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_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)