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icp.py
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#!/usr/bin/env python
"""
Inductive conformal predictors.
"""
# Authors: Henrik Linusson
from __future__ import division
from collections import defaultdict
from functools import partial
import numpy as np
from sklearn.base import BaseEstimator
from nonconformist.base import RegressorMixin, ClassifierMixin
from nonconformist.util import calc_p
# -----------------------------------------------------------------------------
# Base inductive conformal predictor
# -----------------------------------------------------------------------------
class BaseIcp(BaseEstimator):
"""Base class for inductive conformal predictors.
"""
def __init__(self, nc_function, condition=None):
self.cal_x, self.cal_y = None, None
self.nc_function = nc_function
# Check if condition-parameter is the default function (i.e.,
# lambda x: 0). This is so we can safely clone the object without
# the clone accidentally having self.conditional = True.
default_condition = lambda x: 0
is_default = (callable(condition) and
(condition.__code__.co_code ==
default_condition.__code__.co_code))
if is_default:
self.condition = condition
self.conditional = False
elif callable(condition):
self.condition = condition
self.conditional = True
else:
self.condition = lambda x: 0
self.conditional = False
def fit(self, x, y):
"""Fit underlying nonconformity scorer.
Parameters
----------
x : numpy array of shape [n_samples, n_features]
Inputs of examples for fitting the nonconformity scorer.
y : numpy array of shape [n_samples]
Outputs of examples for fitting the nonconformity scorer.
Returns
-------
None
"""
# TODO: incremental?
self.nc_function.fit(x, y)
def calibrate(self, x, y, increment=False):
"""Calibrate conformal predictor based on underlying nonconformity
scorer.
Parameters
----------
x : numpy array of shape [n_samples, n_features]
Inputs of examples for calibrating the conformal predictor.
y : numpy array of shape [n_samples, n_features]
Outputs of examples for calibrating the conformal predictor.
increment : boolean
If ``True``, performs an incremental recalibration of the conformal
predictor. The supplied ``x`` and ``y`` are added to the set of
previously existing calibration examples, and the conformal
predictor is then calibrated on both the old and new calibration
examples.
Returns
-------
None
"""
self._calibrate_hook(x, y, increment)
self._update_calibration_set(x, y, increment)
if self.conditional:
category_map = np.array([self.condition((x[i, :], y[i]))
for i in range(y.size)])
self.categories = np.unique(category_map)
self.cal_scores = defaultdict(partial(np.ndarray, 0))
for cond in self.categories:
idx = category_map == cond
cal_scores = self.nc_function.score(self.cal_x[idx, :],
self.cal_y[idx])
self.cal_scores[cond] = np.sort(cal_scores)[::-1]
else:
self.categories = np.array([0])
cal_scores = self.nc_function.score(self.cal_x, self.cal_y)
self.cal_scores = {0: np.sort(cal_scores)[::-1]}
def _calibrate_hook(self, x, y, increment):
pass
def _update_calibration_set(self, x, y, increment):
if increment and self.cal_x is not None and self.cal_y is not None:
self.cal_x = np.vstack([self.cal_x, x])
self.cal_y = np.hstack([self.cal_y, y])
else:
self.cal_x, self.cal_y = x, y
# -----------------------------------------------------------------------------
# Inductive conformal classifier
# -----------------------------------------------------------------------------
class IcpClassifier(BaseIcp, ClassifierMixin):
"""Inductive conformal classifier.
Parameters
----------
nc_function : BaseScorer
Nonconformity scorer object used to calculate nonconformity of
calibration examples and test patterns. Should implement ``fit(x, y)``
and ``calc_nc(x, y)``.
smoothing : boolean
Decides whether to use stochastic smoothing of p-values.
Attributes
----------
cal_x : numpy array of shape [n_cal_examples, n_features]
Inputs of calibration set.
cal_y : numpy array of shape [n_cal_examples]
Outputs of calibration set.
nc_function : BaseScorer
Nonconformity scorer object used to calculate nonconformity scores.
classes : numpy array of shape [n_classes]
List of class labels, with indices corresponding to output columns
of IcpClassifier.predict()
See also
--------
IcpRegressor
References
----------
.. [1] Papadopoulos, H., & Haralambous, H. (2011). Reliable prediction
intervals with regression neural networks. Neural Networks, 24(8),
842-851.
Examples
--------
>>> import numpy as np
>>> from sklearn.datasets import load_iris
>>> from sklearn.tree import DecisionTreeClassifier
>>> from nonconformist.base import ClassifierAdapter
>>> from nonconformist.icp import IcpClassifier
>>> from nonconformist.nc import ClassifierNc, MarginErrFunc
>>> iris = load_iris()
>>> idx = np.random.permutation(iris.target.size)
>>> train = idx[:int(idx.size / 3)]
>>> cal = idx[int(idx.size / 3):int(2 * idx.size / 3)]
>>> test = idx[int(2 * idx.size / 3):]
>>> model = ClassifierAdapter(DecisionTreeClassifier())
>>> nc = ClassifierNc(model, MarginErrFunc())
>>> icp = IcpClassifier(nc)
>>> icp.fit(iris.data[train, :], iris.target[train])
>>> icp.calibrate(iris.data[cal, :], iris.target[cal])
>>> icp.predict(iris.data[test, :], significance=0.10)
... # doctest: +SKIP
array([[ True, False, False],
[False, True, False],
...,
[False, True, False],
[False, True, False]], dtype=bool)
"""
def __init__(self, nc_function, condition=None, smoothing=True):
super(IcpClassifier, self).__init__(nc_function, condition)
self.classes = None
self.smoothing = smoothing
def _calibrate_hook(self, x, y, increment=False):
self._update_classes(y, increment)
def _update_classes(self, y, increment):
if self.classes is None or not increment:
self.classes = np.unique(y)
else:
self.classes = np.unique(np.hstack([self.classes, y]))
def predict(self, x, significance=None):
"""Predict the output values for a set of input patterns.
Parameters
----------
x : numpy array of shape [n_samples, n_features]
Inputs of patters for which to predict output values.
significance : float or None
Significance level (maximum allowed error rate) of predictions.
Should be a float between 0 and 1. If ``None``, then the p-values
are output rather than the predictions.
Returns
-------
p : numpy array of shape [n_samples, n_classes]
If significance is ``None``, then p contains the p-values for each
sample-class pair; if significance is a float between 0 and 1, then
p is a boolean array denoting which labels are included in the
prediction sets.
"""
# TODO: if x == self.last_x ...
n_test_objects = x.shape[0]
p = np.zeros((n_test_objects, self.classes.size))
ncal_ngt_neq = self._get_stats(x)
for i in range(len(self.classes)):
for j in range(n_test_objects):
p[j, i] = calc_p(ncal_ngt_neq[j, i, 0],
ncal_ngt_neq[j, i, 1],
ncal_ngt_neq[j, i, 2],
self.smoothing)
if significance is not None:
return p > significance
else:
return p
def _get_stats(self, x):
n_test_objects = x.shape[0]
ncal_ngt_neq = np.zeros((n_test_objects, self.classes.size, 3))
for i, c in enumerate(self.classes):
test_class = np.zeros(x.shape[0], dtype=self.classes.dtype)
test_class.fill(c)
# TODO: maybe calculate p-values using cython or similar
# TODO: interpolated p-values
# TODO: nc_function.calc_nc should take X * {y1, y2, ... ,yn}
test_nc_scores = self.nc_function.score(x, test_class)
for j, nc in enumerate(test_nc_scores):
cal_scores = self.cal_scores[self.condition((x[j, :], c))][::-1]
n_cal = cal_scores.size
idx_left = np.searchsorted(cal_scores, nc, 'left')
idx_right = np.searchsorted(cal_scores, nc, 'right')
ncal_ngt_neq[j, i, 0] = n_cal
ncal_ngt_neq[j, i, 1] = n_cal - idx_right
ncal_ngt_neq[j, i, 2] = idx_right - idx_left
return ncal_ngt_neq
def predict_conf(self, x):
"""Predict the output values for a set of input patterns, using
the confidence-and-credibility output scheme.
Parameters
----------
x : numpy array of shape [n_samples, n_features]
Inputs of patters for which to predict output values.
Returns
-------
p : numpy array of shape [n_samples, 3]
p contains three columns: the first column contains the most
likely class for each test pattern; the second column contains
the confidence in the predicted class label, and the third column
contains the credibility of the prediction.
"""
p = self.predict(x, significance=None)
label = p.argmax(axis=1)
credibility = p.max(axis=1)
for i, idx in enumerate(label):
p[i, idx] = -np.inf
confidence = 1 - p.max(axis=1)
return np.array([label, confidence, credibility]).T
# -----------------------------------------------------------------------------
# Inductive conformal regressor
# -----------------------------------------------------------------------------
class IcpRegressor(BaseIcp, RegressorMixin):
"""Inductive conformal regressor.
Parameters
----------
nc_function : BaseScorer
Nonconformity scorer object used to calculate nonconformity of
calibration examples and test patterns. Should implement ``fit(x, y)``,
``calc_nc(x, y)`` and ``predict(x, nc_scores, significance)``.
Attributes
----------
cal_x : numpy array of shape [n_cal_examples, n_features]
Inputs of calibration set.
cal_y : numpy array of shape [n_cal_examples]
Outputs of calibration set.
nc_function : BaseScorer
Nonconformity scorer object used to calculate nonconformity scores.
See also
--------
IcpClassifier
References
----------
.. [1] Papadopoulos, H., Proedrou, K., Vovk, V., & Gammerman, A. (2002).
Inductive confidence machines for regression. In Machine Learning: ECML
2002 (pp. 345-356). Springer Berlin Heidelberg.
.. [2] Papadopoulos, H., & Haralambous, H. (2011). Reliable prediction
intervals with regression neural networks. Neural Networks, 24(8),
842-851.
Examples
--------
>>> import numpy as np
>>> from sklearn.datasets import load_boston
>>> from sklearn.tree import DecisionTreeRegressor
>>> from nonconformist.base import RegressorAdapter
>>> from nonconformist.icp import IcpRegressor
>>> from nonconformist.nc import RegressorNc, AbsErrorErrFunc
>>> boston = load_boston()
>>> idx = np.random.permutation(boston.target.size)
>>> train = idx[:int(idx.size / 3)]
>>> cal = idx[int(idx.size / 3):int(2 * idx.size / 3)]
>>> test = idx[int(2 * idx.size / 3):]
>>> model = RegressorAdapter(DecisionTreeRegressor())
>>> nc = RegressorNc(model, AbsErrorErrFunc())
>>> icp = IcpRegressor(nc)
>>> icp.fit(boston.data[train, :], boston.target[train])
>>> icp.calibrate(boston.data[cal, :], boston.target[cal])
>>> icp.predict(boston.data[test, :], significance=0.10)
... # doctest: +SKIP
array([[ 5. , 20.6],
[ 15.5, 31.1],
...,
[ 14.2, 29.8],
[ 11.6, 27.2]])
"""
def __init__(self, nc_function, condition=None):
super(IcpRegressor, self).__init__(nc_function, condition)
def predict(self, x, significance=None):
"""Predict the output values for a set of input patterns.
Parameters
----------
x : numpy array of shape [n_samples, n_features]
Inputs of patters for which to predict output values.
significance : float
Significance level (maximum allowed error rate) of predictions.
Should be a float between 0 and 1. If ``None``, then intervals for
all significance levels (0.01, 0.02, ..., 0.99) are output in a
3d-matrix.
Returns
-------
p : numpy array of shape [n_samples, 2] or [n_samples, 2, 99}
If significance is ``None``, then p contains the interval (minimum
and maximum boundaries) for each test pattern, and each significance
level (0.01, 0.02, ..., 0.99). If significance is a float between
0 and 1, then p contains the prediction intervals (minimum and
maximum boundaries) for the set of test patterns at the chosen
significance level.
"""
# TODO: interpolated p-values
n_significance = (99 if significance is None
else np.array(significance).size)
if n_significance > 1:
prediction = np.zeros((x.shape[0], 2, n_significance))
else:
prediction = np.zeros((x.shape[0], 2))
condition_map = np.array([self.condition((x[i, :], None))
for i in range(x.shape[0])])
for condition in self.categories:
idx = condition_map == condition
if np.sum(idx) > 0:
p = self.nc_function.predict(x[idx, :],
self.cal_scores[condition],
significance)
if n_significance > 1:
prediction[idx, :, :] = p
else:
prediction[idx, :] = p
return prediction
class OobCpClassifier(IcpClassifier):
def __init__(self,
nc_function,
condition=None,
smoothing=True):
super(OobCpClassifier, self).__init__(nc_function,
condition,
smoothing)
def fit(self, x, y):
super(OobCpClassifier, self).fit(x, y)
super(OobCpClassifier, self).calibrate(x, y, False)
def calibrate(self, x, y, increment=False):
# Should throw exception (or really not be implemented for oob)
pass
class OobCpRegressor(IcpRegressor):
def __init__(self,
nc_function,
condition=None):
super(OobCpRegressor, self).__init__(nc_function,
condition)
def fit(self, x, y):
super(OobCpRegressor, self).fit(x, y)
super(OobCpRegressor, self).calibrate(x, y, False)
def calibrate(self, x, y, increment=False):
# Should throw exception (or really not be implemented for oob)
pass