Beispiel #1
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def test_suffstat_sk_tied():
    # use equation Nk * Sk / N = S_tied
    rng = np.random.RandomState(0)
    n_samples, n_features, n_components = 500, 2, 2

    resp = rng.rand(n_samples, n_components)
    resp = resp / resp.sum(axis=1)[:, np.newaxis]
    X = rng.rand(n_samples, n_features)
    nk = resp.sum(axis=0)
    xk = np.dot(resp.T, X) / nk[:, np.newaxis]

    covars_pred_full = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
    covars_pred_full = np.sum(nk[:, np.newaxis, np.newaxis] * covars_pred_full,
                              0) / n_samples

    covars_pred_tied = _estimate_gaussian_covariances_tied(resp, X, nk, xk, 0)

    ecov = EmpiricalCovariance()
    ecov.covariance_ = covars_pred_full
    assert_almost_equal(ecov.error_norm(covars_pred_tied, norm='frobenius'), 0)
    assert_almost_equal(ecov.error_norm(covars_pred_tied, norm='spectral'), 0)

    # check the precision computation
    precs_chol_pred = _compute_precision_cholesky(covars_pred_tied, 'tied')
    precs_pred = np.dot(precs_chol_pred, precs_chol_pred.T)
    precs_est = linalg.inv(covars_pred_tied)
    assert_array_almost_equal(precs_est, precs_pred)
Beispiel #2
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def test_suffstat_sk_full():
    # compare the precision matrix compute from the
    # EmpiricalCovariance.covariance fitted on X*sqrt(resp)
    # with _sufficient_sk_full, n_components=1
    rng = np.random.RandomState(0)
    n_samples, n_features = 500, 2

    # special case 1, assuming data is "centered"
    X = rng.rand(n_samples, n_features)
    resp = rng.rand(n_samples, 1)
    X_resp = np.sqrt(resp) * X
    nk = np.array([n_samples])
    xk = np.zeros((1, n_features))
    covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
    ecov = EmpiricalCovariance(assume_centered=True)
    ecov.fit(X_resp)
    assert_almost_equal(ecov.error_norm(covars_pred[0], norm='frobenius'), 0)
    assert_almost_equal(ecov.error_norm(covars_pred[0], norm='spectral'), 0)

    # check the precision computation
    precs_chol_pred = _compute_precision_cholesky(covars_pred, 'full')
    precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
    precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
    assert_array_almost_equal(precs_est, precs_pred)

    # special case 2, assuming resp are all ones
    resp = np.ones((n_samples, 1))
    nk = np.array([n_samples])
    xk = X.mean(axis=0).reshape((1, -1))
    covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
    ecov = EmpiricalCovariance(assume_centered=False)
    ecov.fit(X)
    assert_almost_equal(ecov.error_norm(covars_pred[0], norm='frobenius'), 0)
    assert_almost_equal(ecov.error_norm(covars_pred[0], norm='spectral'), 0)

    # check the precision computation
    precs_chol_pred = _compute_precision_cholesky(covars_pred, 'full')
    precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
    precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
    assert_array_almost_equal(precs_est, precs_pred)
Beispiel #3
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def test_gaussian_suffstat_sk_spherical():
    # computing spherical covariance equals to the variance of one-dimension
    # data after flattening, n_components=1
    rng = np.random.RandomState(0)
    n_samples, n_features = 500, 2

    X = rng.rand(n_samples, n_features)
    X = X - X.mean()
    resp = np.ones((n_samples, 1))
    nk = np.array([n_samples])
    xk = X.mean()
    covars_pred_spherical = _estimate_gaussian_covariances_spherical(
        resp, X, nk, xk, 0)
    covars_pred_spherical2 = (np.dot(X.flatten().T, X.flatten()) /
                              (n_features * n_samples))
    assert_almost_equal(covars_pred_spherical, covars_pred_spherical2)

    # check the precision computation
    precs_chol_pred = _compute_precision_cholesky(covars_pred_spherical,
                                                  'spherical')
    assert_almost_equal(covars_pred_spherical, 1. / precs_chol_pred**2)
Beispiel #4
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def test_compute_log_det_cholesky():
    n_features = 2
    rand_data = RandomData(np.random.RandomState(0))

    for covar_type in COVARIANCE_TYPE:
        covariance = rand_data.covariances[covar_type]

        if covar_type == 'full':
            predected_det = np.array([linalg.det(cov) for cov in covariance])
        elif covar_type == 'tied':
            predected_det = linalg.det(covariance)
        elif covar_type == 'diag':
            predected_det = np.array([np.prod(cov) for cov in covariance])
        elif covar_type == 'spherical':
            predected_det = covariance**n_features

        # We compute the cholesky decomposition of the covariance matrix
        expected_det = _compute_log_det_cholesky(_compute_precision_cholesky(
            covariance, covar_type),
                                                 covar_type,
                                                 n_features=n_features)
        assert_array_almost_equal(expected_det, -.5 * np.log(predected_det))
Beispiel #5
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def test_suffstat_sk_diag():
    # test against 'full' case
    rng = np.random.RandomState(0)
    n_samples, n_features, n_components = 500, 2, 2

    resp = rng.rand(n_samples, n_components)
    resp = resp / resp.sum(axis=1)[:, np.newaxis]
    X = rng.rand(n_samples, n_features)
    nk = resp.sum(axis=0)
    xk = np.dot(resp.T, X) / nk[:, np.newaxis]
    covars_pred_full = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
    covars_pred_diag = _estimate_gaussian_covariances_diag(resp, X, nk, xk, 0)

    ecov = EmpiricalCovariance()
    for (cov_full, cov_diag) in zip(covars_pred_full, covars_pred_diag):
        ecov.covariance_ = np.diag(np.diag(cov_full))
        cov_diag = np.diag(cov_diag)
        assert_almost_equal(ecov.error_norm(cov_diag, norm='frobenius'), 0)
        assert_almost_equal(ecov.error_norm(cov_diag, norm='spectral'), 0)

    # check the precision computation
    precs_chol_pred = _compute_precision_cholesky(covars_pred_diag, 'diag')
    assert_almost_equal(covars_pred_diag, 1. / precs_chol_pred**2)