Example #1
0
def test_sample():
    graph = Graph()
    x = array([1, 2, 3])[:, None]

    # Test that it produces random samples. Not sure how to test for
    # correctness.
    f1, e1 = GP(EQ(), graph=graph), GP(1e-1 * Delta(), graph=graph)
    f2, e2 = GP(EQ(), graph=graph), GP(1e-1 * Delta(), graph=graph)
    gpar = GPAR().add_layer(lambda: (f1, e1)).add_layer(lambda: (f2, e2))
    yield ge, B.sum(B.abs(gpar.sample(x) - gpar.sample(x))), 1e-3
    yield ge, \
          B.sum(B.abs(gpar.sample(x, latent=True) -
                      gpar.sample(x, latent=True))), \
          1e-3

    # Test that posterior latent samples are around the data that is
    # conditioned on.
    graph = Graph()
    f1, e1 = GP(EQ(), graph=graph), GP(1e-8 * Delta(), graph=graph)
    f2, e2 = GP(EQ(), graph=graph), GP(1e-8 * Delta(), graph=graph)
    gpar = GPAR().add_layer(lambda: (f1, e1)).add_layer(lambda: (f2, e2))
    y = gpar.sample(x, latent=True)
    gpar = gpar | (x, y)
    yield approx, gpar.sample(x), y, 3
    yield approx, gpar.sample(x, latent=True), y, 3
Example #2
0
def test_logpdf():
    graph = Graph()
    f1, e1 = GP(EQ(), graph=graph), GP(2e-1 * Delta(), graph=graph)
    f2, e2 = GP(Linear(), graph=graph), GP(1e-1 * Delta(), graph=graph)
    gpar = GPAR().add_layer(lambda: (f1, e1)).add_layer(lambda: (f2, e2))

    # Sample some data from GPAR.
    x = B.linspace(0, 2, 10, dtype=torch.float64)[:, None]
    y = gpar.sample(x, latent=True)

    # Compute logpdf.
    logpdf1 = (f1 + e1)(x).logpdf(y[:, 0])
    logpdf2 = (f2 + e2)(B.concat([x, y[:, 0:1]], axis=1)).logpdf(y[:, 1])

    # Test computation of GPAR.
    yield eq, gpar.logpdf(x, y), logpdf1 + logpdf2
    yield eq, gpar.logpdf(x, y, only_last_layer=True), logpdf2

    # Test resuming computation.
    x_int, x_ind_int = gpar.logpdf(x, y, return_inputs=True, outputs=[0])
    yield eq, gpar.logpdf(x_int, y, x_ind=x_ind_int, outputs=[1]), logpdf2

    # Test that sampling missing gives a stochastic estimate.
    y[1, 0] = np.nan
    yield ge, \
          B.abs(gpar.logpdf(x, y, sample_missing=True) -
                gpar.logpdf(x, y, sample_missing=True)).numpy(), \
          1e-3
Example #3
0
def test_conditioning():
    graph = Graph()
    f1, e1 = GP(EQ(), graph=graph), GP(1e-8 * Delta(), graph=graph)
    f2, e2 = GP(EQ(), graph=graph), GP(2e-8 * Delta(), graph=graph)
    gpar = GPAR().add_layer(lambda: (f1, e1)).add_layer(lambda: (f2, e2))

    x = array([[1], [2], [3]])
    y = array([[4, 5], [6, 7], [8, 9]])
    gpar = gpar | (x, y)

    # Extract posterior processes.
    f1_post, e1_post = gpar.layers[0]()
    f2_post, e2_post = gpar.layers[1]()

    # Test independence of noises.
    yield eq, graph.kernels[f1_post, e1_post], ZeroKernel()
    yield eq, graph.kernels[f2_post, e2_post], ZeroKernel()

    # Test form of noises.
    yield eq, e1.mean, e1_post.mean
    yield eq, e1.kernel, e1_post.kernel
    yield eq, e2.mean, e2_post.mean
    yield eq, e2.kernel, e2_post.kernel

    # Test posteriors.
    yield approx, f1_post.mean(x), y[:, 0:1]
    yield approx, f2_post.mean(B.concat([x, y[:, 0:1]], axis=1)), y[:, 1:2]
Example #4
0
def test_conditioning():
    graph = Graph()
    f1, e1 = GP(EQ(), graph=graph), GP(1e-8 * Delta(), graph=graph)
    f2, e2 = GP(EQ(), graph=graph), GP(2e-8 * Delta(), graph=graph)
    gpar = GPAR().add_layer(lambda: (f1, e1)).add_layer(lambda: (f2, e2))

    x = tensor([[1], [2], [3]])
    y = tensor([[4, 5],
                [6, 7],
                [8, 9]])
    gpar = gpar | (x, y)

    # Extract posterior processes.
    f1_post, e1_post = gpar.layers[0]()
    f2_post, e2_post = gpar.layers[1]()

    # Test independence of noises.
    assert graph.kernels[f1_post, e1_post] == ZeroKernel()
    assert graph.kernels[f2_post, e2_post] == ZeroKernel()

    # Test form of noises.
    assert e1.mean == e1_post.mean
    assert e1.kernel == e1_post.kernel
    assert e2.mean == e2_post.mean
    assert e2.kernel == e2_post.kernel

    # Test posteriors.
    approx(f1_post.mean(x), y[:, 0:1])
    approx(f2_post.mean(B.concat(x, y[:, 0:1], axis=1)), y[:, 1:2])
Example #5
0
def model(vs, m):
    """Construct model.

    Args:
        vs (:class:`varz.Vars`): Variable container.
        m (int): Number of latent processes.

    Returns:
        tuple: Tuple containing a list of the latent processes, the
            observation noise, and the noises on the latent processes.
    """
    g = Graph()

    # Observation noise:
    noise_obs = vs.bnd(0.1, name='noise_obs')

    def make_latent_process(i):
        # Long-term trend:
        variance = vs.bnd(0.9, name=f'{i}/long_term/var')
        scale = vs.bnd(2 * 30, name=f'{i}/long_term/scale')
        kernel = variance * EQ().stretch(scale)

        # Short-term trend:
        variance = vs.bnd(0.1, name=f'{i}/short_term/var')
        scale = vs.bnd(20, name=f'{i}/short_term/scale')
        kernel += variance * Matern12().stretch(scale)

        return GP(kernel, graph=g)

    # Latent processes:
    xs = [make_latent_process(i) for i in range(m)]

    # Latent noises:
    noises_latent = vs.bnd(0.1 * B.ones(m), name='noises_latent')

    return xs, noise_obs, noises_latent
Example #6
0
def test_obs():
    graph = Graph()
    f = GP(EQ(), graph=graph)
    e = GP(1e-8 * Delta(), graph=graph)

    # Check that it produces the correct observations.
    x = B.linspace(0, 0.1, 10, dtype=torch.float64)
    y = f(x).sample()

    # Set some observations to be missing.
    y_missing = y.clone()
    y_missing[::2] = np.nan

    # Check dense case.
    gpar = GPAR()
    obs = gpar._obs(x, None, y_missing, f, e)
    yield eq, type(obs), Obs
    yield approx, y, (f | obs).mean(x)

    # Check sparse case.
    gpar = GPAR(x_ind=x)
    obs = gpar._obs(x, x, y_missing, f, e)
    yield eq, type(obs), SparseObs
    yield approx, y, (f | obs).mean(x)
Example #7
0
def test_update_inputs():
    graph = Graph()
    f = GP(EQ(), graph=graph)

    x = array([[1], [2], [3]])
    y = array([[4], [5], [6]])
    res = B.concat([x, y], axis=1)
    x_ind = array([[6], [7]])
    res_ind = array([[6, 0], [7, 0]])

    # Check vanilla case.
    gpar = GPAR(x_ind=x_ind)
    yield allclose, gpar._update_inputs(x, x_ind, y, f, None), (res, res_ind)

    # Check imputation with prior.
    gpar = GPAR(impute=True, x_ind=x_ind)
    this_y = y.clone()
    this_y[1] = np.nan
    this_res = res.clone()
    this_res[1, 1] = 0
    yield allclose, \
          gpar._update_inputs(x, x_ind, this_y, f, None), \
          (this_res, res_ind)

    # Check replacing with prior.
    gpar = GPAR(replace=True, x_ind=x_ind)
    this_y = y.clone()
    this_y[1] = np.nan
    this_res = res.clone()
    this_res[0, 1] = 0
    this_res[1, 1] = np.nan
    this_res[2, 1] = 0
    yield allclose, \
          gpar._update_inputs(x, x_ind, this_y, f, None), \
          (this_res, res_ind)

    # Check imputation and replacing with prior.
    gpar = GPAR(impute=True, replace=True, x_ind=x_ind)
    this_res = res.clone()
    this_res[:, 1] = 0
    yield allclose, \
          gpar._update_inputs(x, x_ind, y, f, None), \
          (this_res, res_ind)

    # Construct observations and update result for inducing points.
    obs = Obs(f(array([1, 2, 3, 6, 7])), array([9, 10, 11, 12, 13]))
    res_ind = array([[6, 12], [7, 13]])

    # Check imputation with posterior.
    gpar = GPAR(impute=True, x_ind=x_ind)
    this_y = y.clone()
    this_y[1] = np.nan
    this_res = res.clone()
    this_res[1, 1] = 10
    yield allclose, \
          gpar._update_inputs(x, x_ind, this_y, f, obs), \
          (this_res, res_ind)

    # Check replacing with posterior.
    gpar = GPAR(replace=True, x_ind=x_ind)
    this_y = y.clone()
    this_y[1] = np.nan
    this_res = res.clone()
    this_res[0, 1] = 9
    this_res[1, 1] = np.nan
    this_res[2, 1] = 11
    yield allclose, \
          gpar._update_inputs(x, x_ind, this_y, f, obs), \
          (this_res, res_ind)

    # Check imputation and replacing with posterior.
    gpar = GPAR(impute=True, replace=True, x_ind=x_ind)
    this_res = res.clone()
    this_res[0, 1] = 9
    this_res[1, 1] = 10
    this_res[2, 1] = 11
    yield allclose, \
          gpar._update_inputs(x, x_ind, y, f, obs), \
          (this_res, res_ind)