K_test1, K_test2, Y_test, X_train1, X_train2, X_test1, X_test2 \
= self.generate_xortask(
trainpos1 = 6,
trainneg1 = 7,
trainpos2 = 6,
trainneg2 = 7,
testpos1 = 26,
testneg1 = 27,
testpos2 = 25,
testneg2 = 25
)
K_train1 = K_train2
K_test1 = K_test2
X_train1 = X_train2
X_test1 = X_test2
Y_train_symm = 0.5 * (Y_train + Y_train.T)
Y_train_asymm = 0.5 * (Y_train - Y_train.T)
Y_train_symm = Y_train_symm.ravel(order = 'F')
Y_train_asymm = Y_train_asymm.ravel(order = 'F')
#Y_test = Y_test.ravel(order = 'F')
train_rows, train_columns = K_train1.shape[0], K_train2.shape[0]
#test_rows, test_columns = K_test1.shape[0], K_test2.shape[0]
trainlabelcount = train_rows * train_columns
def test_symm_and_asymm_cases(Y_train_symm_or_asymm):
#Train (anti-)symmetric kernel two-step RLS with pre-computed kernel matrices
params = {}
params["regparam1"] = regparam2
params["regparam2"] = regparam2
params["K1"] = K_train1
params["K2"] = K_train2
params["Y"] = Y_train_symm_or_asymm
kernel_two_step_learner_symmetric = TwoStepRLS(**params)
#kernel_two_step_testpred = kernel_two_step_learner.predict(K_test1, K_test2).reshape((test_rows, test_columns), order = 'F')
#Train (anti-)symmetric linear two-step RLS with data-matrices
params = {}
params["regparam1"] = regparam2
params["regparam2"] = regparam2
params["X1"] = X_train1
params["X2"] = X_train2
params["Y"] = Y_train_symm_or_asymm
linear_two_step_learner_symmetric = TwoStepRLS(**params)
#Train two-step RLS without out-of-sample rows or columns
rowind, colind = 2, 4
trainrowinds = list(range(K_train1.shape[0]))
trainrowinds.remove(rowind)
trainrowinds.remove(colind)
traincolinds = list(range(K_train2.shape[0]))
traincolinds.remove(rowind)
traincolinds.remove(colind)
params = {}
params["regparam1"] = regparam2
params["regparam2"] = regparam2
params["K1"] = K_train1[np.ix_(trainrowinds, trainrowinds)]
params["K2"] = K_train2[np.ix_(traincolinds, traincolinds)]
params["Y"] = Y_train_symm_or_asymm.reshape((train_rows, train_columns), order = 'F')[np.ix_(trainrowinds, traincolinds)].ravel(order = 'F')
kernel_kron_learner = TwoStepRLS(**params)
kernel_kron_testpred = kernel_kron_learner.predict(K_train1[np.ix_([rowind], trainrowinds)], K_train2[np.ix_([colind], traincolinds)]).reshape((1, 1), order = 'F')
fcsho = kernel_two_step_learner_symmetric.out_of_sample_loo_symmetric().reshape((train_rows, train_columns), order = 'F')
fcsho_linear = linear_two_step_learner_symmetric.out_of_sample_loo_symmetric().reshape((train_rows, train_columns), order = 'F')
print(fcsho)
print(kernel_kron_testpred)
print('')
print('Symmetric double out-of-sample LOO: Test prediction, LOO_kernel, LOO_linear')
print('[2, 4]: ' + str(kernel_kron_testpred[0, 0]) + ' ' + str(fcsho[2, 4]) + ' ' + str(fcsho_linear[2, 4]))
np.testing.assert_almost_equal(kernel_kron_testpred[0, 0], fcsho[2, 4])
np.testing.assert_almost_equal(kernel_kron_testpred[0, 0], fcsho_linear[2, 4])
#Train ordinary kernel RLS in one step with the crazy kernel and symmetric labels for a reference
params = {}
params["regparam"] = 1.
crazykernel = la.inv(regparam2 * regparam2 * np.kron(la.inv(K_train2), la.inv(K_train1))
+ regparam2 * np.kron(np.eye(K_train2.shape[0]), la.inv(K_train1))
+ regparam2 * np.kron(la.inv(K_train2), np.eye(K_train1.shape[0])))
params["X"] = crazykernel
params['kernel'] = 'PrecomputedKernel'
params["Y"] = Y_train_symm_or_asymm
ordinary_one_step_kernel_rls_with_crazy_kernel_whole_data_symmetric = RLS(**params)
allinds = np.arange(trainlabelcount)
allinds_fortran_shaped = allinds.reshape((train_rows, train_columns), order = 'F')
symmhoinds = [allinds_fortran_shaped[2, 3], allinds_fortran_shaped[3, 2]]
crazylto = ordinary_one_step_kernel_rls_with_crazy_kernel_whole_data_symmetric.holdout(symmhoinds)
print()
print('(anti-)symmetric hold-out with crazy kernel RLS, two-step symmetric in-sample LOO, ho')
print(crazylto)
fcsloo = kernel_two_step_learner_symmetric.in_sample_loo_symmetric()#.reshape((train_rows, train_columns), order = 'F')
#Not implemented yet
#fcsloo_linear = linear_two_step_learner_symmetric.in_sample_loo_symmetric()#.reshape((train_rows, train_columns), order = 'F')
print(fcsloo[symmhoinds[0]], fcsloo[symmhoinds[1]])
kernel_iscv_symmetric = kernel_two_step_learner_symmetric.in_sample_kfoldcv([([2, 3], [3, 2])])
print(kernel_iscv_symmetric[symmhoinds])#, kernel_iscv_symmetric[3, 2])
#print(kernel_two_step_learner_symmetric.leave_vertex_out())
test_symm_and_asymm_cases(Y_train_symm)
test_symm_and_asymm_cases(Y_train_asymm)
'''
def test_kron_rls(self):
regparam = 0.001
K_train1, K_train2, Y_train, K_test1, K_test2, Y_test, X_train1, X_train2, X_test1, X_test2 = (
self.generate_xortask()
)
Y_train = Y_train.ravel(order="F")
Y_test = Y_test.ravel(order="F")
train_rows, train_columns = K_train1.shape[0], K_train2.shape[0]
test_rows, test_columns = K_test1.shape[0], K_test2.shape[0]
trainlabelcount = train_rows * train_columns
# Train linear Kronecker RLS with data-matrices
params = {}
params["regparam"] = regparam
params["X1"] = X_train1
params["X2"] = X_train2
params["Y"] = Y_train
linear_kron_learner = KronRLS(**params)
linear_kron_testpred = linear_kron_learner.predict(X_test1, X_test2).reshape(
(test_rows, test_columns), order="F"
)
# Train kernel Kronecker RLS with pre-computed kernel matrices
params = {}
params["regparam"] = regparam
params["K1"] = K_train1
params["K2"] = K_train2
params["Y"] = Y_train
kernel_kron_learner = KronRLS(**params)
kernel_kron_testpred = kernel_kron_learner.predict(K_test1, K_test2).reshape(
(test_rows, test_columns), order="F"
)
# Train an ordinary RLS regressor for reference
K_Kron_train_x = np.kron(K_train2, K_train1)
params = {}
params["X"] = K_Kron_train_x
params["kernel"] = "PrecomputedKernel"
params["Y"] = Y_train.reshape(trainlabelcount, 1, order="F")
ordrls_learner = RLS(**params)
ordrls_learner.solve(regparam)
K_Kron_test_x = np.kron(K_test2, K_test1)
ordrls_testpred = ordrls_learner.predict(K_Kron_test_x)
ordrls_testpred = ordrls_testpred.reshape((test_rows, test_columns), order="F")
print("")
print("Prediction: linear KronRLS, kernel KronRLS, ordinary RLS")
print(
"[0, 0] "
+ str(linear_kron_testpred[0, 0])
+ " "
+ str(kernel_kron_testpred[0, 0])
+ " "
+ str(ordrls_testpred[0, 0])
)
print(
"[0, 1] "
+ str(linear_kron_testpred[0, 1])
+ " "
+ str(kernel_kron_testpred[0, 1])
+ " "
+ str(ordrls_testpred[0, 1])
)
print(
"[1, 0] "
+ str(linear_kron_testpred[1, 0])
+ " "
+ str(kernel_kron_testpred[1, 0])
+ " "
+ str(ordrls_testpred[1, 0])
)
print("Meanabsdiff: linear KronRLS - ordinary RLS, kernel KronRLS - ordinary RLS")
print(
str(np.mean(np.abs(linear_kron_testpred - ordrls_testpred)))
+ " "
+ str(np.mean(np.abs(kernel_kron_testpred - ordrls_testpred)))
)
np.testing.assert_almost_equal(linear_kron_testpred, ordrls_testpred)
np.testing.assert_almost_equal(kernel_kron_testpred, ordrls_testpred)
print("")
ordrls_loopred = ordrls_learner.leave_one_out().reshape((train_rows, train_columns), order="F")
linear_kron_loopred = linear_kron_learner.in_sample_loo().reshape((train_rows, train_columns), order="F")
kernel_kron_loopred = kernel_kron_learner.in_sample_loo().reshape((train_rows, train_columns), order="F")
print("In-sample LOO: linear KronRLS, kernel KronRLS, ordinary RLS")
print(
"[0, 0] "
+ str(linear_kron_loopred[0, 0])
+ " "
+ str(kernel_kron_loopred[0, 0])
+ " "
+ str(ordrls_loopred[0, 0])
)
print(
"[0, 1] "
+ str(linear_kron_loopred[0, 1])
+ " "
+ str(kernel_kron_loopred[0, 1])
+ " "
+ str(ordrls_loopred[0, 1])
)
print(
"[1, 0] "
+ str(linear_kron_loopred[1, 0])
+ " "
+ str(kernel_kron_loopred[1, 0])
+ " "
+ str(ordrls_loopred[1, 0])
)
print("Meanabsdiff: linear KronRLS - ordinary RLS, kernel KronRLS - ordinary RLS")
print(
str(np.mean(np.abs(linear_kron_loopred - ordrls_loopred)))
+ " "
+ str(np.mean(np.abs(kernel_kron_loopred - ordrls_loopred)))
)
np.testing.assert_almost_equal(linear_kron_loopred, ordrls_loopred)
np.testing.assert_almost_equal(kernel_kron_loopred, ordrls_loopred)
