From e8190e2f68a5910a20b5eacc577fa3f83efde27d Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Mon, 7 Jan 2019 16:36:11 -0500 Subject: [PATCH 01/17] add ODR implementation --- sliced/__init__.py | 1 + sliced/odr.py | 145 ++++++++++++++++++++++++++++++++++++++++ sliced/test/test_odr.py | 18 +++++ 3 files changed, 164 insertions(+) create mode 100644 sliced/odr.py create mode 100644 sliced/test/test_odr.py diff --git a/sliced/__init__.py b/sliced/__init__.py index aed628d..dc6a44e 100644 --- a/sliced/__init__.py +++ b/sliced/__init__.py @@ -9,4 +9,5 @@ from sliced.sir import * from sliced.save import * +from sliced.odr import * from sliced.version import * diff --git a/sliced/odr.py b/sliced/odr.py new file mode 100644 index 0000000..af97a50 --- /dev/null +++ b/sliced/odr.py @@ -0,0 +1,145 @@ +from __future__ import absolute_import +from __future__ import division +from __future__ import print_function + +import six + +import numpy as np +import scipy.linalg as linalg + +from scipy import sparse +from sklearn.base import BaseEstimator, TransformerMixin +from sklearn.linear_model import LinearRegression +from sklearn.metrics.pairwise import pairwise_kernels +from sklearn.preprocessing import normalize, StandardScaler + +from .externals import check_array, check_X_y, check_is_fitted +from .base import is_multioutput + + +__all__ = ['OuterProductGradient'] + + +class OuterProductGradient(BaseEstimator, TransformerMixin): + def __init__(self, + n_directions='auto', + kernel='rbf', + gamma='auto', + degree=2, + coef0=1, + kernel_params=None, + copy=True): + self.n_directions = n_directions + self.kernel = kernel + self.gamma = gamma + self.degree = degree + self.coef0 = coef0 + self.kernel_params = kernel_params + self.copy = copy + + def _get_gamma(self, X): + n_samples, n_features = X.shape + if isinstance(self.gamma, six.string_types): + # bandwidth proposed in Xia (2007) + gamma = 2.34 * n_samples ** (-1 / + (np.maximum(n_features, 3) + 6)) + return 1 / (gamma * 2) + return self.gamma + + def _get_kernel(self, X, Y=None): + if callable(self.kernel): + params = self.kernel_params or {} + else: + params = {"gamma": self._get_gamma(X), + "degree": self.degree, + "coef0": self.coef0} + return pairwise_kernels(X, Y, metric=self.kernel, + filter_params=True, **params) + + def fit(self, X, y): + """Fit the model with X and y. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + Training data, where n_samples is the number of samples + and n_features is the number of features. + + y : array-like, shape (n_samples,) + The target values (class labels in classification, real numbers + in regression). + + Returns + ------- + self : object + Returns the instance itself. + """ + if sparse.issparse(X): + raise TypeError("OuterProductGradient does not support " + "sparse input.") + + X, y = check_X_y(X, y, dtype=[np.float64, np.float32], + y_numeric=True, copy=self.copy) + + n_samples, n_features = X.shape + + if isinstance(self.n_directions, six.string_types): + self.n_directions_ = X.shape[1] + else: + self.n_directions_ = self.n_directions + + # validate y + if is_multioutput(y): + raise TypeError("The target `y` cannot be multi-output.") + + # Center and scale feature matrix + scaler = StandardScaler(copy=self.copy) + X = scaler.fit_transform(X) + + # pre-compute the kernel weights + K = self._get_kernel(X) + + # calculate the gradient estimate through a local wls + gradient = np.zeros((n_features, n_samples)) + for i in range(n_samples): + linear_model = LinearRegression(fit_intercept=True) + linear_model.fit(X - X[i, :], y, sample_weight=K[i, :]) + gradient[:, i] = linear_model.coef_ + + # solve eigen-value problem, i.e. outer product of gradient estimates + M = np.dot(gradient, gradient.T) + evals, evecs = linalg.eigh(M) + evecs = evecs[:, ::-1] + evals = evals[::-1] + + # convert back to un-scaled basis + directions = evecs / np.sqrt(scaler.var_) + directions = normalize( + directions[:, :self.n_directions_], norm='l2', axis=0) + self.directions_ = directions.T + self.eigenvalues_ = evals[:self.n_directions_] + + return self + + def transform(self, X): + """Apply dimension reduction on X. + + X is projected onto the central subspace previously extracted from a + training set. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + New data, where n_samples in the number of samples + and n_features is the number of features. + + + Returns + ------- + X_new : array-like, shape (n_samples, n_directions) + + """ + check_is_fitted(self, 'directions_') + + X = check_array(X) + return np.dot(X, self.directions_.T) diff --git a/sliced/test/test_odr.py b/sliced/test/test_odr.py new file mode 100644 index 0000000..a18cc30 --- /dev/null +++ b/sliced/test/test_odr.py @@ -0,0 +1,18 @@ +from __future__ import absolute_import +from __future__ import division +from __future__ import print_function + +import numpy as np +import pytest + +from sliced import OuterProductGradient +from sliced import datasets + + +def test_cubic(): + X, y = datasets.make_cubic(random_state=123) + + odr = OuterProductGradient(n_directions=2).fit(X, y) + print(odr.directions_) + + odr.transform(X) From 6b87edf2c084434e298a80da48940a5d3848d3ba Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Mon, 7 Jan 2019 16:38:17 -0500 Subject: [PATCH 02/17] added a test for odr in the cubic case --- sliced/test/test_odr.py | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/sliced/test/test_odr.py b/sliced/test/test_odr.py index a18cc30..08ad00e 100644 --- a/sliced/test/test_odr.py +++ b/sliced/test/test_odr.py @@ -12,7 +12,9 @@ def test_cubic(): X, y = datasets.make_cubic(random_state=123) - odr = OuterProductGradient(n_directions=2).fit(X, y) - print(odr.directions_) - + odr = OuterProductGradient().fit(X, y) odr.transform(X) + + true_beta = (1 / np.sqrt(2)) * np.hstack((np.ones(2), np.zeros(8))) + angle = np.dot(true_beta, odr.directions_[0, :]) + np.testing.assert_allclose(np.abs(angle), 1, rtol=1e-1) From df4701eb39d7c7fa49edfd6dff6dbc425d87e988 Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Mon, 7 Jan 2019 17:08:06 -0500 Subject: [PATCH 03/17] renamed and added docs for opg --- sliced/__init__.py | 2 +- sliced/{odr.py => opg.py} | 88 +++++++++++++++++++++--- sliced/test/{test_odr.py => test_opg.py} | 4 +- 3 files changed, 82 insertions(+), 12 deletions(-) rename sliced/{odr.py => opg.py} (54%) rename sliced/test/{test_odr.py => test_opg.py} (84%) diff --git a/sliced/__init__.py b/sliced/__init__.py index dc6a44e..4adf3a7 100644 --- a/sliced/__init__.py +++ b/sliced/__init__.py @@ -9,5 +9,5 @@ from sliced.sir import * from sliced.save import * -from sliced.odr import * +from sliced.opg import * from sliced.version import * diff --git a/sliced/odr.py b/sliced/opg.py similarity index 54% rename from sliced/odr.py rename to sliced/opg.py index af97a50..999b4a9 100644 --- a/sliced/odr.py +++ b/sliced/opg.py @@ -17,12 +17,84 @@ from .base import is_multioutput -__all__ = ['OuterProductGradient'] - - -class OuterProductGradient(BaseEstimator, TransformerMixin): +__all__ = ['OuterProductGradients'] + + +class OuterProductGradients(BaseEstimator, TransformerMixin): + """Outer Product of Gradients (OPG) [1] + + Forward regression methods estimate the span of the + central mean subspace S_{E[y|X]} using ideas from more familiar + estimates of the regression function E[y|X]. The advantage of these methods + is that they do not need to place distribution assumptions on the predictors + X such as SIR or SAVE. However, they rely on high dimension kernel functions + which are especially in-efficient for small sample sizes. In addition, + they assume the response y is continous. + + The Outer Product of Gradients method of Xia et al (2002) takes advantage + of the fact that span{E[grad(E[y|X])grad(E[y|X])^T]} = S_{E[y|X]}. In + order to estimate this span, the OPG method estimates the local gradient + using local linear regression. The sample expectation of the outer + product of estimated gradients is formed, and the spectral decomposition + of this product is used to estimated the span of the central mean subspace. + + Parameters + ---------- + n_directions : int, str or None (default='auto') + Number of directions to keep. Corresponds to the dimension of + the central mean subpace. If n_directions==None, + the number of directions equals the number of features. + + kernel : string or callable, default='rbf' + Kernel mapping used internally. A callable should accept two arguments + and the keyword arguments passed to his object as kernel_params, and + should return a floating point number. Set to "precomputed" in order + to pass a precomputed kernel matrix to the estimator methods instead of + samples. + + gamma : float, default='auto' + Gamma parameter for the RBF, laplacian, polynomial, exponential, chi2, + and sigmoid kernels. If gamma='auto, the default for the RBF kernel + in Xia et al. is used. + + degree : float, default=2 + Degree of the polynomial kernel. Ignored by other kernels. + + coef0 : float, default=1 + Zero coefficient for polynomial and sigmoid kernels. + Ignored by other kernels. + + kernel_params : mapping of string to any, optional + Additional parameters (keyword arguments) for a kernel function + passed as a callable object. + + copy : bool (default=True) + If False, data passed to fit are overwritten and running + fit(X).transform(X) will not yield the expected results, + use fit_transform(X) instead. + + Attributes + ---------- + directions_ : array, shape (n_directions, n_features) + The directions in feature space, representing the + central mean subspace which is sufficient to describe the conditional + mean E[y|X]. The directions are sorted by ``eigenvalues_``. + + eigenvalues_ : array, shape (n_directions,) + The eigenvalues corresponding to each of the selected directions. + These are the eigenvalues of the expected outer product of gradients. + Larger eigenvalues indicate more prevalent directions. + + References + ---------- + + [1] Xia, Y., Tong, H., Li, W. K., and Zhu, L.-X. (2002), + “An adaptive estimation of di- mension reduction space,” + Journal of the Royal Statistical Society: Series B (Statistical Methodology), + 64, 363–410. + """ def __init__(self, - n_directions='auto', + n_directions=None, kernel='rbf', gamma='auto', degree=2, @@ -83,10 +155,8 @@ def fit(self, X, y): n_samples, n_features = X.shape - if isinstance(self.n_directions, six.string_types): - self.n_directions_ = X.shape[1] - else: - self.n_directions_ = self.n_directions + self.n_directions_ = (n_features if self.n_directions is None else + self.n_directions) # validate y if is_multioutput(y): diff --git a/sliced/test/test_odr.py b/sliced/test/test_opg.py similarity index 84% rename from sliced/test/test_odr.py rename to sliced/test/test_opg.py index 08ad00e..763b107 100644 --- a/sliced/test/test_odr.py +++ b/sliced/test/test_opg.py @@ -5,14 +5,14 @@ import numpy as np import pytest -from sliced import OuterProductGradient +from sliced import OuterProductGradients from sliced import datasets def test_cubic(): X, y = datasets.make_cubic(random_state=123) - odr = OuterProductGradient().fit(X, y) + odr = OuterProductGradients().fit(X, y) odr.transform(X) true_beta = (1 / np.sqrt(2)) * np.hstack((np.ones(2), np.zeros(8))) From 8f8bc782be8e9bbfea7cf60b174410c8c5a7e1da Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Mon, 7 Jan 2019 17:09:31 -0500 Subject: [PATCH 04/17] gradient -> gradients --- sliced/opg.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/sliced/opg.py b/sliced/opg.py index 999b4a9..d00f169 100644 --- a/sliced/opg.py +++ b/sliced/opg.py @@ -170,14 +170,14 @@ def fit(self, X, y): K = self._get_kernel(X) # calculate the gradient estimate through a local wls - gradient = np.zeros((n_features, n_samples)) + gradients = np.zeros((n_features, n_samples)) for i in range(n_samples): linear_model = LinearRegression(fit_intercept=True) linear_model.fit(X - X[i, :], y, sample_weight=K[i, :]) - gradient[:, i] = linear_model.coef_ + gradients[:, i] = linear_model.coef_ # solve eigen-value problem, i.e. outer product of gradient estimates - M = np.dot(gradient, gradient.T) + M = np.dot(gradients, gradients.T) evals, evecs = linalg.eigh(M) evecs = evecs[:, ::-1] evals = evals[::-1] From 587792748130f02a165c250644028850eb5d7e5d Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Mon, 7 Jan 2019 17:40:32 -0500 Subject: [PATCH 05/17] beginning of MAVE --- sliced/opg.py | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/sliced/opg.py b/sliced/opg.py index d00f169..cf10376 100644 --- a/sliced/opg.py +++ b/sliced/opg.py @@ -48,9 +48,7 @@ class OuterProductGradients(BaseEstimator, TransformerMixin): kernel : string or callable, default='rbf' Kernel mapping used internally. A callable should accept two arguments and the keyword arguments passed to his object as kernel_params, and - should return a floating point number. Set to "precomputed" in order - to pass a precomputed kernel matrix to the estimator methods instead of - samples. + should return a floating point number. gamma : float, default='auto' Gamma parameter for the RBF, laplacian, polynomial, exponential, chi2, @@ -128,7 +126,7 @@ def _get_kernel(self, X, Y=None): return pairwise_kernels(X, Y, metric=self.kernel, filter_params=True, **params) - def fit(self, X, y): + def fit(self, X, y, kernel=None): """Fit the model with X and y. Parameters @@ -141,6 +139,9 @@ def fit(self, X, y): The target values (class labels in classification, real numbers in regression). + kernel : array-like, shape (n_samples, n_samples) + Precomputed kernel matrix. + Returns ------- self : object @@ -167,7 +168,7 @@ def fit(self, X, y): X = scaler.fit_transform(X) # pre-compute the kernel weights - K = self._get_kernel(X) + K = self._get_kernel(X) if kernel is None else kernel # calculate the gradient estimate through a local wls gradients = np.zeros((n_features, n_samples)) From 192a4f6bf2a07a8f7b38ede8156aa11516c9e43b Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Tue, 8 Jan 2019 23:57:23 -0500 Subject: [PATCH 06/17] maybe working phd and iht methods --- sliced/__init__.py | 2 + sliced/iht.py | 131 +++++++++++++++++++++++++++++++ sliced/opg.py | 8 +- sliced/phd.py | 190 +++++++++++++++++++++++++++++++++++++++++++++ sliced/save.py | 12 ++- sliced/sir.py | 12 ++- 6 files changed, 348 insertions(+), 7 deletions(-) create mode 100644 sliced/iht.py create mode 100644 sliced/phd.py diff --git a/sliced/__init__.py b/sliced/__init__.py index 4adf3a7..4ba5d63 100644 --- a/sliced/__init__.py +++ b/sliced/__init__.py @@ -9,5 +9,7 @@ from sliced.sir import * from sliced.save import * +from sliced.phd import * +from sliced.iht import * from sliced.opg import * from sliced.version import * diff --git a/sliced/iht.py b/sliced/iht.py new file mode 100644 index 0000000..ee13beb --- /dev/null +++ b/sliced/iht.py @@ -0,0 +1,131 @@ +from __future__ import absolute_import +from __future__ import division +from __future__ import print_function + +import six + +import numpy as np +import scipy.linalg as linalg + +from scipy import sparse +from sklearn.base import BaseEstimator, TransformerMixin +from sklearn.linear_model import LinearRegression +from sklearn.metrics.pairwise import pairwise_kernels +from sklearn.preprocessing import normalize, StandardScaler + +from .externals import check_array, check_X_y, check_is_fitted +from .base import is_multioutput + + +__all__ = ['IterativeHessianTransformation'] + + +class IterativeHessianTransformation(BaseEstimator, TransformerMixin): + def __init__(self, n_directions=None, copy=True): + self.n_directions = n_directions + self.copy = copy + + def fit(self, X, y): + """Fit the model with X and y. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + Training data, where n_samples is the number of samples + and n_features is the number of features. + + y : array-like, shape (n_samples,) + The target values (class labels in classification, real numbers + in regression). + + Returns + ------- + self : object + Returns the instance itself. + """ + if sparse.issparse(X): + raise TypeError("PrincipalHessianDirections does not support " + "sparse input.") + + X, y = check_X_y(X, y, dtype=[np.float64, np.float32], + y_numeric=True, copy=self.copy) + n_samples, n_features = X.shape + + self.n_directions_ = (n_features if self.n_directions is None else + self.n_directions) + + # validate y + if is_multioutput(y): + raise TypeError("The target `y` cannot be multi-output.") + + # Center and Whiten feature matrix using a QR decomposition + # (this is the approach used in the dr package) + if self.copy: + X = X - np.mean(X, axis=0) + #y = y - np.mean(y) + else: + X -= np.mean(X, axis=0) + #y -= np.mean(y) + Q, R = linalg.qr(X, mode='economic') + Z = np.sqrt(n_samples) * Q + + lm = LinearRegression(fit_intercept=True).fit(Z, y) + #Szy = np.zeros(n_features) + #for p in range(n_features): + # Szy[p] = np.cov(Z[:, p], y)[0, 1] + Szy = lm.coef_ + + Zy = Z * (y - np.mean(y) - lm.predict(Z)).reshape(-1, 1) + #Zy = Z * y.reshape(-1, 1) + Szzy = np.dot(Zy.T, Z) / n_samples + #Szzy = np.dot(Z.T, Z) / n_samples + M = np.zeros((n_features, n_features)) + for p in range(1, n_features): + M[:, p] = np.dot(np.linalg.matrix_power(Szzy, p), Szy) + + evals, evecs = linalg.eigh(np.dot(M, M.T)) + evecs = evecs[:, ::-1] + evals = evals[::-1] + + try: + # TODO: internally handle zero variance features. This would not + # be a problem if we used svd, but does not match DR. + directions = linalg.solve_triangular(np.sqrt(n_samples) * R, evecs) + except (linalg.LinAlgError, TypeError): + # NOTE: The TypeError is because of a bug in the reporting of scipy + raise linalg.LinAlgError( + "Unable to back-solve R for the dimension " + "reducing directions. This is usually caused by the presents " + "of zero variance features. Try removing these features with " + "`sklearn.feature_selection.VarianceThreshold(threshold=0.)` " + "and refitting.") + + directions = normalize( + directions[:, :self.n_directions_], norm='l2', axis=0) + self.directions_ = directions.T + self.eigenvalues_ = evals[:self.n_directions_] + + return self + + def transform(self, X): + """Apply dimension reduction on X. + + X is projected onto the central subspace previously extracted from a + training set. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + New data, where n_samples in the number of samples + and n_features is the number of features. + + + Returns + ------- + X_new : array-like, shape (n_samples, n_directions) + + """ + check_is_fitted(self, 'directions_') + + X = check_array(X) + return np.dot(X, self.directions_.T) diff --git a/sliced/opg.py b/sliced/opg.py index cf10376..655c95b 100644 --- a/sliced/opg.py +++ b/sliced/opg.py @@ -83,6 +83,11 @@ class OuterProductGradients(BaseEstimator, TransformerMixin): These are the eigenvalues of the expected outer product of gradients. Larger eigenvalues indicate more prevalent directions. + mean_ : array, shape (n_features,) + The column means of the training data used to estimate the basis + of the central mean subspace. Used to project new data onto the + central mean subspace. + References ---------- @@ -166,6 +171,7 @@ def fit(self, X, y, kernel=None): # Center and scale feature matrix scaler = StandardScaler(copy=self.copy) X = scaler.fit_transform(X) + self.mean_ = scaler.mean_ # pre-compute the kernel weights K = self._get_kernel(X) if kernel is None else kernel @@ -213,4 +219,4 @@ def transform(self, X): check_is_fitted(self, 'directions_') X = check_array(X) - return np.dot(X, self.directions_.T) + return np.dot(X - self.mean_, self.directions_.T) diff --git a/sliced/phd.py b/sliced/phd.py new file mode 100644 index 0000000..282858b --- /dev/null +++ b/sliced/phd.py @@ -0,0 +1,190 @@ +from __future__ import absolute_import +from __future__ import division +from __future__ import print_function + +import six + +import numpy as np +import scipy.linalg as linalg + +from scipy import sparse +from sklearn.base import BaseEstimator, TransformerMixin +from sklearn.linear_model import LinearRegression +from sklearn.metrics.pairwise import pairwise_kernels +from sklearn.preprocessing import normalize, StandardScaler + +from .externals import check_array, check_X_y, check_is_fitted +from .base import is_multioutput + + +__all__ = ['PrincipalHessianDirections'] + + +class PrincipalHessianDirections(BaseEstimator, TransformerMixin): + """Principal Hessian Directions (PHD) [1] + + The Principal Hessian Directions (PHD) method of Li (1992) estimates the span of + the central mean subspace S_{E[y|X]}. This in attractive when one is primarly + interested in estimating the condtional mean E[X|Y] as opposed to full conditional + distribution F_{X|Y}. For example in machine learning and non-parametric regression + where one is interested in the model: + Y = m(X) + epsilon + where m(X) is the regression function, E[X|Y]. + + The algorithm performs an eigen-decomposition of the the third-moment E[XX^T Y]. + This estimator also supports the residual based method suggested by Li, which uses + the estimate E[XX^T r] where r is the residual of the least squares fit of y on X. + Note that PHD reguires the linear conditional moment and concstant conditional + variance condition to hold. + + Parameters + ---------- + n_directions : int, str or None (default='auto') + Number of directions to keep. Corresponds to the dimension of + the central mean subpace. If n_directions==None, + the number of directions equals the number of features. + + target_type : str, 'response' or 'residual', (default='residuals') + Transformation of the target to use when estimating the third moment. + The default is to use the residual based E[XX^T r] as opposed to the response + based moment E[XX^T y]. + + copy : bool (default=True) + If False, data passed to fit are overwritten and running + fit(X).transform(X) will not yield the expected results, + use fit_transform(X) instead. + + Attributes + ---------- + directions_ : array, shape (n_directions, n_features) + The directions in feature space, representing the + central mean subspace which is sufficient to describe the conditional + mean E[y|X]. The directions are sorted by ``eigenvalues_``. + + eigenvalues_ : array, shape (n_directions,) + The eigenvalues corresponding to each of the selected directions. + These are the eigenvalues of the expected outer product of gradients. + Larger eigenvalues indicate more prevalent directions. + + mean_ : array, shape (n_features,) + The column means of the training data used to estimate the basis + of the central mean subspace. Used to project new data onto the + central mean subspace. + + References + ---------- + + [1] Ker-Chau Li (1992), + "On Principal Hessian Directions for Data Visualization and Dimension Reduction: + Another Application of Stein's Lemma", + Journal of the American Statistical Society, 1992 vol. 87 (420) pp. 1025-1039. + """ + def __init__(self, n_directions=None, target_type="residuals", copy=True): + self.n_directions = n_directions + self.target_type = target_type + self.copy = copy + + def fit(self, X, y): + """Fit the model with X and y. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + Training data, where n_samples is the number of samples + and n_features is the number of features. + + y : array-like, shape (n_samples,) + The target values (class labels in classification, real numbers + in regression). + + Returns + ------- + self : object + Returns the instance itself. + """ + if sparse.issparse(X): + raise TypeError("PrincipalHessianDirections does not support " + "sparse input.") + + X, y = check_X_y(X, y, dtype=[np.float64, np.float32], + y_numeric=True, copy=self.copy) + n_samples, n_features = X.shape + + if self.target_type not in {'response', 'residual'}: + raise ValueError("`target_type` must be one of {'response', 'residual'}") + + self.n_directions_ = (n_features if self.n_directions is None else + self.n_directions) + + # validate y + if is_multioutput(y): + raise TypeError("The target `y` cannot be multi-output.") + + # transform the target for the computation of sigma_{yxx} + if self.target_type == 'response': + y = y - np.mean(y) + else: + linear_model = LinearRegression(fit_intercept=True).fit(X, y) + y = y - linear_model.predict(X) + + # Center and Whiten feature matrix using a QR decomposition + # (this is the approach used in the dr package) + self.mean_ = np.mean(X, axis=0) + if self.copy: + X = X - self.mean_ + else: + X -= self.mean_ + Q, R = linalg.qr(X, mode='economic') + Z = np.sqrt(n_samples) * Q + + # calculate sigma_{yzz} + Zy = Z * y.reshape(-1, 1) + M = np.dot(Zy.T, Z) / n_samples + + # eigen-decomposition to determine the basis + evals, evecs = linalg.eigh(M) + evecs = evecs[:, ::-1] + evals = evals[::-1] + + try: + # TODO: internally handle zero variance features. This would not + # be a problem if we used svd, but does not match DR. + directions = linalg.solve_triangular(np.sqrt(n_samples) * R, evecs) + except (linalg.LinAlgError, TypeError): + # NOTE: The TypeError is because of a bug in the reporting of scipy + raise linalg.LinAlgError( + "Unable to back-solve R for the dimension " + "reducing directions. This is usually caused by the presents " + "of zero variance features. Try removing these features with " + "`sklearn.feature_selection.VarianceThreshold(threshold=0.)` " + "and refitting.") + + directions = normalize( + directions[:, :self.n_directions_], norm='l2', axis=0) + self.directions_ = directions.T + self.eigenvalues_ = evals[:self.n_directions_] + + return self + + def transform(self, X): + """Apply dimension reduction on X. + + X is projected onto the central subspace previously extracted from a + training set. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + New data, where n_samples in the number of samples + and n_features is the number of features. + + + Returns + ------- + X_new : array-like, shape (n_samples, n_directions) + + """ + check_is_fitted(self, 'directions_') + + X = check_array(X) + return np.dot(X - self.mean_, self.directions_.T) diff --git a/sliced/save.py b/sliced/save.py index 9012c2a..23eb013 100644 --- a/sliced/save.py +++ b/sliced/save.py @@ -67,6 +67,11 @@ class SlicedAverageVarianceEstimation(BaseEstimator, TransformerMixin): of the inverse regression curve. Larger eigenvalues indicate more prevelant directions. + mean_ : array, shape (n_features,) + The column means of the training data used to estimate the basis + of the central subspace. Used to project new data onto the + central subspace. + Examples -------- @@ -135,10 +140,11 @@ def fit(self, X, y): # Center and Whiten feature matrix using a QR decomposition # (this is the approach used in the dr package) + self.mean_ = np.mean(X, axis=0) if self.copy: - X = X - np.mean(X, axis=0) + X = X - self.mean_ else: - X -= np.mean(X, axis=0) + X -= self.mean_ Q, R = linalg.qr(X, mode='economic') Z = np.sqrt(n_samples) * Q @@ -216,4 +222,4 @@ def transform(self, X): check_is_fitted(self, 'directions_') X = check_array(X) - return np.dot(X, self.directions_.T) + return np.dot(X - self.mean_, self.directions_.T) diff --git a/sliced/sir.py b/sliced/sir.py index 09628bd..4ab981f 100644 --- a/sliced/sir.py +++ b/sliced/sir.py @@ -109,6 +109,11 @@ class SlicedInverseRegression(BaseEstimator, TransformerMixin): of the inverse regression curve. Larger eigenvalues indicate more prevalent directions. + mean_ : array, shape (n_features,) + The column means of the training data used to estimate the basis + of the central subspace. Used to project new data onto the + central subspace. + Examples -------- @@ -185,10 +190,11 @@ def fit(self, X, y): # Center and Whiten feature matrix using a QR decomposition # (this is the approach used in the dr package) + self.mean_ = np.mean(X, axis=0) if self.copy: - X = X - np.mean(X, axis=0) + X = X - self.mean_ else: - X -= np.mean(X, axis=0) + X -= self.mean_ Q, R = linalg.qr(X, mode='economic') Z = np.sqrt(n_samples) * Q Z = Z[np.argsort(y), :] @@ -278,4 +284,4 @@ def transform(self, X): check_is_fitted(self, 'directions_') X = check_array(X) - return np.dot(X, self.directions_.T) + return np.dot(X - self.mean_, self.directions_.T) From 05b0d4a3b9a6fd95946e15a8c31ad7b62915506d Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Wed, 9 Jan 2019 00:33:21 -0500 Subject: [PATCH 07/17] fixed eigenvalue ordering for phd --- sliced/iht.py | 9 +++++++-- sliced/phd.py | 8 ++++++-- 2 files changed, 13 insertions(+), 4 deletions(-) diff --git a/sliced/iht.py b/sliced/iht.py index ee13beb..1e0111a 100644 --- a/sliced/iht.py +++ b/sliced/iht.py @@ -83,9 +83,14 @@ def fit(self, X, y): for p in range(1, n_features): M[:, p] = np.dot(np.linalg.matrix_power(Szzy, p), Szy) + # eigen-decomposition to determine the basis evals, evecs = linalg.eigh(np.dot(M, M.T)) - evecs = evecs[:, ::-1] - evals = evals[::-1] + + # re-order eigenvectors based on magnitude + # NOTE: M is not psd, so eigenvalues may be negative. + order = np.argsort(np.abs(evals))[::-1] + evecs = evecs[:, order] + evals = evals[order] try: # TODO: internally handle zero variance features. This would not diff --git a/sliced/phd.py b/sliced/phd.py index 282858b..4df86b5 100644 --- a/sliced/phd.py +++ b/sliced/phd.py @@ -143,8 +143,12 @@ def fit(self, X, y): # eigen-decomposition to determine the basis evals, evecs = linalg.eigh(M) - evecs = evecs[:, ::-1] - evals = evals[::-1] + + # re-order eigenvectors based on magnitude + # NOTE: M is not psd, so eigenvalues may be negative. + order = np.argsort(np.abs(evals))[::-1] + evecs = evecs[:, order] + evals = evals[order] try: # TODO: internally handle zero variance features. This would not From 78b5733d57bf0da61e3aa0163e8af87958272ad0 Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Wed, 9 Jan 2019 09:04:05 -0500 Subject: [PATCH 08/17] added tests for phd --- sliced/phd.py | 2 +- sliced/test/test_phd.py | 42 +++++++++++++++++++++++++++++++++++++++++ 2 files changed, 43 insertions(+), 1 deletion(-) create mode 100644 sliced/test/test_phd.py diff --git a/sliced/phd.py b/sliced/phd.py index 4df86b5..f994ad7 100644 --- a/sliced/phd.py +++ b/sliced/phd.py @@ -79,7 +79,7 @@ class PrincipalHessianDirections(BaseEstimator, TransformerMixin): Another Application of Stein's Lemma", Journal of the American Statistical Society, 1992 vol. 87 (420) pp. 1025-1039. """ - def __init__(self, n_directions=None, target_type="residuals", copy=True): + def __init__(self, n_directions=None, target_type="residual", copy=True): self.n_directions = n_directions self.target_type = target_type self.copy = copy diff --git a/sliced/test/test_phd.py b/sliced/test/test_phd.py new file mode 100644 index 0000000..100b87c --- /dev/null +++ b/sliced/test/test_phd.py @@ -0,0 +1,42 @@ +from __future__ import absolute_import +from __future__ import division +from __future__ import print_function + +import numpy as np +import pytest + +from sliced import PrincipalHessianDirections +from sliced import datasets + + +def test_athletes_matches_dr(): + X, y = datasets.load_athletes() + + phd = PrincipalHessianDirections(n_directions=4).fit(X, y) + X_phd = phd.transform(X) + assert X_phd.shape == (X.shape[0], 4) + + expected_directions = np.array( + [[-0.03675, 0.59536, -0.36061, 0.21613, 0.02948, -0.29816, 0.61429, -0.01761], + [-0.23340, 0.03252, -0.47699, -0.08133, -0.07203, -0.13669, 0.82846, 0.01068], + [0.001928, -0.238599, -0.014747, 0.959780, 0.065847, -0.123638, 0.044891, + -0.005824], + [0.006563, 0.025140, -0.596972, -0.038954, -0.047897, -0.166642, 0.781899, + -0.001390]] + ) + np.testing.assert_allclose( + np.abs(phd.directions_), np.abs(expected_directions), atol=1e-5) + + expected_eigenvalues = np.array([2.8583, -1.4478, 0.9612, -0.5621]) + np.testing.assert_allclose(phd.eigenvalues_, expected_eigenvalues, atol=1e-4) + +def test_response_based_phd(): + X, y = datasets.make_quadratic() + + phd = PrincipalHessianDirections(target_type='response', n_directions=1).fit(X, y) + X_phd = phd.transform(X) + assert X_phd.shape == (X.shape[0], 1) + + # check fit_transform matches + X_phd2 = phd.fit_transform(X, y) + np.testing.assert_allclose(X_phd, X_phd2) From 9a64911d0ea03aa56f033396e0465e8fe7ae46e3 Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Wed, 9 Jan 2019 10:56:42 -0500 Subject: [PATCH 09/17] added iterative hessian transformation --- examples/plot_iht.py | 27 + examples/plot_opg.py | 35 + examples/plot_phd.py | 27 + sliced/datasets/__init__.py | 1 + sliced/datasets/data/pendigits.tes | 3499 +++++++++++++ sliced/datasets/data/pendigits.tra | 7495 ++++++++++++++++++++++++++++ sliced/datasets/penn_digits.py | 61 + sliced/iht.py | 93 +- sliced/phd.py | 3 +- 9 files changed, 11221 insertions(+), 20 deletions(-) create mode 100644 examples/plot_iht.py create mode 100644 examples/plot_opg.py create mode 100644 examples/plot_phd.py create mode 100644 sliced/datasets/data/pendigits.tes create mode 100644 sliced/datasets/data/pendigits.tra create mode 100644 sliced/datasets/penn_digits.py diff --git a/examples/plot_iht.py b/examples/plot_iht.py new file mode 100644 index 0000000..d6827fb --- /dev/null +++ b/examples/plot_iht.py @@ -0,0 +1,27 @@ +""" +================================ +Iterative Hessian Transformation +================================ + +An example plot of :class:`sliced.iht.IterativeHessianTransformation` +applied to the Penn Digits Dataset. +""" +import numpy as np +import matplotlib.pyplot as plt + +from sliced import IterativeHessianTransformation +from sliced.datasets import load_penn_digits + +X_train, y_train = load_penn_digits(subset='train', digits=[0, 6, 9]) +X_test, y_test = load_penn_digits(subset='test', digits=[0, 6, 9]) + + +iht = IterativeHessianTransformation(target_type='response').fit(X_train, y_train) +X_iht = iht.transform(X_test) + +# plot data projected onto the first direction +plt.scatter(X_iht[:, 0], X_iht[:, 1], c=y_test, linewidth=0.5, edgecolor='k') +plt.xlabel("$X\hat{\\beta_1}$") +plt.ylabel("$X\hat{\\beta_2}$") + +plt.show() diff --git a/examples/plot_opg.py b/examples/plot_opg.py new file mode 100644 index 0000000..3c710de --- /dev/null +++ b/examples/plot_opg.py @@ -0,0 +1,35 @@ +""" +====================== +Outer Product Gradient +====================== + +An example plot of :class:`sliced.odr.OuterProductGradient` +""" +import numpy as np +import matplotlib.pyplot as plt + +from sliced import OuterProductGradients +from sliced import datasets + +X, y = datasets.make_cubic(random_state=123) + +opg = OuterProductGradients() +X_opg = opg.fit_transform(X, y) + +# estimate of the first dimension reducing directions +beta1_hat = opg.directions_[0, :] + + +# plot data projected onto the first direction +plt.scatter(X_opg[:, 0], y, c=y, cmap='viridis', linewidth=0.5, edgecolor='k') +plt.xlabel("$X\hat{\\beta_1}$") +plt.ylabel("y") + +# annotation showing the direction found +beta_text = "$\\beta_1$ = " + "{0}".format([0.707, 0.707]) +plt.annotate(beta_text, xy=(-2, 6.5)) +beta1_hat_text = "$\hat{\\beta_1}$ = " + "{0}".format( + np.round(beta1_hat, 3).tolist()[:2]) +plt.annotate(beta1_hat_text, xy=(-2, 7.5)) + +plt.show() diff --git a/examples/plot_phd.py b/examples/plot_phd.py new file mode 100644 index 0000000..1f8578b --- /dev/null +++ b/examples/plot_phd.py @@ -0,0 +1,27 @@ +""" +================================== +Principal Hessian Directions (PHD) +================================== + +An example plot of :class:`sliced.phd.PrincipalHessianDirections` +""" +import numpy as np +import matplotlib.pyplot as plt + +from sliced import PrincipalHessianDirections +from sliced import datasets + + +from sliced.datasets import load_athletes + +X, y = load_athletes() + +phd = PrincipalHessianDirections(target_type='residual') +X_phd = phd.fit_transform(X, y) + +# plot data projected onto the first direction +plt.scatter(X_phd[:, 0], y, c=y, cmap='viridis', linewidth=0.5, edgecolor='k') +plt.xlabel("$X\hat{\\beta_1}$") +plt.ylabel("y") + +plt.show() diff --git a/sliced/datasets/__init__.py b/sliced/datasets/__init__.py index a48c159..445833c 100644 --- a/sliced/datasets/__init__.py +++ b/sliced/datasets/__init__.py @@ -1,3 +1,4 @@ from sliced.datasets.synthetic import * from sliced.datasets.banknote import load_banknote from sliced.datasets.athletes import load_athletes +from sliced.datasets.penn_digits import load_penn_digits diff --git a/sliced/datasets/data/pendigits.tes b/sliced/datasets/data/pendigits.tes new file mode 100644 index 0000000..75f3160 --- /dev/null +++ b/sliced/datasets/data/pendigits.tes @@ -0,0 +1,3499 @@ +3498,16 + 88, 92, 2, 99, 16, 66, 94, 37, 70, 0, 0, 24, 42, 65,100,100, 8 + 80,100, 18, 98, 60, 66,100, 29, 42, 0, 0, 23, 42, 61, 56, 98, 8 + 0, 94, 9, 57, 20, 19, 7, 0, 20, 36, 70, 68,100,100, 18, 92, 8 + 95, 82, 71,100, 27, 77, 77, 73,100, 80, 93, 42, 56, 13, 0, 0, 9 + 68,100, 6, 88, 47, 75, 87, 82, 85, 56,100, 29, 75, 6, 0, 0, 9 + 70,100,100, 97, 70, 81, 45, 65, 30, 49, 20, 33, 0, 16, 0, 0, 1 + 40,100, 0, 81, 15, 58,100, 57, 47, 87, 50, 88, 40, 42, 36, 0, 4 + 3, 71, 0, 95, 45,100,100, 99, 79, 78, 48, 53, 31, 24, 54, 0, 7 + 79, 87, 98, 81, 71,100, 72, 73,100, 66, 91, 21, 48, 0, 0, 13, 9 + 92, 95, 30,100, 34, 68, 87, 89, 84, 78,100, 35, 64, 0, 0, 19, 9 + 58, 64,100, 96, 27,100, 0, 63, 79, 65, 91, 72, 48, 36, 10, 0, 9 + 34, 89, 3, 70, 1, 25, 49, 0,100, 23,100, 67, 56, 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1 + 0, 78, 29,100, 94, 86, 70, 48, 42, 11, 32, 0, 25, 36,100, 40, 7 diff --git a/sliced/datasets/penn_digits.py b/sliced/datasets/penn_digits.py new file mode 100644 index 0000000..b30b67b --- /dev/null +++ b/sliced/datasets/penn_digits.py @@ -0,0 +1,61 @@ +import csv +import numpy as np + +from os.path import dirname + +from sliced.datasets.base import load_data + + +def load_penn_digits(digits='all', subset='train'): + """Load and return the Penn Digits dataset (classification). + + This dataset concerns the identificatino of hand-written digits {0, 1, ..., 9}. + It contains handwritten digits by 44 subjects, each of whom were asked to write + 250 random digits. Eight pairs of 2-dimensional locations were recorded on each digit, + yielding a 16 dimensional feature vector. The 44 subjects are divided into two groups + of size 30 and 14, in which the first form the training set (of size 7,494) and the + second formed the test set (of sample size 3,498). The data set was taken from the + UCI machine-learning repository at + + https://archive.ics.uci.edu/ml/datasets/Pen-Based+Recognition+of+Handwritten+Digits + + ================= ================== + Classes 10 + Dimensionality 16 + Features integer, positive + ================= ================== + + Parameters + ---------- + digits : str or list (default='all') + Which digits to include in the sample. The default is 'all' indicating + all digits are included. Can be a list of digits for example [0, 6, 9] + will only include digits 0, 6, and 9. + + subset : str {'train', 'test', 'all'}, (default='train') + Which subset of the data to return. 'train' indicates the training set, + 'test' indicates the test set, and 'all' indicates a combination of + both. Note that all does not shuffle the dataset, so the first samples + are training and the remaining samples are test. + """ + module_path = dirname(__file__) + + if subset not in ['train', 'test', 'all']: + raise ValueError("`subset` must be one of {'train', 'test', 'all'}") + + if subset == 'train': + data, target = load_data(module_path, 'pendigits.tra') + elif subset == 'test': + data, target = load_data(module_path, 'pendigits.tes') + else: + data_train, target_train = load_data(module_path, 'pendigits.tra') + data_test, target_test = load_data(module_path, 'pendigits.tes') + data = np.vstack((data_train, data_test)) + target = np.concatenate((target_train, target_test)) + + if isinstance(digits, list): + digit_mask = np.isin(target, digits) + return data[digit_mask], target[digit_mask] + + return data, target + diff --git a/sliced/iht.py b/sliced/iht.py index 1e0111a..01596af 100644 --- a/sliced/iht.py +++ b/sliced/iht.py @@ -10,8 +10,7 @@ from scipy import sparse from sklearn.base import BaseEstimator, TransformerMixin from sklearn.linear_model import LinearRegression -from sklearn.metrics.pairwise import pairwise_kernels -from sklearn.preprocessing import normalize, StandardScaler +from sklearn.preprocessing import normalize from .externals import check_array, check_X_y, check_is_fitted from .base import is_multioutput @@ -21,8 +20,62 @@ class IterativeHessianTransformation(BaseEstimator, TransformerMixin): - def __init__(self, n_directions=None, copy=True): + """Iterative Hessian Transformation (IHT) [1] + + Estimation of the central mean subspace using a eigen-decomposition + of various higher order moments. + + This method was developed in Cook and Li (2002) in order to overcome + two common weakness of sufficient dimension reduction methods. It removes + the constant conditional variance assumption that is necessary for + Principal Hessian Directions. In addition, it can recover more sufficient + predictors than SIR or SAVE. For example, if y has `k` levels, then SIR and + SAVE can only recover `k - 1` predictors. This is not the case for IHT. + + Parameters + ---------- + n_directions : int, str or None (default='auto') + Number of directions to keep. Corresponds to the dimension of + the central mean subpace. If n_directions==None, + the number of directions equals the number of features. + + target_type : str, 'response' or 'residual', (default='response') + Transformation of the target to use when estimating the powers of the + third moment. The default is to use the response based moment E[XX^T y] as + opposed to the residual based moment E[XX^T r]. + + copy : bool (default=True) + If False, data passed to fit are overwritten and running + fit(X).transform(X) will not yield the expected results, + use fit_transform(X) instead. + + Attributes + ---------- + directions_ : array, shape (n_directions, n_features) + The directions in feature space, representing the + central mean subspace which is sufficient to describe the conditional + mean E[y|X]. The directions are sorted by ``eigenvalues_``. + + eigenvalues_ : array, shape (n_directions,) + The eigenvalues corresponding to each of the selected directions. + These are the eigenvalues of the expected outer product of gradients. + Larger eigenvalues indicate more prevalent directions. + + mean_ : array, shape (n_features,) + The column means of the training data used to estimate the basis + of the central mean subspace. Used to project new data onto the + central mean subspace. + + References + ---------- + + [1] R Dennis Cook and Bing Li (2002), + "Dimension Reduction for Conditional Mean in Regression", + The Annals of Statistics, 2002 vol. 30 (2) pp. 455-474. + """ + def __init__(self, n_directions=None, target_type="response", copy=True): self.n_directions = n_directions + self.target_type = target_type self.copy = copy def fit(self, X, y): @@ -44,13 +97,16 @@ def fit(self, X, y): Returns the instance itself. """ if sparse.issparse(X): - raise TypeError("PrincipalHessianDirections does not support " + raise TypeError("IterativeHessianTransformation does not support " "sparse input.") X, y = check_X_y(X, y, dtype=[np.float64, np.float32], y_numeric=True, copy=self.copy) n_samples, n_features = X.shape + if self.target_type not in {'response', 'residual'}: + raise ValueError("`target_type` must be one of {'response', 'residual'}") + self.n_directions_ = (n_features if self.n_directions is None else self.n_directions) @@ -58,27 +114,29 @@ def fit(self, X, y): if is_multioutput(y): raise TypeError("The target `y` cannot be multi-output.") + # transform the target for the computation of sigma_{yxx} + if self.target_type == 'residual': + linear_model = LinearRegression(fit_intercept=True).fit(X, y) + y = y - linear_model.predict(X) + # Center and Whiten feature matrix using a QR decomposition # (this is the approach used in the dr package) + self.mean_ = np.mean(X, axis=0) if self.copy: - X = X - np.mean(X, axis=0) - #y = y - np.mean(y) + X = X - self.mean_ else: - X -= np.mean(X, axis=0) - #y -= np.mean(y) + X -= self.mean_ Q, R = linalg.qr(X, mode='economic') Z = np.sqrt(n_samples) * Q - lm = LinearRegression(fit_intercept=True).fit(Z, y) - #Szy = np.zeros(n_features) - #for p in range(n_features): - # Szy[p] = np.cov(Z[:, p], y)[0, 1] - Szy = lm.coef_ + # covariance between Z and y + Szy = np.zeros(n_features) + for p in range(n_features): + Szy[p] = np.cov(Z[:, p], y)[0, 1] - Zy = Z * (y - np.mean(y) - lm.predict(Z)).reshape(-1, 1) - #Zy = Z * y.reshape(-1, 1) + # iterative moment calculations + Zy = Z * y.reshape(-1, 1) Szzy = np.dot(Zy.T, Z) / n_samples - #Szzy = np.dot(Z.T, Z) / n_samples M = np.zeros((n_features, n_features)) for p in range(1, n_features): M[:, p] = np.dot(np.linalg.matrix_power(Szzy, p), Szy) @@ -87,7 +145,6 @@ def fit(self, X, y): evals, evecs = linalg.eigh(np.dot(M, M.T)) # re-order eigenvectors based on magnitude - # NOTE: M is not psd, so eigenvalues may be negative. order = np.argsort(np.abs(evals))[::-1] evecs = evecs[:, order] evals = evals[order] @@ -133,4 +190,4 @@ def transform(self, X): check_is_fitted(self, 'directions_') X = check_array(X) - return np.dot(X, self.directions_.T) + return np.dot(X - self.mean_, self.directions_.T) diff --git a/sliced/phd.py b/sliced/phd.py index f994ad7..4126076 100644 --- a/sliced/phd.py +++ b/sliced/phd.py @@ -10,8 +10,7 @@ from scipy import sparse from sklearn.base import BaseEstimator, TransformerMixin from sklearn.linear_model import LinearRegression -from sklearn.metrics.pairwise import pairwise_kernels -from sklearn.preprocessing import normalize, StandardScaler +from sklearn.preprocessing import normalize from .externals import check_array, check_X_y, check_is_fitted from .base import is_multioutput From bb1456bfa5e684aa64cb4a4e3124fa5d33340212 Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Wed, 9 Jan 2019 11:06:04 -0500 Subject: [PATCH 10/17] added test for iht --- sliced/test/test_iht.py | 35 +++++++++++++++++++++++ sliced/test/test_opg.py | 7 +++-- sliced/test/test_sklearn_compatibility.py | 9 +++++- 3 files changed, 47 insertions(+), 4 deletions(-) create mode 100644 sliced/test/test_iht.py diff --git a/sliced/test/test_iht.py b/sliced/test/test_iht.py new file mode 100644 index 0000000..7ac166f --- /dev/null +++ b/sliced/test/test_iht.py @@ -0,0 +1,35 @@ +from __future__ import absolute_import +from __future__ import division +from __future__ import print_function + +import numpy as np +import pytest + +from sliced import IterativeHessianTransformation +from sliced import datasets + + +def test_quadratic_response(): + X, y = datasets.make_quadratic(random_state=123) + + iht = IterativeHessianTransformation(n_directions=4).fit(X, y) + X_iht = iht.transform(X) + assert X_iht.shape == (X.shape[0], 4) + + true_beta = (1 / np.sqrt(2)) * np.hstack((np.ones(2), np.zeros(8))) + angle = np.dot(true_beta, iht.directions_[0, :]) + np.testing.assert_allclose(np.abs(angle), 1, rtol=1e-1) + + +def test_quadratic_residual(): + X, y = datasets.make_quadratic(random_state=123) + + iht = IterativeHessianTransformation(n_directions=4, + target_type='residual') + iht.fit(X, y) + X_iht = iht.transform(X) + assert X_iht.shape == (X.shape[0], 4) + + true_beta = (1 / np.sqrt(2)) * np.hstack((np.ones(2), np.zeros(8))) + angle = np.dot(true_beta, iht.directions_[0, :]) + np.testing.assert_allclose(np.abs(angle), 1, rtol=1e-1) diff --git a/sliced/test/test_opg.py b/sliced/test/test_opg.py index 763b107..4728b11 100644 --- a/sliced/test/test_opg.py +++ b/sliced/test/test_opg.py @@ -12,9 +12,10 @@ def test_cubic(): X, y = datasets.make_cubic(random_state=123) - odr = OuterProductGradients().fit(X, y) - odr.transform(X) + opg = OuterProductGradients(n_directions=4).fit(X, y) + X_opg = opg.transform(X) + assert X_opg.shape == (X.shape[0], 4) true_beta = (1 / np.sqrt(2)) * np.hstack((np.ones(2), np.zeros(8))) - angle = np.dot(true_beta, odr.directions_[0, :]) + angle = np.dot(true_beta, opg.directions_[0, :]) np.testing.assert_allclose(np.abs(angle), 1, rtol=1e-1) diff --git a/sliced/test/test_sklearn_compatibility.py b/sliced/test/test_sklearn_compatibility.py index 138e47b..bc8eec0 100644 --- a/sliced/test/test_sklearn_compatibility.py +++ b/sliced/test/test_sklearn_compatibility.py @@ -4,7 +4,14 @@ from sklearn.utils.estimator_checks import check_estimator -from sliced import SlicedInverseRegression, SlicedAverageVarianceEstimation +from sliced import ( + SlicedInverseRegression, + SlicedAverageVarianceEstimation, + PrincipalHessianDirections, + IterativeHessianTransformation, + OuterProductGradients + #MinimumAverageVarianceEstimation +) def test_sir(): From 0c575a386b65d2275a0ea380a0a551efbb710058 Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Fri, 11 Jan 2019 15:28:46 -0500 Subject: [PATCH 11/17] added kernal sliced inverse regression --- examples/plot_kir.py | 36 ++++++ sliced/__init__.py | 1 + sliced/kir.py | 241 ++++++++++++++++++++++++++++++++++++++++ sliced/test/test_kir.py | 21 ++++ 4 files changed, 299 insertions(+) create mode 100644 examples/plot_kir.py create mode 100644 sliced/kir.py create mode 100644 sliced/test/test_kir.py diff --git a/examples/plot_kir.py b/examples/plot_kir.py new file mode 100644 index 0000000..053c0f2 --- /dev/null +++ b/examples/plot_kir.py @@ -0,0 +1,36 @@ +""" +========================= +Kernal Inverse Regression +========================= + +An example plot of :class:`sliced.kir.KernalInverseRegression` +""" +import numpy as np +import matplotlib.pyplot as plt + +from sliced import KernalInverseRegression +from sliced import datasets + + +X, y = datasets.make_cubic(random_state=123) + +kir = KernalInverseRegression(gamma=1e-2) +X_kir = kir.fit_transform(X, y) + +# estimate of the first dimension reducing directions +beta1_hat = kir.directions_[0, :] + + +# plot data projected onto the first direction +plt.scatter(X_kir[:, 0], y, c=y, cmap='viridis', linewidth=0.5, edgecolor='k') +plt.xlabel("$X\hat{\\beta_1}$") +plt.ylabel("y") + +# annotation showing the direction found +beta_text = "$\\beta_1$ = " + "{0}".format([0.707, 0.707]) +plt.annotate(beta_text, xy=(-2, 6.5)) +beta1_hat_text = "$\hat{\\beta_1}$ = " + "{0}".format( + np.round(beta1_hat, 3).tolist()[:2]) +plt.annotate(beta1_hat_text, xy=(-2, 7.5)) + +plt.show() diff --git a/sliced/__init__.py b/sliced/__init__.py index 4ba5d63..07ed70e 100644 --- a/sliced/__init__.py +++ b/sliced/__init__.py @@ -8,6 +8,7 @@ from sliced import externals from sliced.sir import * +from sliced.kir import * from sliced.save import * from sliced.phd import * from sliced.iht import * diff --git a/sliced/kir.py b/sliced/kir.py new file mode 100644 index 0000000..9fc864f --- /dev/null +++ b/sliced/kir.py @@ -0,0 +1,241 @@ +from __future__ import absolute_import +from __future__ import division +from __future__ import print_function + +import six + +import numpy as np +import scipy.linalg as linalg + +from scipy import sparse +from sklearn.base import BaseEstimator, TransformerMixin +from sklearn.metrics.pairwise import pairwise_kernels +from sklearn.preprocessing import normalize + +from .externals import check_array, check_X_y, check_is_fitted +from .base import is_multioutput + + +__all__ = ['KernalInverseRegression'] + + +class KernalInverseRegression(BaseEstimator, TransformerMixin): + """Kernel Inverse Regression [1] + + Linear dimensionality reduction using the inverse regression curve, + E[X|y], to identify the directions defining the central subspace of + the data. The inverse comes from the fact that X and y are reversed with respect + to the standard regression framework (estimating E[y|X]). + + Sliced Inverse Regression estimates the inverse regression curve through + binning the response and calculating E[X|y] in each bin. Fang and Zhu (1996) + proposed replacing the bins by a kernel smoothing method. The central subspace + is determined by performing a weighted principal component analysis on the + kernel estimate of E[X|y]. Note that for the best results a method such + as cross-validation should be used to choose the bandwidth of the kernel. + + Parameters + ---------- + n_directions : int, str or None (default='auto') + Number of directions to keep. Corresponds to the dimension of + the central subpace. If n_directions==None, + the number of directions equals the number of features. + + kernel : string or callable, default='rbf' + Kernel mapping used internally. A callable should accept two arguments + and the keyword arguments passed to his object as kernel_params, and + should return a floating point number. + + gamma : float, default='auto' + Gamma parameter for the RBF, laplacian, polynomial, exponential, chi2, + and sigmoid kernels. If gamma='auto, the default for the RBF kernel + is an (0.75 * n_samples) ** (-0.2), i.e. an undersmoothed version of + the optimal kernel if this was a non-parametric regression problem. + + degree : float, default=2 + Degree of the polynomial kernel. Ignored by other kernels. + + coef0 : float, default=1 + Zero coefficient for polynomial and sigmoid kernels. + Ignored by other kernels. + + kernel_params : mapping of string to any, optional + Additional parameters (keyword arguments) for a kernel function + passed as a callable object. + + epsilon : float, default=0.1 + Regularization parameter used to avoid division by zero in the + kernel estimator of E[X|y]. + + copy : bool (default=True) + If False, data passed to fit are overwritten and running + fit(X).transform(X) will not yield the expected results, + use fit_transform(X) instead. + + Attributes + ---------- + directions_ : array, shape (n_directions, n_features) + The directions in feature space, representing the + central mean subspace which is sufficient to describe the conditional + mean E[y|X]. The directions are sorted by ``eigenvalues_``. + + eigenvalues_ : array, shape (n_directions,) + The eigenvalues corresponding to each of the selected directions. + These are the eigenvalues of the expected outer product of gradients. + Larger eigenvalues indicate more prevalent directions. + + mean_ : array, shape (n_features,) + The column means of the training data used to estimate the basis + of the central mean subspace. Used to project new data onto the + central mean subspace. + + References + ---------- + + [1] Fang, K., Zhu, L. (1996), + "Asymptotics of kernel estimate of sliced inverse regression", + Annals of Statistics, 24, 1053-1068 + + """ + def __init__(self, + n_directions=None, + kernel='rbf', + gamma='auto', + degree=2, + coef0=1, + kernel_params=None, + epsilon=1e-1, + copy=True): + self.n_directions = n_directions + self.kernel = kernel + self.gamma = gamma + self.degree = degree + self.coef0 = coef0 + self.kernel_params = kernel_params + self.epsilon = epsilon + self.copy = copy + + def _get_gamma(self, y): + if isinstance(self.gamma, six.string_types): + # undersmoothed optimal bandwidth (n^(-1/(1 + 4))) + n_samples = y.shape[0] + gamma = (0.75 * n_samples) ** (-0.2) + return 1 / (gamma * 2) + return self.gamma + + def _get_kernel(self, y): + if callable(self.kernel): + params = self.kernel_params or {} + else: + params = {"gamma": self._get_gamma(y), + "degree": self.degree, + "coef0": self.coef0} + return pairwise_kernels(y.reshape(-1, 1), metric=self.kernel, + filter_params=True, **params) + + def fit(self, X, y, kernel=None): + """Fit the model with X and y. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + Training data, where n_samples is the number of samples + and n_features is the number of features. + + y : array-like, shape (n_samples,) + The target values (class labels in classification, real numbers + in regression). + + kernel : array-like, shape (n_samples, n_samples) + Precomputed kernel matrix. + + Returns + ------- + self : object + Returns the instance itself. + """ + if sparse.issparse(X): + raise TypeError("OuterProductGradient does not support " + "sparse input.") + + X, y = check_X_y(X, y, dtype=[np.float64, np.float32], + y_numeric=True, copy=self.copy) + + n_samples, n_features = X.shape + + self.n_directions_ = (n_features if self.n_directions is None else + self.n_directions) + + # validate y + if is_multioutput(y): + raise TypeError("The target `y` cannot be multi-output.") + + # Center and Whiten feature matrix using a QR decomposition + # (this is the approach used in the dr package) + self.mean_ = np.mean(X, axis=0) + if self.copy: + X = X - self.mean_ + else: + X -= self.mean_ + Q, R = linalg.qr(X, mode='economic') + Z = np.sqrt(n_samples) * Q + + # standardize target + y = (y - np.mean(y)) / np.std(y) + + # kernel function + K = self._get_kernel(y) if kernel is None else kernel + + # kernel version of var(E[X|y]) + K_mean = np.mean(K, axis=1) + scale = np.mean(K_mean) + weights = 1 / np.maximum(K_mean, self.epsilon * scale) ** 2 + EZy = np.dot(K, Z) * weights.reshape(-1, 1) + M = np.dot(EZy.T, EZy) + + # solve eigen-value problem, i.e. outer product of gradient estimates + evals, evecs = linalg.eigh(M) + evecs = evecs[:, ::-1] + evals = evals[::-1] + try: + # TODO: internally handle zero variance features. This would not + # be a problem if we used svd, but does not match DR. + directions = linalg.solve_triangular(np.sqrt(n_samples) * R, evecs) + except (linalg.LinAlgError, TypeError): + # NOTE: The TypeError is because of a bug in the reporting of scipy + raise linalg.LinAlgError( + "Unable to back-solve R for the dimension " + "reducing directions. This is usually caused by the presents " + "of zero variance features. Try removing these features with " + "`sklearn.feature_selection.VarianceThreshold(threshold=0.)` " + "and refitting.") + + directions = normalize( + directions[:, :self.n_directions_], norm='l2', axis=0) + self.directions_ = directions.T + self.eigenvalues_ = evals[:self.n_directions_] + + return self + + def transform(self, X): + """Apply dimension reduction on X. + + X is projected onto the central subspace previously extracted from a + training set. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + New data, where n_samples in the number of samples + and n_features is the number of features. + + + Returns + ------- + X_new : array-like, shape (n_samples, n_directions) + + """ + check_is_fitted(self, 'directions_') + + X = check_array(X) + return np.dot(X - self.mean_, self.directions_.T) diff --git a/sliced/test/test_kir.py b/sliced/test/test_kir.py new file mode 100644 index 0000000..fe71075 --- /dev/null +++ b/sliced/test/test_kir.py @@ -0,0 +1,21 @@ +from __future__ import absolute_import +from __future__ import division +from __future__ import print_function + +import numpy as np +import pytest + +from sliced import KernalInverseRegression +from sliced import datasets + + +def test_cubic(): + X, y = datasets.make_cubic(random_state=123) + + kir = KernalInverseRegression(n_directions=4).fit(X, y) + X_kir = kir.transform(X) + assert X_kir.shape == (X.shape[0], 4) + + true_beta = (1 / np.sqrt(2)) * np.hstack((np.ones(2), np.zeros(8))) + angle = np.dot(true_beta, kir.directions_[0, :]) + np.testing.assert_allclose(np.abs(angle), 1, rtol=1e-1) From f1c387569dea5a727877f575507f6af1ae628715 Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Fri, 11 Jan 2019 15:33:15 -0500 Subject: [PATCH 12/17] fixed misspelling of kernel --- examples/plot_kir.py | 8 ++++---- sliced/kir.py | 4 ++-- sliced/test/test_kir.py | 4 ++-- 3 files changed, 8 insertions(+), 8 deletions(-) diff --git a/examples/plot_kir.py b/examples/plot_kir.py index 053c0f2..c66fb09 100644 --- a/examples/plot_kir.py +++ b/examples/plot_kir.py @@ -1,20 +1,20 @@ """ ========================= -Kernal Inverse Regression +Kernel Inverse Regression ========================= -An example plot of :class:`sliced.kir.KernalInverseRegression` +An example plot of :class:`sliced.kir.KernelInverseRegression` """ import numpy as np import matplotlib.pyplot as plt -from sliced import KernalInverseRegression +from sliced import KernelInverseRegression from sliced import datasets X, y = datasets.make_cubic(random_state=123) -kir = KernalInverseRegression(gamma=1e-2) +kir = KernelInverseRegression(gamma=1e-2) X_kir = kir.fit_transform(X, y) # estimate of the first dimension reducing directions diff --git a/sliced/kir.py b/sliced/kir.py index 9fc864f..f0a2cd9 100644 --- a/sliced/kir.py +++ b/sliced/kir.py @@ -16,10 +16,10 @@ from .base import is_multioutput -__all__ = ['KernalInverseRegression'] +__all__ = ['KernelInverseRegression'] -class KernalInverseRegression(BaseEstimator, TransformerMixin): +class KernelInverseRegression(BaseEstimator, TransformerMixin): """Kernel Inverse Regression [1] Linear dimensionality reduction using the inverse regression curve, diff --git a/sliced/test/test_kir.py b/sliced/test/test_kir.py index fe71075..d422129 100644 --- a/sliced/test/test_kir.py +++ b/sliced/test/test_kir.py @@ -5,14 +5,14 @@ import numpy as np import pytest -from sliced import KernalInverseRegression +from sliced import KernelInverseRegression from sliced import datasets def test_cubic(): X, y = datasets.make_cubic(random_state=123) - kir = KernalInverseRegression(n_directions=4).fit(X, y) + kir = KernelInverseRegression(n_directions=4).fit(X, y) X_kir = kir.transform(X) assert X_kir.shape == (X.shape[0], 4) From eb7e39c0903266fed625e515ad2934f58c6bbd76 Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Fri, 11 Jan 2019 15:37:53 -0500 Subject: [PATCH 13/17] updated manifest --- MANIFEST.in | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/MANIFEST.in b/MANIFEST.in index ae68b4a..1fd2cf2 100644 --- a/MANIFEST.in +++ b/MANIFEST.in @@ -1,7 +1,7 @@ include *.rst recursive-include doc * recursive-include examples * -recursive-include sliced/datasets *.csv +recursive-include sliced/datasets *.csv *.tes *.tra include README.rst include requirements.txt include test_requirements.txt From 75fad16af54236b2bcb9ae634c31a56b29d1c7f6 Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Tue, 14 May 2019 15:44:29 -0400 Subject: [PATCH 14/17] a few fixes --- sliced/opg.py | 2 +- sliced/version.py | 2 +- test_requirements.txt | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/sliced/opg.py b/sliced/opg.py index 655c95b..22ddedd 100644 --- a/sliced/opg.py +++ b/sliced/opg.py @@ -92,7 +92,7 @@ class OuterProductGradients(BaseEstimator, TransformerMixin): ---------- [1] Xia, Y., Tong, H., Li, W. K., and Zhu, L.-X. (2002), - “An adaptive estimation of di- mension reduction space,” + “An adaptive estimation of dimension reduction space,” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64, 363–410. """ diff --git a/sliced/version.py b/sliced/version.py index d551127..f501830 100644 --- a/sliced/version.py +++ b/sliced/version.py @@ -4,5 +4,5 @@ __all__ = ['__version__', 'VERSION'] -__version__ = '0.7.0' +__version__ = '0.8.0' VERSION = __version__ diff --git a/test_requirements.txt b/test_requirements.txt index 60b3e9f..c287279 100644 --- a/test_requirements.txt +++ b/test_requirements.txt @@ -1,4 +1,4 @@ pytest pytest-pep8 -pytest-cov +pytest-cov>=4.0 nose>=1.1.2 From 389679e7668e941656343c104993d72429964476 Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Sat, 18 Jan 2020 10:50:29 -0500 Subject: [PATCH 15/17] added directional regression --- sliced/__init__.py | 1 + sliced/dr.py | 161 +++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 162 insertions(+) create mode 100644 sliced/dr.py diff --git a/sliced/__init__.py b/sliced/__init__.py index 07ed70e..9946134 100644 --- a/sliced/__init__.py +++ b/sliced/__init__.py @@ -13,4 +13,5 @@ from sliced.phd import * from sliced.iht import * from sliced.opg import * +from sliced.dr import * from sliced.version import * diff --git a/sliced/dr.py b/sliced/dr.py new file mode 100644 index 0000000..e45bf6a --- /dev/null +++ b/sliced/dr.py @@ -0,0 +1,161 @@ +from __future__ import absolute_import +from __future__ import division +from __future__ import print_function + +import six + +import numpy as np +import scipy.linalg as linalg + +from scipy import sparse +from sklearn.base import BaseEstimator, TransformerMixin +from sklearn.preprocessing import normalize + +from .externals import check_array, check_X_y, check_is_fitted +from .base import slice_y, is_multioutput + + +__all__ = ['DirectionalRegression'] + + +class DirectionalRegression(BaseEstimator, TransformerMixin): + """Directional Regression (DR)""" + def __init__(self, n_directions=None, n_slices=10, copy=True): + self.n_directions = n_directions + self.n_slices = n_slices + self.copy = copy + + def fit(self, X, y): + """Fit the model with X and y. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + Training data, where n_samples is the number of samples + and n_features is the number of features. + + y : array-like, shape (n_samples,) + The target values (class labels in classification, real numbers + in regression). + + Returns + ------- + self : object + Returns the instance itself. + """ + if sparse.issparse(X): + raise TypeError("DirectionalRegression does not support " + "sparse input.") + + X, y = check_X_y(X, y, dtype=[np.float64, np.float32], + accept_sparse=['csr'], + y_numeric=True, copy=self.copy) + + if self.n_directions is None: + n_directions = X.shape[1] + elif (not isinstance(self.n_directions, six.string_types) and + self.n_directions < 1): + raise ValueError('The number of directions `n_directions` ' + 'must be >= 1. Got `n_directions`={}'.format( + self.n_directions)) + else: + n_directions = self.n_directions + + # validate y + if is_multioutput(y): + raise TypeError("The target `y` cannot be multi-output.") + + n_samples, n_features = X.shape + + # Center and Whiten feature matrix using a QR decomposition + # (this is the approach used in the dr package) + self.mean_ = np.mean(X, axis=0) + if self.copy: + X = X - self.mean_ + else: + X -= self.mean_ + Q, R = linalg.qr(X, mode='economic') + Z = np.sqrt(n_samples) * Q + Z = Z[np.argsort(y), :] + + # determine slice indices and counts per slice + slices, counts = slice_y(y, self.n_slices) + self.n_slices_ = counts.shape[0] + + # Construct moment matrices + Mz = np.zeros((n_features, n_features)) + Mzzt = np.zeros((n_features, n_features)) + for slice_idx in range(self.n_slices_): + n_slice = counts[slice_idx] + p_slice = n_samples / n_slice + + # extract entries in the slice + Z_slice = Z[slices == slice_idx, :] + + # extract empirical moments + Ez = np.mean(Z_slice, axis=0).reshape(-1, 1) + Ezzt = np.dot(Z_slice.T, Z_slice) / n_slice + + # first moment matrix + Mz += p_slice * np.dot(Ez, Ez.T) + + # second moment matrix + Mzzt += p_slice * np.dot(Ezzt, Ezzt) + + M = 2 * Mzzt + 2 * np.dot(Mz, Mz) + 2 * np.trace(Mz) * Mz + M -= 2 * np.eye(n_features) + + # eigen-decomposition of slice matrix + evals, evecs = linalg.eigh(M) + evecs = evecs[:, ::-1] + evals = evals[::-1] + try: + # TODO: internally handle zero variance features. This would not + # be a problem if we used svd, but does not match DR. + directions = linalg.solve_triangular(np.sqrt(n_samples) * R, evecs) + except (linalg.LinAlgError, TypeError): + # NOTE: The TypeError is because of a bug in the reporting of scipy + raise linalg.LinAlgError( + "Unable to back-solve R for the dimension " + "reducing directions. This is usually caused by the presents " + "of zero variance features. Try removing these features with " + "`sklearn.feature_selection.VarianceThreshold(threshold=0.)` " + "and refitting.") + + # the number of directions is chosen by finding the maximum gap among + # the ordered eigenvalues. + if self.n_directions == 'auto': + n_directions = np.argmax(np.abs(np.diff(evals))) + 1 + self.n_directions_ = n_directions + + # normalize directions + directions = normalize( + directions[:, :self.n_directions_], norm='l2', axis=0) + self.directions_ = directions.T + + self.eigenvalues_ = evals[:self.n_directions_] + + return self + + def transform(self, X): + """Apply dimension reduction on X. + + X is projected onto the EDR-directions previously extracted from a + training set. + + Parameters + ---------- + X : array-like, shape (n_samples, n_features) + New data, where n_samples in the number of samples + and n_features is the number of features. + + + Returns + ------- + X_new : array-like, shape (n_samples, n_directions) + + """ + check_is_fitted(self, 'directions_') + + X = check_array(X) + return np.dot(X - self.mean_, self.directions_.T) From 194e414035f928048c78d409923ab95b9942aa78 Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Sat, 18 Jan 2020 19:45:39 -0500 Subject: [PATCH 16/17] added smoke test for DR and changed default n_directions=None --- sliced/save.py | 2 +- sliced/sir.py | 4 ++-- sliced/test/test_dr.py | 24 ++++++++++++++++++++++++ 3 files changed, 27 insertions(+), 3 deletions(-) create mode 100644 sliced/test/test_dr.py diff --git a/sliced/save.py b/sliced/save.py index 23eb013..9c3f791 100644 --- a/sliced/save.py +++ b/sliced/save.py @@ -91,7 +91,7 @@ class SlicedAverageVarianceEstimation(BaseEstimator, TransformerMixin): "Marginal Tests with Sliced Average Variance Estimation", Biometrika, 94, 285-296. """ - def __init__(self, n_directions='auto', n_slices=10, copy=True): + def __init__(self, n_directions=None, n_slices=10, copy=True): self.n_directions = n_directions self.n_slices = n_slices self.copy = copy diff --git a/sliced/sir.py b/sliced/sir.py index 4ab981f..e4a4368 100644 --- a/sliced/sir.py +++ b/sliced/sir.py @@ -72,7 +72,7 @@ class SlicedInverseRegression(BaseEstimator, TransformerMixin): Parameters ---------- - n_directions : int, str or None (default='auto') + n_directions : int, str or None (default=None) Number of directions to keep. Corresponds to the dimension of the central subpace. If n_directions=='auto', the number of directions is chosen by finding the maximum gap in the ordered eigenvalues of @@ -135,7 +135,7 @@ class SlicedInverseRegression(BaseEstimator, TransformerMixin): [2] Chen, C.H., and Li, K.C. (1998), "Can SIR Be as Popular as Multiple Linear Regression?" Statistica Sinica, 8, 289-316. """ - def __init__(self, n_directions='auto', n_slices=10, alpha=None, copy=True): + def __init__(self, n_directions=None, n_slices=10, alpha=None, copy=True): self.n_directions = n_directions self.n_slices = n_slices self.alpha = alpha diff --git a/sliced/test/test_dr.py b/sliced/test/test_dr.py new file mode 100644 index 0000000..b5608b2 --- /dev/null +++ b/sliced/test/test_dr.py @@ -0,0 +1,24 @@ +from __future__ import absolute_import +from __future__ import division +from __future__ import print_function + +import sys + +import numpy as np +import pytest + +from scipy import sparse +from scipy import linalg + +from sliced import DirectionalRegression +from sliced import datasets + + +def test_cubic(): + X, y = datasets.make_cubic(random_state=123) + + dr = DirectionalRegression(n_slices=3).fit(X, y) + + true_beta = (1 / np.sqrt(2)) * np.hstack((np.ones(2), np.zeros(8))) + angle = np.dot(true_beta, dr.directions_[0, :]) + np.testing.assert_allclose(np.abs(angle), 1, rtol=1e-1) From 58f228d8dd336ceb591fa562820e34087110846c Mon Sep 17 00:00:00 2001 From: Joshua Loyal Date: Sat, 21 Mar 2020 10:45:10 -0500 Subject: [PATCH 17/17] added LADLE and BIC order determination methods --- sliced/__init__.py | 2 ++ sliced/bic.py | 48 +++++++++++++++++++++++++++++++++++++ sliced/dr.py | 1 + sliced/iht.py | 1 + sliced/kir.py | 1 + sliced/ladle.py | 59 ++++++++++++++++++++++++++++++++++++++++++++++ sliced/phd.py | 1 + sliced/save.py | 7 ++++++ sliced/sir.py | 9 ++++++- 9 files changed, 128 insertions(+), 1 deletion(-) create mode 100644 sliced/bic.py create mode 100644 sliced/ladle.py diff --git a/sliced/__init__.py b/sliced/__init__.py index 9946134..aecfecb 100644 --- a/sliced/__init__.py +++ b/sliced/__init__.py @@ -14,4 +14,6 @@ from sliced.iht import * from sliced.opg import * from sliced.dr import * +from sliced.ladle import * +from sliced.bic import * from sliced.version import * diff --git a/sliced/bic.py b/sliced/bic.py new file mode 100644 index 0000000..b196c6e --- /dev/null +++ b/sliced/bic.py @@ -0,0 +1,48 @@ +import numpy as np + +from sklearn.base import clone, BaseEstimator, MetaEstimatorMixin +from sklearn.base import TransformerMixin +from sklearn.utils import resample, check_random_state, check_array + + +__all__ = ['BICDimensionSelector'] + + +class BICDimensionSelector(MetaEstimatorMixin, BaseEstimator, TransformerMixin): + def __init__(self, estimator, criterion='log'): + self.estimator = estimator + self.criterion = criterion + + def fit(self, X, y): + n_samples, n_features = X.shape + + # fit sufficient dimension reduction method + self.estimator_ = clone(self.estimator) + self.estimator_.fit(X, y) + + evals = self.estimator_.eigenvalues_ + self.criterion_ = np.zeros(n_features + 1) + if self.criterion == 'sum': + penalty = 2 * evals[0] * ((n_samples)**(-0.5)) * np.log(n_samples) + for k in range(n_features + 1): + if k == 0: + self.criterion_[k] = 0 + else: + self.criterion_[k] = np.sum(evals[:k]) + self.criterion_[k] -= penalty * k + elif self.criterion == 'log': + penalty = (evals[0] / 3.) * (np.log(n_samples) + np.sqrt(n_samples)) + penalty /= (2. * n_samples) + for k in range(n_features + 1): + if k != n_features: + self.criterion_[k] = np.sum(np.log(evals[k:] + 1) - evals[k:]) + self.criterion_[k] -= penalty * k * (2 * n_features - k + 1) + else: + raise ValueError('Unrecognized criterion {}'.format(self.criterion)) + + self.n_directions_ = np.argmax(self.criterion_) + + return self + + def transform(self, X): + return self.estimator_.transform(X) diff --git a/sliced/dr.py b/sliced/dr.py index e45bf6a..4d06c41 100644 --- a/sliced/dr.py +++ b/sliced/dr.py @@ -134,6 +134,7 @@ def fit(self, X, y): self.directions_ = directions.T self.eigenvalues_ = evals[:self.n_directions_] + self.eigenvectors_ = evecs[:, :self.n_directions_].T return self diff --git a/sliced/iht.py b/sliced/iht.py index 01596af..733d2e9 100644 --- a/sliced/iht.py +++ b/sliced/iht.py @@ -166,6 +166,7 @@ def fit(self, X, y): directions[:, :self.n_directions_], norm='l2', axis=0) self.directions_ = directions.T self.eigenvalues_ = evals[:self.n_directions_] + self.eigenvectors_ = evecs[:, :self.n_directions_].T return self diff --git a/sliced/kir.py b/sliced/kir.py index f0a2cd9..efc1257 100644 --- a/sliced/kir.py +++ b/sliced/kir.py @@ -214,6 +214,7 @@ def fit(self, X, y, kernel=None): directions[:, :self.n_directions_], norm='l2', axis=0) self.directions_ = directions.T self.eigenvalues_ = evals[:self.n_directions_] + self.eigenvectors_ = evecs[:, :self.n_directions_].T return self diff --git a/sliced/ladle.py b/sliced/ladle.py new file mode 100644 index 0000000..58509fe --- /dev/null +++ b/sliced/ladle.py @@ -0,0 +1,59 @@ +import numpy as np + +from sklearn.base import clone, BaseEstimator, MetaEstimatorMixin +from sklearn.base import TransformerMixin +from sklearn.utils import resample, check_random_state, check_array + + +__all__ = ['LadleDimensionSelector'] + + +class LadleDimensionSelector(MetaEstimatorMixin, BaseEstimator, TransformerMixin): + def __init__(self, estimator, n_boot=200, random_state=None): + self.estimator = estimator + self.n_boot = n_boot + self.random_state = random_state + + def fit(self, X, y): + n_samples, n_features = X.shape + + # calculate k_max + self.k_max_ = (n_features - 2 if n_features <= 10 else + int(n_features / np.log(n_features))) + + # fit sufficient dimension reduction method + self.estimator_ = clone(self.estimator) + self.estimator_.fit(X, y) + + # matrix with eigenvectors as columns + B = self.estimator_.eigenvectors_.T + evals = self.estimator_.eigenvalues_ + + # bootstrap eigenvector variation statistic + random_state = check_random_state(self.random_state) + D = np.zeros((self.n_boot, self.k_max_)) + for b in range(self.n_boot): + X_boot, y_boot = resample(X, y, random_state=random_state) + B_boot = clone(self.estimator).fit(X_boot, y_boot).eigenvectors_.T + for k in range(self.k_max_): + if k > 0: + D[b, k] = 1 - np.abs( + np.linalg.det( + np.dot(B[:, :(k+1)].T, B_boot[:, :(k+1)]))) + else: + D[b, k] = 1 - np.abs(np.dot(B[:, 0].T, B_boot[:, 0])) + + # calculate test statistics + eigvec_variation = np.r_[0, np.mean(D, axis=0)] + eigvec_variation /= (1 + np.sum(eigvec_variation)) + eigval_magnitude = (evals[:(self.k_max_ + 1)] / + (1 + np.sum(evals[:(self.k_max_ + 1)]))) + + # record number directions and ladle criterion values for each k + self.criterion_ = eigvec_variation + eigval_magnitude + self.n_directions_ = np.argmin(self.criterion_) + + return self + + def transform(self, X): + return self.estimator_.transform(X) diff --git a/sliced/phd.py b/sliced/phd.py index 4126076..f5ed392 100644 --- a/sliced/phd.py +++ b/sliced/phd.py @@ -166,6 +166,7 @@ def fit(self, X, y): directions[:, :self.n_directions_], norm='l2', axis=0) self.directions_ = directions.T self.eigenvalues_ = evals[:self.n_directions_] + self.eigenvectors_ = evecs[:, :self.n_directions_].T return self diff --git a/sliced/save.py b/sliced/save.py index 9c3f791..5ade49e 100644 --- a/sliced/save.py +++ b/sliced/save.py @@ -67,6 +67,12 @@ class SlicedAverageVarianceEstimation(BaseEstimator, TransformerMixin): of the inverse regression curve. Larger eigenvalues indicate more prevelant directions. + eigenvectors_ : array, shape (n_directions,) + The eigenvectors on the z-scale corresponding to each selected + direction. These are the eigenvectors of the covariance of the + inverse regression curve. This is used primary for order + determination. + mean_ : array, shape (n_features,) The column means of the training data used to estimate the basis of the central subspace. Used to project new data onto the @@ -198,6 +204,7 @@ def fit(self, X, y): self.directions_ = directions.T self.eigenvalues_ = evals[:self.n_directions_] + self.eigenvectors_ = evecs[:, :self.n_directions_].T return self diff --git a/sliced/sir.py b/sliced/sir.py index e4a4368..bd414af 100644 --- a/sliced/sir.py +++ b/sliced/sir.py @@ -104,11 +104,17 @@ class SlicedInverseRegression(BaseEstimator, TransformerMixin): distribution y|X. The directions are sorted by ``eigenvalues_``. eigenvalues_ : array, shape (n_directions,) - The eigenvalues corresponding to each of the selected directions. + The eigenvalues corresponding to each selected direction. These are the eigenvalues of the covariance matrix of the inverse regression curve. Larger eigenvalues indicate more prevalent directions. + eigenvectors_ : array, shape (n_directions, n_features) + The eigenvectors on the z-scale corresponding to each selected + direction. These are the eigenvectors of the covariance of the + inverse regression curve. This is used primary for order + determination. + mean_ : array, shape (n_features,) The column means of the training data used to estimate the basis of the central subspace. Used to project new data onto the @@ -234,6 +240,7 @@ def fit(self, X, y): directions[:, :self.n_directions_], norm='l2', axis=0) self.directions_ = directions.T self.eigenvalues_ = evals[:self.n_directions_] + self.eigenvectors_ = evecs[:, :self.n_directions_].T # Drop components in each direction using the t-ratio approach # suggested in section 4 of Chen and Li (1998).