Source code for sklearn.linear_model.ransac

# coding: utf-8

# Author: Johannes Schönberger
# License: BSD 3 clause

import numpy as np
import warnings

from ..base import BaseEstimator, MetaEstimatorMixin, RegressorMixin, clone
from ..utils import check_random_state, check_array, check_consistent_length
from ..utils.random import sample_without_replacement
from ..utils.validation import check_is_fitted
from .base import LinearRegression
from ..utils.validation import has_fit_parameter

_EPSILON = np.spacing(1)

def _dynamic_max_trials(n_inliers, n_samples, min_samples, probability):
    """Determine number trials such that at least one outlier-free subset is
    sampled for the given inlier/outlier ratio.

    n_inliers : int
        Number of inliers in the data.

    n_samples : int
        Total number of samples in the data.

    min_samples : int
        Minimum number of samples chosen randomly from original data.

    probability : float
        Probability (confidence) that one outlier-free sample is generated.

    trials : int
        Number of trials.

    inlier_ratio = n_inliers / float(n_samples)
    nom = max(_EPSILON, 1 - probability)
    denom = max(_EPSILON, 1 - inlier_ratio ** min_samples)
    if nom == 1:
        return 0
    if denom == 1:
        return float('inf')
    return abs(float(np.ceil(np.log(nom) / np.log(denom))))

class RANSACRegressor(BaseEstimator, MetaEstimatorMixin, RegressorMixin):
    """RANSAC (RANdom SAmple Consensus) algorithm.

    RANSAC is an iterative algorithm for the robust estimation of parameters
    from a subset of inliers from the complete data set. More information can
    be found in the general documentation of linear models.

    A detailed description of the algorithm can be found in the documentation
    of the ``linear_model`` sub-package.

    Read more in the :ref:`User Guide <ransac_regression>`.

    base_estimator : object, optional
        Base estimator object which implements the following methods:

         * `fit(X, y)`: Fit model to given training data and target values.
         * `score(X, y)`: Returns the mean accuracy on the given test data,
           which is used for the stop criterion defined by `stop_score`.
           Additionally, the score is used to decide which of two equally
           large consensus sets is chosen as the better one.

        If `base_estimator` is None, then
        ``base_estimator=sklearn.linear_model.LinearRegression()`` is used for
        target values of dtype float.

        Note that the current implementation only supports regression

    min_samples : int (>= 1) or float ([0, 1]), optional
        Minimum number of samples chosen randomly from original data. Treated
        as an absolute number of samples for `min_samples >= 1`, treated as a
        relative number `ceil(min_samples * X.shape[0]`) for
        `min_samples < 1`. This is typically chosen as the minimal number of
        samples necessary to estimate the given `base_estimator`. By default a
        ``sklearn.linear_model.LinearRegression()`` estimator is assumed and
        `min_samples` is chosen as ``X.shape[1] + 1``.

    residual_threshold : float, optional
        Maximum residual for a data sample to be classified as an inlier.
        By default the threshold is chosen as the MAD (median absolute
        deviation) of the target values `y`.

    is_data_valid : callable, optional
        This function is called with the randomly selected data before the
        model is fitted to it: `is_data_valid(X, y)`. If its return value is
        False the current randomly chosen sub-sample is skipped.

    is_model_valid : callable, optional
        This function is called with the estimated model and the randomly
        selected data: `is_model_valid(model, X, y)`. If its return value is
        False the current randomly chosen sub-sample is skipped.
        Rejecting samples with this function is computationally costlier than
        with `is_data_valid`. `is_model_valid` should therefore only be used if
        the estimated model is needed for making the rejection decision.

    max_trials : int, optional
        Maximum number of iterations for random sample selection.

    max_skips : int, optional
        Maximum number of iterations that can be skipped due to finding zero
        inliers or invalid data defined by ``is_data_valid`` or invalid models
        defined by ``is_model_valid``.

        .. versionadded:: 0.19

    stop_n_inliers : int, optional
        Stop iteration if at least this number of inliers are found.

    stop_score : float, optional
        Stop iteration if score is greater equal than this threshold.

    stop_probability : float in range [0, 1], optional
        RANSAC iteration stops if at least one outlier-free set of the training
        data is sampled in RANSAC. This requires to generate at least N
        samples (iterations)::

            N >= log(1 - probability) / log(1 - e**m)

        where the probability (confidence) is typically set to high value such
        as 0.99 (the default) and e is the current fraction of inliers w.r.t.
        the total number of samples.

    residual_metric : callable, optional
        Metric to reduce the dimensionality of the residuals to 1 for
        multi-dimensional target values ``y.shape[1] > 1``. By default the sum
        of absolute differences is used::

            lambda dy: np.sum(np.abs(dy), axis=1)

        .. deprecated:: 0.18
           ``residual_metric`` is deprecated from 0.18 and will be removed in
           0.20. Use ``loss`` instead.

    loss : string, callable, optional, default "absolute_loss"
        String inputs, "absolute_loss" and "squared_loss" are supported which
        find the absolute loss and squared loss per sample

        If ``loss`` is a callable, then it should be a function that takes
        two arrays as inputs, the true and predicted value and returns a 1-D
        array with the i-th value of the array corresponding to the loss
        on ``X[i]``.

        If the loss on a sample is greater than the ``residual_threshold``,
        then this sample is classified as an outlier.

    random_state : int, RandomState instance or None, optional, default None
        The generator used to initialize the centers.  If int, random_state is
        the seed used by the random number generator; If RandomState instance,
        random_state is the random number generator; If None, the random number
        generator is the RandomState instance used by `np.random`.

    estimator_ : object
        Best fitted model (copy of the `base_estimator` object).

    n_trials_ : int
        Number of random selection trials until one of the stop criteria is
        met. It is always ``<= max_trials``.

    inlier_mask_ : bool array of shape [n_samples]
        Boolean mask of inliers classified as ``True``.

    n_skips_no_inliers_ : int
        Number of iterations skipped due to finding zero inliers.

        .. versionadded:: 0.19

    n_skips_invalid_data_ : int
        Number of iterations skipped due to invalid data defined by

        .. versionadded:: 0.19

    n_skips_invalid_model_ : int
        Number of iterations skipped due to an invalid model defined by

        .. versionadded:: 0.19

    .. [1]
    .. [2]
    .. [3]

    def __init__(self, base_estimator=None, min_samples=None,
                 residual_threshold=None, is_data_valid=None,
                 is_model_valid=None, max_trials=100, max_skips=np.inf,
                 stop_n_inliers=np.inf, stop_score=np.inf,
                 stop_probability=0.99, residual_metric=None,
                 loss='absolute_loss', random_state=None):

        self.base_estimator = base_estimator
        self.min_samples = min_samples
        self.residual_threshold = residual_threshold
        self.is_data_valid = is_data_valid
        self.is_model_valid = is_model_valid
        self.max_trials = max_trials
        self.max_skips = max_skips
        self.stop_n_inliers = stop_n_inliers
        self.stop_score = stop_score
        self.stop_probability = stop_probability
        self.residual_metric = residual_metric
        self.random_state = random_state
        self.loss = loss

[docs] def fit(self, X, y, sample_weight=None): """Fit estimator using RANSAC algorithm. Parameters ---------- X : array-like or sparse matrix, shape [n_samples, n_features] Training data. y : array-like, shape = [n_samples] or [n_samples, n_targets] Target values. sample_weight : array-like, shape = [n_samples] Individual weights for each sample raises error if sample_weight is passed and base_estimator fit method does not support it. Raises ------ ValueError If no valid consensus set could be found. This occurs if `is_data_valid` and `is_model_valid` return False for all `max_trials` randomly chosen sub-samples. """ X = check_array(X, accept_sparse='csr') y = check_array(y, ensure_2d=False) check_consistent_length(X, y) if self.base_estimator is not None: base_estimator = clone(self.base_estimator) else: base_estimator = LinearRegression() if self.min_samples is None: # assume linear model by default min_samples = X.shape[1] + 1 elif 0 < self.min_samples < 1: min_samples = np.ceil(self.min_samples * X.shape[0]) elif self.min_samples >= 1: if self.min_samples % 1 != 0: raise ValueError("Absolute number of samples must be an " "integer value.") min_samples = self.min_samples else: raise ValueError("Value for `min_samples` must be scalar and " "positive.") if min_samples > X.shape[0]: raise ValueError("`min_samples` may not be larger than number " "of samples ``X.shape[0]``.") if self.stop_probability < 0 or self.stop_probability > 1: raise ValueError("`stop_probability` must be in range [0, 1].") if self.residual_threshold is None: # MAD (median absolute deviation) residual_threshold = np.median(np.abs(y - np.median(y))) else: residual_threshold = self.residual_threshold if self.residual_metric is not None: warnings.warn( "'residual_metric' was deprecated in version 0.18 and " "will be removed in version 0.20. Use 'loss' instead.", DeprecationWarning) if self.loss == "absolute_loss": if y.ndim == 1: loss_function = lambda y_true, y_pred: np.abs(y_true - y_pred) else: loss_function = lambda \ y_true, y_pred: np.sum(np.abs(y_true - y_pred), axis=1) elif self.loss == "squared_loss": if y.ndim == 1: loss_function = lambda y_true, y_pred: (y_true - y_pred) ** 2 else: loss_function = lambda \ y_true, y_pred: np.sum((y_true - y_pred) ** 2, axis=1) elif callable(self.loss): loss_function = self.loss else: raise ValueError( "loss should be 'absolute_loss', 'squared_loss' or a callable." "Got %s. " % self.loss) random_state = check_random_state(self.random_state) try: # Not all estimator accept a random_state base_estimator.set_params(random_state=random_state) except ValueError: pass estimator_fit_has_sample_weight = has_fit_parameter(base_estimator, "sample_weight") estimator_name = type(base_estimator).__name__ if (sample_weight is not None and not estimator_fit_has_sample_weight): raise ValueError("%s does not support sample_weight. Samples" " weights are only used for the calibration" " itself." % estimator_name) if sample_weight is not None: sample_weight = np.asarray(sample_weight) n_inliers_best = 1 score_best = -np.inf inlier_mask_best = None X_inlier_best = None y_inlier_best = None self.n_skips_no_inliers_ = 0 self.n_skips_invalid_data_ = 0 self.n_skips_invalid_model_ = 0 # number of data samples n_samples = X.shape[0] sample_idxs = np.arange(n_samples) n_samples, _ = X.shape self.n_trials_ = 0 max_trials = self.max_trials while self.n_trials_ < max_trials: self.n_trials_ += 1 if (self.n_skips_no_inliers_ + self.n_skips_invalid_data_ + self.n_skips_invalid_model_) > self.max_skips: break # choose random sample set subset_idxs = sample_without_replacement(n_samples, min_samples, random_state=random_state) X_subset = X[subset_idxs] y_subset = y[subset_idxs] # check if random sample set is valid if (self.is_data_valid is not None and not self.is_data_valid(X_subset, y_subset)): self.n_skips_invalid_data_ += 1 continue # fit model for current random sample set if sample_weight is None:, y_subset) else:, y_subset, sample_weight=sample_weight[subset_idxs]) # check if estimated model is valid if (self.is_model_valid is not None and not self.is_model_valid(base_estimator, X_subset, y_subset)): self.n_skips_invalid_model_ += 1 continue # residuals of all data for current random sample model y_pred = base_estimator.predict(X) # XXX: Deprecation: Remove this if block in 0.20 if self.residual_metric is not None: diff = y_pred - y if diff.ndim == 1: diff = diff.reshape(-1, 1) residuals_subset = self.residual_metric(diff) else: residuals_subset = loss_function(y, y_pred) # classify data into inliers and outliers inlier_mask_subset = residuals_subset < residual_threshold n_inliers_subset = np.sum(inlier_mask_subset) # less inliers -> skip current random sample if n_inliers_subset < n_inliers_best: self.n_skips_no_inliers_ += 1 continue # extract inlier data set inlier_idxs_subset = sample_idxs[inlier_mask_subset] X_inlier_subset = X[inlier_idxs_subset] y_inlier_subset = y[inlier_idxs_subset] # score of inlier data set score_subset = base_estimator.score(X_inlier_subset, y_inlier_subset) # same number of inliers but worse score -> skip current random # sample if (n_inliers_subset == n_inliers_best and score_subset < score_best): continue # save current random sample as best sample n_inliers_best = n_inliers_subset score_best = score_subset inlier_mask_best = inlier_mask_subset X_inlier_best = X_inlier_subset y_inlier_best = y_inlier_subset max_trials = min( max_trials, _dynamic_max_trials(n_inliers_best, n_samples, min_samples, self.stop_probability)) # break if sufficient number of inliers or score is reached if n_inliers_best >= self.stop_n_inliers or \ score_best >= self.stop_score: break # if none of the iterations met the required criteria if inlier_mask_best is None: if ((self.n_skips_no_inliers_ + self.n_skips_invalid_data_ + self.n_skips_invalid_model_) > self.max_skips): raise ValueError( "RANSAC skipped more iterations than `max_skips` without" " finding a valid consensus set. Iterations were skipped" " because each randomly chosen sub-sample failed the" " passing criteria. See estimator attributes for" " diagnostics (n_skips*).") else: raise ValueError( "RANSAC could not find a valid consensus set. All" " `max_trials` iterations were skipped because each" " randomly chosen sub-sample failed the passing criteria." " See estimator attributes for diagnostics (n_skips*).") else: if (self.n_skips_no_inliers_ + self.n_skips_invalid_data_ + self.n_skips_invalid_model_) > self.max_skips: warnings.warn("RANSAC found a valid consensus set but exited" " early due to skipping more iterations than" " `max_skips`. See estimator attributes for" " diagnostics (n_skips*).", UserWarning) # estimate final model using all inliers, y_inlier_best) self.estimator_ = base_estimator self.inlier_mask_ = inlier_mask_best return self
[docs] def predict(self, X): """Predict using the estimated model. This is a wrapper for `estimator_.predict(X)`. Parameters ---------- X : numpy array of shape [n_samples, n_features] Returns ------- y : array, shape = [n_samples] or [n_samples, n_targets] Returns predicted values. """ check_is_fitted(self, 'estimator_') return self.estimator_.predict(X)
[docs] def score(self, X, y): """Returns the score of the prediction. This is a wrapper for `estimator_.score(X, y)`. Parameters ---------- X : numpy array or sparse matrix of shape [n_samples, n_features] Training data. y : array, shape = [n_samples] or [n_samples, n_targets] Target values. Returns ------- z : float Score of the prediction. """ check_is_fitted(self, 'estimator_') return self.estimator_.score(X, y)