Python EmpiricalCovariance.error_norm方法代码示例

# 需要导入模块: from sklearn.covariance import EmpiricalCovariance [as 别名]
# 或者: from sklearn.covariance.EmpiricalCovariance import error_norm [as 别名]
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)

# 需要导入模块: from sklearn.covariance import EmpiricalCovariance [as 别名]
# 或者: from sklearn.covariance.EmpiricalCovariance import error_norm [as 别名]
def test_suffstat_sk_full():
    # compare 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_covariance_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)

    # special case 2, assuming resp are all ones
    resp = np.ones((n_samples, 1))
    nk = np.array([n_samples])
    xk = X.mean().reshape((1, -1))
    covars_pred = _estimate_gaussian_covariance_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)

# 需要导入模块: from sklearn.covariance import EmpiricalCovariance [as 别名]
# 或者: from sklearn.covariance.EmpiricalCovariance import error_norm [as 别名]
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]
    precs_pred_full = _estimate_gaussian_precisions_cholesky_full(resp, X,
                                                                  nk, xk, 0)
    covars_pred_full = [linalg.inv(np.dot(precision_chol, precision_chol.T))
                        for precision_chol in precs_pred_full]

    precs_pred_diag = _estimate_gaussian_precisions_cholesky_diag(resp, X,
                                                                  nk, xk, 0)
    covars_pred_diag = np.array([np.diag(1. / d) ** 2
                                 for d in precs_pred_diag])

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

# 需要导入模块: from sklearn.covariance import EmpiricalCovariance [as 别名]
# 或者: from sklearn.covariance.EmpiricalCovariance import error_norm [as 别名]
def test_covariance():
    """Tests Covariance module on a simple dataset.

    """
    # test covariance fit from data
    cov = EmpiricalCovariance()
    cov.fit(X)
    assert_array_almost_equal(empirical_covariance(X), cov.covariance_, 4)
    assert_almost_equal(cov.error_norm(empirical_covariance(X)), 0)
    assert_almost_equal(
        cov.error_norm(empirical_covariance(X), norm='spectral'), 0)
    assert_almost_equal(
        cov.error_norm(empirical_covariance(X), norm='frobenius'), 0)
    assert_almost_equal(
        cov.error_norm(empirical_covariance(X), scaling=False), 0)
    assert_almost_equal(
        cov.error_norm(empirical_covariance(X), squared=False), 0)
    # Mahalanobis distances computation test
    mahal_dist = cov.mahalanobis(X)
    assert(np.amax(mahal_dist) < 250)
    assert(np.amin(mahal_dist) > 50)

    # test with n_features = 1
    X_1d = X[:, 0].reshape((-1, 1))
    cov = EmpiricalCovariance()
    cov.fit(X_1d)
    assert_array_almost_equal(empirical_covariance(X_1d), cov.covariance_, 4)
    assert_almost_equal(cov.error_norm(empirical_covariance(X_1d)), 0)
    assert_almost_equal(
        cov.error_norm(empirical_covariance(X_1d), norm='spectral'), 0)

    # test integer type
    X_integer = np.asarray([[0, 1], [1, 0]])
    result = np.asarray([[0.25, -0.25], [-0.25, 0.25]])
    assert_array_almost_equal(empirical_covariance(X_integer), result)

# 需要导入模块: from sklearn.covariance import EmpiricalCovariance [as 别名]
# 或者: from sklearn.covariance.EmpiricalCovariance import error_norm [as 别名]
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_covariance_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_covariance_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)

# 需要导入模块: from sklearn.covariance import EmpiricalCovariance [as 别名]
# 或者: from sklearn.covariance.EmpiricalCovariance import error_norm [as 别名]
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)

# 需要导入模块: from sklearn.covariance import EmpiricalCovariance [as 别名]
# 或者: from sklearn.covariance.EmpiricalCovariance import error_norm [as 别名]
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)

# 需要导入模块: from sklearn.covariance import EmpiricalCovariance [as 别名]
# 或者: from sklearn.covariance.EmpiricalCovariance import error_norm [as 别名]
def test_covariance():
    """Tests Covariance module on a simple dataset.

    """
    # test covariance fit from data
    cov = EmpiricalCovariance()
    cov.fit(X)
    emp_cov = empirical_covariance(X)
    assert_array_almost_equal(emp_cov, cov.covariance_, 4)
    assert_almost_equal(cov.error_norm(emp_cov), 0)
    assert_almost_equal(
        cov.error_norm(emp_cov, norm='spectral'), 0)
    assert_almost_equal(
        cov.error_norm(emp_cov, norm='frobenius'), 0)
    assert_almost_equal(
        cov.error_norm(emp_cov, scaling=False), 0)
    assert_almost_equal(
        cov.error_norm(emp_cov, squared=False), 0)
    assert_raises(NotImplementedError,
                  cov.error_norm, emp_cov, norm='foo')
    # Mahalanobis distances computation test
    mahal_dist = cov.mahalanobis(X)
    print(np.amin(mahal_dist), np.amax(mahal_dist))
    assert(np.amin(mahal_dist) > 0)

    # test with n_features = 1
    X_1d = X[:, 0].reshape((-1, 1))
    cov = EmpiricalCovariance()
    cov.fit(X_1d)
    assert_array_almost_equal(empirical_covariance(X_1d), cov.covariance_, 4)
    assert_almost_equal(cov.error_norm(empirical_covariance(X_1d)), 0)
    assert_almost_equal(
        cov.error_norm(empirical_covariance(X_1d), norm='spectral'), 0)

    # test with one sample
    # FIXME I don't know what this test does
    X_1sample = np.arange(5)
    cov = EmpiricalCovariance()
    assert_warns(UserWarning, cov.fit, X_1sample)
    assert_array_almost_equal(cov.covariance_,
                              np.zeros(shape=(5, 5), dtype=np.float64))

    # test integer type
    X_integer = np.asarray([[0, 1], [1, 0]])
    result = np.asarray([[0.25, -0.25], [-0.25, 0.25]])
    assert_array_almost_equal(empirical_covariance(X_integer), result)

    # test centered case
    cov = EmpiricalCovariance(assume_centered=True)
    cov.fit(X)
    assert_array_equal(cov.location_, np.zeros(X.shape[1]))

# 需要导入模块: from sklearn.covariance import EmpiricalCovariance [as 别名]
# 或者: from sklearn.covariance.EmpiricalCovariance import error_norm [as 别名]
def test_gaussian_mixture_fit():
    # recover the ground truth
    rng = np.random.RandomState(0)
    rand_data = RandomData(rng)
    n_features = rand_data.n_features
    n_components = rand_data.n_components

    for covar_type in COVARIANCE_TYPE:
        X = rand_data.X[covar_type]
        g = GaussianMixture(n_components=n_components, n_init=20,
                            reg_covar=0, random_state=rng,
                            covariance_type=covar_type)
        g.fit(X)

        # needs more data to pass the test with rtol=1e-7
        assert_allclose(np.sort(g.weights_), np.sort(rand_data.weights),
                        rtol=0.1, atol=1e-2)

        arg_idx1 = g.means_[:, 0].argsort()
        arg_idx2 = rand_data.means[:, 0].argsort()
        assert_allclose(g.means_[arg_idx1], rand_data.means[arg_idx2],
                        rtol=0.1, atol=1e-2)

        if covar_type == 'full':
            prec_pred = g.precisions_
            prec_test = rand_data.precisions['full']
        elif covar_type == 'tied':
            prec_pred = np.array([g.precisions_] * n_components)
            prec_test = np.array([rand_data.precisions['tied']] * n_components)
        elif covar_type == 'spherical':
            prec_pred = np.array([np.eye(n_features) * c
                                 for c in g.precisions_])
            prec_test = np.array([np.eye(n_features) * c for c in
                                 rand_data.precisions['spherical']])
        elif covar_type == 'diag':
            prec_pred = np.array([np.diag(d) for d in g.precisions_])
            prec_test = np.array([np.diag(d) for d in
                                 rand_data.precisions['diag']])

        arg_idx1 = np.trace(prec_pred, axis1=1, axis2=2).argsort()
        arg_idx2 = np.trace(prec_test, axis1=1, axis2=2).argsort()
        for k, h in zip(arg_idx1, arg_idx2):
            ecov = EmpiricalCovariance()
            ecov.covariance_ = prec_test[h]
            # the accuracy depends on the number of data and randomness, rng
            assert_allclose(ecov.error_norm(prec_pred[k]), 0, atol=0.1)

# 需要导入模块: from sklearn.covariance import EmpiricalCovariance [as 别名]
# 或者: from sklearn.covariance.EmpiricalCovariance import error_norm [as 别名]
def launch_mcd_on_dataset(n_samples, n_features, n_outliers,
                          tol_loc, tol_cov, tol_support, correction):
    """

    """
    data = np.random.randn(n_samples, n_features)
    # add some outliers
    outliers_index = np.random.permutation(n_samples)[:n_outliers]
    outliers_offset = 10. * \
        (np.random.randint(2, size=(n_outliers, n_features)) - 0.5)
    data[outliers_index] += outliers_offset
    inliers_mask = np.ones(n_samples).astype(bool)
    inliers_mask[outliers_index] = False

    # compute MCD directly
    T, S, H = fast_mcd(data, correction=correction)
    # compare with the estimates learnt from the inliers
    pure_data = data[inliers_mask]
    error_location = np.sum((pure_data.mean(0) - T) ** 2)
    assert(error_location < tol_loc)
    emp_cov = EmpiricalCovariance().fit(pure_data)
    #print emp_cov.error_norm(S)
    assert(emp_cov.error_norm(S) < tol_cov)
    assert(np.sum(H) > tol_support)
    # check improvement
    if (n_outliers / float(n_samples) > 0.1) and (n_features > 1):
        error_bad_location = np.sum((data.mean(0) - T) ** 2)
        assert(error_bad_location > error_location)
        bad_emp_cov = EmpiricalCovariance().fit(data)
        assert(emp_cov.error_norm(S) < bad_emp_cov.error_norm(S))

    # compute MCD by fitting an object
    mcd_fit = MCD().fit(data)
    T = mcd_fit.location_
    S = mcd_fit.covariance_
    H = mcd_fit.support_
    # compare with the estimates learnt from the inliers
    error_location = np.sum((pure_data.mean(0) - T) ** 2)
    assert(error_location < tol_loc)
    assert(emp_cov.error_norm(S) < tol_cov)
    assert(np.sum(H) > tol_support)
    # check improvement
    if (n_outliers / float(n_samples) > 0.1) and (n_features > 1):
        error_bad_location = np.sum((data.mean(0) - T) ** 2)
        assert(error_bad_location > error_location)
        bad_emp_cov = EmpiricalCovariance().fit(data)
        assert(emp_cov.error_norm(S) < bad_emp_cov.error_norm(S))

# 需要导入模块: from sklearn.covariance import EmpiricalCovariance [as 别名]
# 或者: from sklearn.covariance.EmpiricalCovariance import error_norm [as 别名]
def test_covariance():
    """Tests Covariance module on a simple dataset.

    """
    # test covariance fit from data
    cov = EmpiricalCovariance()
    cov.fit(X)
    emp_cov = empirical_covariance(X)
    assert_array_almost_equal(emp_cov, cov.covariance_, 4)
    assert_almost_equal(cov.error_norm(emp_cov), 0)
    assert_almost_equal(cov.error_norm(emp_cov, norm="spectral"), 0)
    assert_almost_equal(cov.error_norm(emp_cov, norm="frobenius"), 0)
    assert_almost_equal(cov.error_norm(emp_cov, scaling=False), 0)
    assert_almost_equal(cov.error_norm(emp_cov, squared=False), 0)
    assert_raises(NotImplementedError, cov.error_norm, emp_cov, norm="foo")
    # Mahalanobis distances computation test
    mahal_dist = cov.mahalanobis(X)
    print(np.amin(mahal_dist), np.amax(mahal_dist))
    assert np.amin(mahal_dist) > 0

    # test with n_features = 1
    X_1d = X[:, 0].reshape((-1, 1))
    cov = EmpiricalCovariance()
    cov.fit(X_1d)
    assert_array_almost_equal(empirical_covariance(X_1d), cov.covariance_, 4)
    assert_almost_equal(cov.error_norm(empirical_covariance(X_1d)), 0)
    assert_almost_equal(cov.error_norm(empirical_covariance(X_1d), norm="spectral"), 0)

    # test with one sample
    X_1sample = np.arange(5)
    cov = EmpiricalCovariance()
    with warnings.catch_warnings(record=True):
        cov.fit(X_1sample)

    # test integer type
    X_integer = np.asarray([[0, 1], [1, 0]])
    result = np.asarray([[0.25, -0.25], [-0.25, 0.25]])
    assert_array_almost_equal(empirical_covariance(X_integer), result)

    # test centered case
    cov = EmpiricalCovariance(assume_centered=True)
    cov.fit(X)
    assert_array_equal(cov.location_, np.zeros(X.shape[1]))

# 需要导入模块: from sklearn.covariance import EmpiricalCovariance [as 别名]
# 或者: from sklearn.covariance.EmpiricalCovariance import error_norm [as 别名]
        # fit a Minimum Covariance Determinant (MCD) robust estimator to data
        S = MinCovDet().fit(X)
        # compare raw robust estimates with the true location and covariance
        err_loc_mcd[i, j] = np.sum(S.location_ ** 2)
        err_cov_mcd[i, j] = S.error_norm(np.eye(n_features))
        # compare estimators learnt from the full data set with true parameters
        err_loc_emp_full[i, j] = np.sum(X.mean(0) ** 2)
        err_cov_emp_full[i, j] = EmpiricalCovariance().fit(X).error_norm(
            np.eye(n_features))
        # compare with an empirical covariance learnt from a pure data set
        # (i.e. "perfect" MCD)
        pure_X = X[inliers_mask]
        pure_location = pure_X.mean(0)
        pure_emp_cov = EmpiricalCovariance().fit(pure_X)
        err_loc_emp_pure[i, j] = np.sum(pure_location ** 2)
        err_cov_emp_pure[i, j] = pure_emp_cov.error_norm(np.eye(n_features))

# Display results
font_prop = matplotlib.font_manager.FontProperties(size=11)
pl.subplot(2, 1, 1)
pl.errorbar(range_n_outliers, err_loc_mcd.mean(1),
            yerr=err_loc_mcd.std(1) / np.sqrt(repeat),
            label="Robust location", color='m')
pl.errorbar(range_n_outliers, err_loc_emp_full.mean(1),
            yerr=err_loc_emp_full.std(1) / np.sqrt(repeat),
            label="Full data set mean", color='green')
pl.errorbar(range_n_outliers, err_loc_emp_pure.mean(1),
            yerr=err_loc_emp_pure.std(1) / np.sqrt(repeat),
            label="Pure data set mean", color='black')
pl.title("Influence of outliers on the location estimation")
pl.ylabel(r"Error ($||\mu - \hat{\mu}||_2^2$)")