/usr/lib/python2.7/dist-packages/sklearn/isotonic.py is in python-sklearn 0.14.1-3.
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# 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 .base import BaseEstimator, TransformerMixin, RegressorMixin
from .utils import as_float_array, check_arrays
from ._isotonic import _isotonic_regression
import warnings
def isotonic_regression(y, sample_weight=None, y_min=None, y_max=None,
weight=None, increasing=True):
"""Solve the isotonic regression model::
min sum w[i] (y[i] - y_[i]) ** 2
subject to y_min = y_[1] <= y_[2] ... <= y_[n] = y_max
where:
- y[i] are inputs (real numbers)
- y_[i] are fitted
- w[i] are optional strictly positive weights (default to 1.0)
Parameters
----------
y : iterable of floating-point values
The data.
sample_weight : iterable of floating-point values, optional, default: None
Weights on each point of the regression.
If None, weight is set to 1 (equal weights).
y_min : optional, default: None
If not None, set the lowest value of the fit to y_min.
y_max : optional, default: None
If not None, set the highest value of the fit to y_max.
increasing : boolean, optional, default: True
Whether to compute ``y_`` is increasing (if set to True) or decreasing
(if set to False)
Returns
-------
`y_` : list of floating-point values
Isotonic fit of y.
References
----------
"Active set algorithms for isotonic regression; A unifying framework"
by Michael J. Best and Nilotpal Chakravarti, section 3.
"""
if weight is not None:
warnings.warn("'weight' was renamed to 'sample_weight' and will "
"be removed in 0.16.",
DeprecationWarning)
sample_weight = weight
y = np.asarray(y, dtype=np.float)
if sample_weight is None:
sample_weight = np.ones(len(y), dtype=y.dtype)
else:
sample_weight = np.asarray(sample_weight, dtype=np.float)
if not increasing:
y = y[::-1]
sample_weight = sample_weight[::-1]
if y_min is not None or y_max is not None:
y = np.copy(y)
sample_weight = np.copy(sample_weight)
# upper bound on the cost function
C = np.dot(sample_weight, y * y) * 10
if y_min is not None:
y[0] = y_min
sample_weight[0] = C
if y_max is not None:
y[-1] = y_max
sample_weight[-1] = C
solution = np.empty(len(y))
y_ = _isotonic_regression(y, sample_weight, solution)
if increasing:
return y_
else:
return y_[::-1]
class IsotonicRegression(BaseEstimator, TransformerMixin, RegressorMixin):
"""Isotonic regression model.
The isotonic regression optimization problem is defined by::
min sum w_i (y[i] - y_[i]) ** 2
subject to y_[i] <= y_[j] whenever X[i] <= X[j]
and min(y_) = y_min, max(y_) = y_max
where:
- ``y[i]`` are inputs (real numbers)
- ``y_[i]`` are fitted
- ``X`` specifies the order.
If ``X`` is non-decreasing then ``y_`` is non-decreasing.
- ``w[i]`` are optional strictly positive weights (default to 1.0)
Parameters
----------
y_min : optional, default: None
If not None, set the lowest value of the fit to y_min.
y_max : optional, default: None
If not None, set the highest value of the fit to y_max.
Attributes
----------
`X_` : ndarray (n_samples, )
A copy of the input X.
`y_` : ndarray (n_samples, )
Isotonic fit of y.
References
----------
Isotonic Median Regression: A Linear Programming Approach
Nilotpal Chakravarti
Mathematics of Operations Research
Vol. 14, No. 2 (May, 1989), pp. 303-308
"""
def __init__(self, y_min=None, y_max=None, increasing=True):
self.y_min = y_min
self.y_max = y_max
self.increasing = increasing
def _check_fit_data(self, X, y, sample_weight=None):
if len(X.shape) != 1:
raise ValueError("X should be a vector")
def fit(self, X, y, sample_weight=None, weight=None):
"""Fit the model using X, y as training data.
Parameters
----------
X : array-like, shape=(n_samples,)
Training data.
y : array-like, shape=(n_samples,)
Training target.
sample_weight : array-like, shape=(n_samples,), optional, 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 `transform` needs X to interpolate
new input data.
"""
if weight is not None:
warnings.warn("'weight' was renamed to 'sample_weight' and will "
"be removed in 0.16.",
DeprecationWarning)
sample_weight = weight
X, y, sample_weight = check_arrays(X, y, sample_weight,
sparse_format='dense')
y = as_float_array(y)
self._check_fit_data(X, y, sample_weight)
order = np.argsort(X)
self.X_ = as_float_array(X[order], copy=False)
self.y_ = isotonic_regression(y[order], sample_weight, self.y_min,
self.y_max, increasing=self.increasing)
return self
def transform(self, T):
"""Transform new data by linear interpolation
Parameters
----------
T : array-like, shape=(n_samples,)
Data to transform.
Returns
-------
`T_` : array, shape=(n_samples,)
The transformed data
"""
T = as_float_array(T)
if len(T.shape) != 1:
raise ValueError("X should be a vector")
f = interpolate.interp1d(self.X_, self.y_, kind='linear',
bounds_error=True)
return f(T)
def fit_transform(self, X, y, sample_weight=None, weight=None):
"""Fit model and transform y by linear interpolation.
Parameters
----------
X : array-like, shape=(n_samples,)
Training data.
y : array-like, shape=(n_samples,)
Training target.
sample_weight : array-like, shape=(n_samples,), optional, default: None
Weights. If set to None, all weights will be equal to 1 (equal
weights).
Returns
-------
`y_` : array, shape=(n_samples,)
The transformed data.
Notes
-----
X doesn't influence the result of `fit_transform`. It is however stored
for future use, as `transform` needs X to interpolate new input
data.
"""
if weight is not None:
warnings.warn("'weight' was renamed to 'sample_weight' and will "
"be removed in 0.16.",
DeprecationWarning)
sample_weight = weight
X, y, sample_weight = check_arrays(X, y, sample_weight,
sparse_format='dense')
y = as_float_array(y)
self._check_fit_data(X, y, sample_weight)
order = np.lexsort((y, X))
order_inv = np.argsort(order)
self.X_ = as_float_array(X[order], copy=False)
self.y_ = isotonic_regression(y[order], sample_weight, self.y_min,
self.y_max, increasing=self.increasing)
return self.y_[order_inv]
def predict(self, T):
"""Predict new data by linear interpolation.
Parameters
----------
T : array-like, shape=(n_samples,)
Data to transform.
Returns
-------
`T_` : array, shape=(n_samples,)
Transformed data.
"""
return self.transform(T)
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