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1 | 1 | # pylint:disable=unused-variable
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2 | 2 | from functools import reduce
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| 3 | +from ..math import cartesian, kronecker |
3 | 4 | from operator import add
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4 | 5 | import pymc3 as pm
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5 | 6 | import theano
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|
10 | 11 |
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11 | 12 | np.random.seed(101)
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12 | 13 |
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| 14 | + |
13 | 15 | class TestZeroMean(object):
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14 | 16 | def test_value(self):
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15 | 17 | X = np.linspace(0, 1, 10)[:, None]
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@@ -222,6 +224,37 @@ def test_multiops(self):
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222 | 224 | npt.assert_allclose(np.diag(K2), K1d, atol=1e-5)
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223 | 225 |
|
224 | 226 |
|
| 227 | +class TestCovKron(object): |
| 228 | + def test_symprod_cov(self): |
| 229 | + X1 = np.linspace(0, 1, 10)[:, None] |
| 230 | + X2 = np.linspace(0, 1, 10)[:, None] |
| 231 | + X = cartesian(X1, X2) |
| 232 | + with pm.Model() as model: |
| 233 | + cov1 = pm.gp.cov.ExpQuad(1, 0.1) |
| 234 | + cov2 = pm.gp.cov.ExpQuad(1, 0.1) |
| 235 | + cov = pm.gp.cov.Kron([cov1, cov2]) |
| 236 | + K = theano.function([], cov(X))() |
| 237 | + npt.assert_allclose(K[0, 1], 1 * 0.53940, atol=1e-3) |
| 238 | + npt.assert_allclose(K[0, 11], 0.53940 * 0.53940, atol=1e-3) |
| 239 | + # check diagonal |
| 240 | + Kd = theano.function([], cov(X, diag=True))() |
| 241 | + npt.assert_allclose(np.diag(K), Kd, atol=1e-5) |
| 242 | + |
| 243 | + def test_multiops(self): |
| 244 | + X1 = np.linspace(0, 1, 3)[:, None] |
| 245 | + X21 = np.linspace(0, 1, 5)[:, None] |
| 246 | + X22 = np.linspace(0, 1, 4)[:, None] |
| 247 | + X2 = cartesian(X21, X22) |
| 248 | + X = cartesian(X1, X21, X22) |
| 249 | + with pm.Model() as model: |
| 250 | + cov1 = 3 + pm.gp.cov.ExpQuad(1, 0.1) + pm.gp.cov.ExpQuad(1, 0.1) * pm.gp.cov.ExpQuad(1, 0.1) |
| 251 | + cov2 = pm.gp.cov.ExpQuad(1, 0.1) * pm.gp.cov.ExpQuad(2, 0.1) |
| 252 | + cov = pm.gp.cov.Kron([cov1, cov2]) |
| 253 | + K_true = kronecker(theano.function([], cov1(X1))(), theano.function([], cov2(X2))()).eval() |
| 254 | + K = theano.function([], cov(X))() |
| 255 | + npt.assert_allclose(K_true, K) |
| 256 | + |
| 257 | + |
225 | 258 | class TestCovSliceDim(object):
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226 | 259 | def test_slice1(self):
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227 | 260 | X = np.linspace(0, 1, 30).reshape(10, 3)
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@@ -538,6 +571,74 @@ def func_twoarg(x, a, b):
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538 | 571 | assert func_twoarg(x, a, b) == func_twoarg2(x, args=(a, b))
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539 | 572 |
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540 | 573 |
|
| 574 | +class TestCoregion(object): |
| 575 | + def setup_method(self): |
| 576 | + self.nrows = 6 |
| 577 | + self.ncols = 3 |
| 578 | + self.W = np.random.rand(self.nrows, self.ncols) |
| 579 | + self.kappa = np.random.rand(self.nrows) |
| 580 | + self.B = np.dot(self.W, self.W.T) + np.diag(self.kappa) |
| 581 | + self.rand_rows = np.random.randint(0, self.nrows, size=(20, 1)) |
| 582 | + self.rand_cols = np.random.randint(0, self.ncols, size=(10, 1)) |
| 583 | + self.X = np.concatenate((self.rand_rows, np.random.rand(20, 1)), axis=1) |
| 584 | + self.Xs = np.concatenate((self.rand_cols, np.random.rand(10, 1)), axis=1) |
| 585 | + |
| 586 | + def test_full(self): |
| 587 | + B_mat = self.B[self.rand_rows, self.rand_rows.T] |
| 588 | + with pm.Model() as model: |
| 589 | + B = pm.gp.cov.Coregion(2, W=self.W, kappa=self.kappa, active_dims=[0]) |
| 590 | + npt.assert_allclose( |
| 591 | + B(np.array([[2, 1.5], [3, -42]])).eval(), |
| 592 | + self.B[2:4, 2:4] |
| 593 | + ) |
| 594 | + npt.assert_allclose(B(self.X).eval(), B_mat) |
| 595 | + |
| 596 | + def test_fullB(self): |
| 597 | + B_mat = self.B[self.rand_rows, self.rand_rows.T] |
| 598 | + with pm.Model() as model: |
| 599 | + B = pm.gp.cov.Coregion(1, B=self.B) |
| 600 | + npt.assert_allclose( |
| 601 | + B(np.array([[2], [3]])).eval(), |
| 602 | + self.B[2:4, 2:4] |
| 603 | + ) |
| 604 | + npt.assert_allclose(B(self.X).eval(), B_mat) |
| 605 | + |
| 606 | + def test_Xs(self): |
| 607 | + B_mat = self.B[self.rand_rows, self.rand_cols.T] |
| 608 | + with pm.Model() as model: |
| 609 | + B = pm.gp.cov.Coregion(2, W=self.W, kappa=self.kappa, active_dims=[0]) |
| 610 | + npt.assert_allclose( |
| 611 | + B(np.array([[2, 1.5]]), np.array([[3, -42]])).eval(), |
| 612 | + self.B[2, 3] |
| 613 | + ) |
| 614 | + npt.assert_allclose(B(self.X, self.Xs).eval(), B_mat) |
| 615 | + |
| 616 | + def test_diag(self): |
| 617 | + B_diag = np.diag(self.B)[self.rand_rows.ravel()] |
| 618 | + with pm.Model() as model: |
| 619 | + B = pm.gp.cov.Coregion(2, W=self.W, kappa=self.kappa, active_dims=[0]) |
| 620 | + npt.assert_allclose( |
| 621 | + B(np.array([[2, 1.5]]), diag=True).eval(), |
| 622 | + np.diag(self.B)[2] |
| 623 | + ) |
| 624 | + npt.assert_allclose(B(self.X, diag=True).eval(), B_diag) |
| 625 | + |
| 626 | + def test_raises(self): |
| 627 | + with pm.Model() as model: |
| 628 | + with pytest.raises(ValueError): |
| 629 | + B = pm.gp.cov.Coregion(2, W=self.W, kappa=self.kappa) |
| 630 | + |
| 631 | + def test_raises2(self): |
| 632 | + with pm.Model() as model: |
| 633 | + with pytest.raises(ValueError): |
| 634 | + B = pm.gp.cov.Coregion(1, W=self.W, kappa=self.kappa, B=self.B) |
| 635 | + |
| 636 | + def test_raises3(self): |
| 637 | + with pm.Model() as model: |
| 638 | + with pytest.raises(ValueError): |
| 639 | + B = pm.gp.cov.Coregion(1) |
| 640 | + |
| 641 | + |
541 | 642 | class TestMarginalVsLatent(object):
|
542 | 643 | R"""
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543 | 644 | Compare the logp of models Marginal, noise=0 and Latent.
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@@ -579,7 +680,7 @@ def testLatent2(self):
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579 | 680 | chol = np.linalg.cholesky(cov_func(self.X).eval())
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580 | 681 | y_rotated = np.linalg.solve(chol, self.y - 0.5)
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581 | 682 | latent_logp = model.logp({"f_rotated_": y_rotated, "p": self.pnew})
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582 |
| - npt.assert_allclose(latent_logp, self.logp, atol=0, rtol=1e-2) |
| 683 | + npt.assert_allclose(latent_logp, self.logp, atol=5) |
583 | 684 |
|
584 | 685 |
|
585 | 686 | class TestMarginalVsMarginalSparse(object):
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@@ -810,13 +911,59 @@ def testAdditiveTPRaises(self):
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810 | 911 | gp1 + gp2
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812 | 913 |
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| 914 | +class TestMarginalKron(object): |
| 915 | + def setup_method(self): |
| 916 | + self.Xs = [np.linspace(0, 1, 7)[:, None], |
| 917 | + np.linspace(0, 1, 5)[:, None], |
| 918 | + np.linspace(0, 1, 6)[:, None]] |
| 919 | + self.X = cartesian(*self.Xs) |
| 920 | + self.N = np.prod([len(X) for X in self.Xs]) |
| 921 | + self.y = np.random.randn(self.N) * 0.1 |
| 922 | + self.Xnews = [np.random.randn(5, 1), |
| 923 | + np.random.randn(5, 1), |
| 924 | + np.random.randn(5, 1)] |
| 925 | + self.Xnew = np.concatenate(tuple(self.Xnews), axis=1) |
| 926 | + self.sigma = 0.2 |
| 927 | + self.pnew = np.random.randn(len(self.Xnew))*0.01 |
| 928 | + ls = 0.2 |
| 929 | + with pm.Model() as model: |
| 930 | + self.cov_funcs = [pm.gp.cov.ExpQuad(1, ls), |
| 931 | + pm.gp.cov.ExpQuad(1, ls), |
| 932 | + pm.gp.cov.ExpQuad(1, ls)] |
| 933 | + cov_func = pm.gp.cov.Kron(self.cov_funcs) |
| 934 | + self.mean = pm.gp.mean.Constant(0.5) |
| 935 | + gp = pm.gp.Marginal(mean_func=self.mean, cov_func=cov_func) |
| 936 | + f = gp.marginal_likelihood("f", self.X, self.y, noise=self.sigma) |
| 937 | + p = gp.conditional("p", self.Xnew) |
| 938 | + self.mu, self.cov = gp.predict(self.Xnew) |
| 939 | + self.logp = model.logp({"p": self.pnew}) |
| 940 | + |
| 941 | + def testMarginalKronvsMarginalpredict(self): |
| 942 | + with pm.Model() as kron_model: |
| 943 | + kron_gp = pm.gp.MarginalKron(mean_func=self.mean, |
| 944 | + cov_funcs=self.cov_funcs) |
| 945 | + f = kron_gp.marginal_likelihood('f', self.Xs, self.y, |
| 946 | + sigma=self.sigma, shape=self.N) |
| 947 | + p = kron_gp.conditional('p', self.Xnew) |
| 948 | + mu, cov = kron_gp.predict(self.Xnew) |
| 949 | + npt.assert_allclose(mu, self.mu, atol=0, rtol=1e-2) |
| 950 | + npt.assert_allclose(cov, self.cov, atol=0, rtol=1e-2) |
| 951 | + |
| 952 | + def testMarginalKronvsMarginal(self): |
| 953 | + with pm.Model() as kron_model: |
| 954 | + kron_gp = pm.gp.MarginalKron(mean_func=self.mean, |
| 955 | + cov_funcs=self.cov_funcs) |
| 956 | + f = kron_gp.marginal_likelihood('f', self.Xs, self.y, |
| 957 | + sigma=self.sigma, shape=self.N) |
| 958 | + p = kron_gp.conditional('p', self.Xnew) |
| 959 | + kron_logp = kron_model.logp({'p': self.pnew}) |
| 960 | + npt.assert_allclose(kron_logp, self.logp, atol=0, rtol=1e-2) |
| 961 | + |
| 962 | + def testMarginalKronRaises(self): |
| 963 | + with pm.Model() as kron_model: |
| 964 | + gp1 = pm.gp.MarginalKron(mean_func=self.mean, |
| 965 | + cov_funcs=self.cov_funcs) |
| 966 | + gp2 = pm.gp.MarginalKron(mean_func=self.mean, |
| 967 | + cov_funcs=self.cov_funcs) |
| 968 | + with pytest.raises(TypeError): |
| 969 | + gp1 + gp2 |
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