420 lines
14 KiB
Python
420 lines
14 KiB
Python
|
# Authors: Fabian Pedregosa <fabian@fseoane.net>
|
||
|
|
# Alexandre Gramfort <alexandre.gramfort@inria.fr>
|
||
|
|
# Nelle Varoquaux <nelle.varoquaux@gmail.com>
|
||
|
|
# License: BSD 3 clause
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
from scipy import interpolate
|
||
|
|
from scipy.stats import spearmanr
|
||
|
|
import warnings
|
||
|
|
import math
|
||
|
|
|
||
|
|
from .base import BaseEstimator, TransformerMixin, RegressorMixin
|
||
|
|
from .utils import check_array, check_consistent_length
|
||
|
|
from .utils.validation import _check_sample_weight, _deprecate_positional_args
|
||
|
|
from ._isotonic import _inplace_contiguous_isotonic_regression, _make_unique
|
||
|
|
|
||
|
|
|
||
|
|
__all__ = ['check_increasing', 'isotonic_regression',
|
||
|
|
'IsotonicRegression']
|
||
|
|
|
||
|
|
|
||
|
|
def check_increasing(x, y):
|
||
|
|
"""Determine whether y is monotonically correlated with x.
|
||
|
|
|
||
|
|
y is found increasing or decreasing with respect to x based on a Spearman
|
||
|
|
correlation test.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
x : array-like of shape (n_samples,)
|
||
|
|
Training data.
|
||
|
|
|
||
|
|
y : array-like of shape (n_samples,)
|
||
|
|
Training target.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
increasing_bool : boolean
|
||
|
|
Whether the relationship is increasing or decreasing.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
The Spearman correlation coefficient is estimated from the data, and the
|
||
|
|
sign of the resulting estimate is used as the result.
|
||
|
|
|
||
|
|
In the event that the 95% confidence interval based on Fisher transform
|
||
|
|
spans zero, a warning is raised.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
Fisher transformation. Wikipedia.
|
||
|
|
https://en.wikipedia.org/wiki/Fisher_transformation
|
||
|
|
"""
|
||
|
|
|
||
|
|
# Calculate Spearman rho estimate and set return accordingly.
|
||
|
|
rho, _ = spearmanr(x, y)
|
||
|
|
increasing_bool = rho >= 0
|
||
|
|
|
||
|
|
# Run Fisher transform to get the rho CI, but handle rho=+/-1
|
||
|
|
if rho not in [-1.0, 1.0] and len(x) > 3:
|
||
|
|
F = 0.5 * math.log((1. + rho) / (1. - rho))
|
||
|
|
F_se = 1 / math.sqrt(len(x) - 3)
|
||
|
|
|
||
|
|
# Use a 95% CI, i.e., +/-1.96 S.E.
|
||
|
|
# https://en.wikipedia.org/wiki/Fisher_transformation
|
||
|
|
rho_0 = math.tanh(F - 1.96 * F_se)
|
||
|
|
rho_1 = math.tanh(F + 1.96 * F_se)
|
||
|
|
|
||
|
|
# Warn if the CI spans zero.
|
||
|
|
if np.sign(rho_0) != np.sign(rho_1):
|
||
|
|
warnings.warn("Confidence interval of the Spearman "
|
||
|
|
"correlation coefficient spans zero. "
|
||
|
|
"Determination of ``increasing`` may be "
|
||
|
|
"suspect.")
|
||
|
|
|
||
|
|
return increasing_bool
|
||
|
|
|
||
|
|
|
||
|
|
@_deprecate_positional_args
|
||
|
|
def isotonic_regression(y, *, sample_weight=None, y_min=None, y_max=None,
|
||
|
|
increasing=True):
|
||
|
|
"""Solve the isotonic regression model.
|
||
|
|
|
||
|
|
Read more in the :ref:`User Guide <isotonic>`.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
y : array-like of shape (n_samples,)
|
||
|
|
The data.
|
||
|
|
|
||
|
|
sample_weight : array-like of shape (n_samples,), default=None
|
||
|
|
Weights on each point of the regression.
|
||
|
|
If None, weight is set to 1 (equal weights).
|
||
|
|
|
||
|
|
y_min : float, default=None
|
||
|
|
Lower bound on the lowest predicted value (the minimum value may
|
||
|
|
still be higher). If not set, defaults to -inf.
|
||
|
|
|
||
|
|
y_max : float, default=None
|
||
|
|
Upper bound on the highest predicted value (the maximum may still be
|
||
|
|
lower). If not set, defaults to +inf.
|
||
|
|
|
||
|
|
increasing : bool, default=True
|
||
|
|
Whether to compute ``y_`` is increasing (if set to True) or decreasing
|
||
|
|
(if set to False)
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
y_ : list of floats
|
||
|
|
Isotonic fit of y.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
"Active set algorithms for isotonic regression; A unifying framework"
|
||
|
|
by Michael J. Best and Nilotpal Chakravarti, section 3.
|
||
|
|
"""
|
||
|
|
order = np.s_[:] if increasing else np.s_[::-1]
|
||
|
|
y = check_array(y, ensure_2d=False, dtype=[np.float64, np.float32])
|
||
|
|
y = np.array(y[order], dtype=y.dtype)
|
||
|
|
sample_weight = _check_sample_weight(sample_weight, y, dtype=y.dtype)
|
||
|
|
sample_weight = np.ascontiguousarray(sample_weight[order])
|
||
|
|
|
||
|
|
_inplace_contiguous_isotonic_regression(y, sample_weight)
|
||
|
|
if y_min is not None or y_max is not None:
|
||
|
|
# Older versions of np.clip don't accept None as a bound, so use np.inf
|
||
|
|
if y_min is None:
|
||
|
|
y_min = -np.inf
|
||
|
|
if y_max is None:
|
||
|
|
y_max = np.inf
|
||
|
|
np.clip(y, y_min, y_max, y)
|
||
|
|
return y[order]
|
||
|
|
|
||
|
|
|
||
|
|
class IsotonicRegression(RegressorMixin, TransformerMixin, BaseEstimator):
|
||
|
|
"""Isotonic regression model.
|
||
|
|
|
||
|
|
Read more in the :ref:`User Guide <isotonic>`.
|
||
|
|
|
||
|
|
.. versionadded:: 0.13
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
y_min : float, default=None
|
||
|
|
Lower bound on the lowest predicted value (the minimum value may
|
||
|
|
still be higher). If not set, defaults to -inf.
|
||
|
|
|
||
|
|
y_max : float, default=None
|
||
|
|
Upper bound on the highest predicted value (the maximum may still be
|
||
|
|
lower). If not set, defaults to +inf.
|
||
|
|
|
||
|
|
increasing : bool or 'auto', default=True
|
||
|
|
Determines whether the predictions should be constrained to increase
|
||
|
|
or decrease with `X`. 'auto' will decide based on the Spearman
|
||
|
|
correlation estimate's sign.
|
||
|
|
|
||
|
|
out_of_bounds : {'nan', 'clip', 'raise'}, default='nan'
|
||
|
|
Handles how `X` values outside of the training domain are handled
|
||
|
|
during prediction.
|
||
|
|
|
||
|
|
- 'nan', predictions will be NaN.
|
||
|
|
- 'clip', predictions will be set to the value corresponding to
|
||
|
|
the nearest train interval endpoint.
|
||
|
|
- 'raise', a `ValueError` is raised.
|
||
|
|
|
||
|
|
Attributes
|
||
|
|
----------
|
||
|
|
X_min_ : float
|
||
|
|
Minimum value of input array `X_` for left bound.
|
||
|
|
|
||
|
|
X_max_ : float
|
||
|
|
Maximum value of input array `X_` for right bound.
|
||
|
|
|
||
|
|
X_thresholds_ : ndarray of shape (n_thresholds,)
|
||
|
|
Unique ascending `X` values used to interpolate
|
||
|
|
the y = f(X) monotonic function.
|
||
|
|
|
||
|
|
.. versionadded:: 0.24
|
||
|
|
|
||
|
|
y_thresholds_ : ndarray of shape (n_thresholds,)
|
||
|
|
De-duplicated `y` values suitable to interpolate the y = f(X)
|
||
|
|
monotonic function.
|
||
|
|
|
||
|
|
.. versionadded:: 0.24
|
||
|
|
|
||
|
|
f_ : function
|
||
|
|
The stepwise interpolating function that covers the input domain ``X``.
|
||
|
|
|
||
|
|
increasing_ : bool
|
||
|
|
Inferred value for ``increasing``.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
Ties are broken using the secondary method from de Leeuw, 1977.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
Isotonic Median Regression: A Linear Programming Approach
|
||
|
|
Nilotpal Chakravarti
|
||
|
|
Mathematics of Operations Research
|
||
|
|
Vol. 14, No. 2 (May, 1989), pp. 303-308
|
||
|
|
|
||
|
|
Isotone Optimization in R : Pool-Adjacent-Violators
|
||
|
|
Algorithm (PAVA) and Active Set Methods
|
||
|
|
de Leeuw, Hornik, Mair
|
||
|
|
Journal of Statistical Software 2009
|
||
|
|
|
||
|
|
Correctness of Kruskal's algorithms for monotone regression with ties
|
||
|
|
de Leeuw, Psychometrica, 1977
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from sklearn.datasets import make_regression
|
||
|
|
>>> from sklearn.isotonic import IsotonicRegression
|
||
|
|
>>> X, y = make_regression(n_samples=10, n_features=1, random_state=41)
|
||
|
|
>>> iso_reg = IsotonicRegression().fit(X, y)
|
||
|
|
>>> iso_reg.predict([.1, .2])
|
||
|
|
array([1.8628..., 3.7256...])
|
||
|
|
"""
|
||
|
|
@_deprecate_positional_args
|
||
|
|
def __init__(self, *, y_min=None, y_max=None, increasing=True,
|
||
|
|
out_of_bounds='nan'):
|
||
|
|
self.y_min = y_min
|
||
|
|
self.y_max = y_max
|
||
|
|
self.increasing = increasing
|
||
|
|
self.out_of_bounds = out_of_bounds
|
||
|
|
|
||
|
|
def _check_input_data_shape(self, X):
|
||
|
|
if not (X.ndim == 1 or (X.ndim == 2 and X.shape[1] == 1)):
|
||
|
|
msg = "Isotonic regression input X should be a 1d array or " \
|
||
|
|
"2d array with 1 feature"
|
||
|
|
raise ValueError(msg)
|
||
|
|
|
||
|
|
def _build_f(self, X, y):
|
||
|
|
"""Build the f_ interp1d function."""
|
||
|
|
|
||
|
|
# Handle the out_of_bounds argument by setting bounds_error
|
||
|
|
if self.out_of_bounds not in ["raise", "nan", "clip"]:
|
||
|
|
raise ValueError("The argument ``out_of_bounds`` must be in "
|
||
|
|
"'nan', 'clip', 'raise'; got {0}"
|
||
|
|
.format(self.out_of_bounds))
|
||
|
|
|
||
|
|
bounds_error = self.out_of_bounds == "raise"
|
||
|
|
if len(y) == 1:
|
||
|
|
# single y, constant prediction
|
||
|
|
self.f_ = lambda x: y.repeat(x.shape)
|
||
|
|
else:
|
||
|
|
self.f_ = interpolate.interp1d(X, y, kind='linear',
|
||
|
|
bounds_error=bounds_error)
|
||
|
|
|
||
|
|
def _build_y(self, X, y, sample_weight, trim_duplicates=True):
|
||
|
|
"""Build the y_ IsotonicRegression."""
|
||
|
|
self._check_input_data_shape(X)
|
||
|
|
X = X.reshape(-1) # use 1d view
|
||
|
|
|
||
|
|
# Determine increasing if auto-determination requested
|
||
|
|
if self.increasing == 'auto':
|
||
|
|
self.increasing_ = check_increasing(X, y)
|
||
|
|
else:
|
||
|
|
self.increasing_ = self.increasing
|
||
|
|
|
||
|
|
# If sample_weights is passed, removed zero-weight values and clean
|
||
|
|
# order
|
||
|
|
sample_weight = _check_sample_weight(sample_weight, X, dtype=X.dtype)
|
||
|
|
mask = sample_weight > 0
|
||
|
|
X, y, sample_weight = X[mask], y[mask], sample_weight[mask]
|
||
|
|
|
||
|
|
order = np.lexsort((y, X))
|
||
|
|
X, y, sample_weight = [array[order] for array in [X, y, sample_weight]]
|
||
|
|
unique_X, unique_y, unique_sample_weight = _make_unique(
|
||
|
|
X, y, sample_weight)
|
||
|
|
|
||
|
|
X = unique_X
|
||
|
|
y = isotonic_regression(unique_y, sample_weight=unique_sample_weight,
|
||
|
|
y_min=self.y_min, y_max=self.y_max,
|
||
|
|
increasing=self.increasing_)
|
||
|
|
|
||
|
|
# Handle the left and right bounds on X
|
||
|
|
self.X_min_, self.X_max_ = np.min(X), np.max(X)
|
||
|
|
|
||
|
|
if trim_duplicates:
|
||
|
|
# Remove unnecessary points for faster prediction
|
||
|
|
keep_data = np.ones((len(y),), dtype=bool)
|
||
|
|
# Aside from the 1st and last point, remove points whose y values
|
||
|
|
# are equal to both the point before and the point after it.
|
||
|
|
keep_data[1:-1] = np.logical_or(
|
||
|
|
np.not_equal(y[1:-1], y[:-2]),
|
||
|
|
np.not_equal(y[1:-1], y[2:])
|
||
|
|
)
|
||
|
|
return X[keep_data], y[keep_data]
|
||
|
|
else:
|
||
|
|
# The ability to turn off trim_duplicates is only used to it make
|
||
|
|
# easier to unit test that removing duplicates in y does not have
|
||
|
|
# any impact the resulting interpolation function (besides
|
||
|
|
# prediction speed).
|
||
|
|
return X, y
|
||
|
|
|
||
|
|
def fit(self, X, y, sample_weight=None):
|
||
|
|
"""Fit the model using X, y as training data.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : array-like of shape (n_samples,) or (n_samples, 1)
|
||
|
|
Training data.
|
||
|
|
|
||
|
|
.. versionchanged:: 0.24
|
||
|
|
Also accepts 2d array with 1 feature.
|
||
|
|
|
||
|
|
y : array-like of shape (n_samples,)
|
||
|
|
Training target.
|
||
|
|
|
||
|
|
sample_weight : array-like of shape (n_samples,), default=None
|
||
|
|
Weights. If set to None, all weights will be set to 1 (equal
|
||
|
|
weights).
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
self : object
|
||
|
|
Returns an instance of self.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
X is stored for future use, as :meth:`transform` needs X to interpolate
|
||
|
|
new input data.
|
||
|
|
"""
|
||
|
|
check_params = dict(accept_sparse=False, ensure_2d=False)
|
||
|
|
X = check_array(X, dtype=[np.float64, np.float32], **check_params)
|
||
|
|
y = check_array(y, dtype=X.dtype, **check_params)
|
||
|
|
check_consistent_length(X, y, sample_weight)
|
||
|
|
|
||
|
|
# Transform y by running the isotonic regression algorithm and
|
||
|
|
# transform X accordingly.
|
||
|
|
X, y = self._build_y(X, y, sample_weight)
|
||
|
|
|
||
|
|
# It is necessary to store the non-redundant part of the training set
|
||
|
|
# on the model to make it possible to support model persistence via
|
||
|
|
# the pickle module as the object built by scipy.interp1d is not
|
||
|
|
# picklable directly.
|
||
|
|
self.X_thresholds_, self.y_thresholds_ = X, y
|
||
|
|
|
||
|
|
# Build the interpolation function
|
||
|
|
self._build_f(X, y)
|
||
|
|
return self
|
||
|
|
|
||
|
|
def transform(self, T):
|
||
|
|
"""Transform new data by linear interpolation
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
T : array-like of shape (n_samples,) or (n_samples, 1)
|
||
|
|
Data to transform.
|
||
|
|
|
||
|
|
.. versionchanged:: 0.24
|
||
|
|
Also accepts 2d array with 1 feature.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
y_pred : ndarray of shape (n_samples,)
|
||
|
|
The transformed data
|
||
|
|
"""
|
||
|
|
|
||
|
|
if hasattr(self, 'X_thresholds_'):
|
||
|
|
dtype = self.X_thresholds_.dtype
|
||
|
|
else:
|
||
|
|
dtype = np.float64
|
||
|
|
|
||
|
|
T = check_array(T, dtype=dtype, ensure_2d=False)
|
||
|
|
|
||
|
|
self._check_input_data_shape(T)
|
||
|
|
T = T.reshape(-1) # use 1d view
|
||
|
|
|
||
|
|
# Handle the out_of_bounds argument by clipping if needed
|
||
|
|
if self.out_of_bounds not in ["raise", "nan", "clip"]:
|
||
|
|
raise ValueError("The argument ``out_of_bounds`` must be in "
|
||
|
|
"'nan', 'clip', 'raise'; got {0}"
|
||
|
|
.format(self.out_of_bounds))
|
||
|
|
|
||
|
|
if self.out_of_bounds == "clip":
|
||
|
|
T = np.clip(T, self.X_min_, self.X_max_)
|
||
|
|
|
||
|
|
res = self.f_(T)
|
||
|
|
|
||
|
|
# on scipy 0.17, interp1d up-casts to float64, so we cast back
|
||
|
|
res = res.astype(T.dtype)
|
||
|
|
|
||
|
|
return res
|
||
|
|
|
||
|
|
def predict(self, T):
|
||
|
|
"""Predict new data by linear interpolation.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
T : array-like of shape (n_samples,) or (n_samples, 1)
|
||
|
|
Data to transform.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
y_pred : ndarray of shape (n_samples,)
|
||
|
|
Transformed data.
|
||
|
|
"""
|
||
|
|
return self.transform(T)
|
||
|
|
|
||
|
|
def __getstate__(self):
|
||
|
|
"""Pickle-protocol - return state of the estimator. """
|
||
|
|
state = super().__getstate__()
|
||
|
|
# remove interpolation method
|
||
|
|
state.pop('f_', None)
|
||
|
|
return state
|
||
|
|
|
||
|
|
def __setstate__(self, state):
|
||
|
|
"""Pickle-protocol - set state of the estimator.
|
||
|
|
|
||
|
|
We need to rebuild the interpolation function.
|
||
|
|
"""
|
||
|
|
super().__setstate__(state)
|
||
|
|
if hasattr(self, 'X_thresholds_') and hasattr(self, 'y_thresholds_'):
|
||
|
|
self._build_f(self.X_thresholds_, self.y_thresholds_)
|
||
|
|
|
||
|
|
def _more_tags(self):
|
||
|
|
return {'X_types': ['1darray']}
|