# coding: utf-8 # Author: Johannes Schönberger # # License: BSD 3 clause import numpy as np 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 _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. Parameters ---------- 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. Returns ------- 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 `. Parameters ---------- 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 estimators. 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. 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) random_state : integer or numpy.RandomState, optional The generator used to initialize the centers. If an integer is given, it fixes the seed. Defaults to the global numpy random number generator. Attributes ---------- 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``. References ---------- .. [1] http://en.wikipedia.org/wiki/RANSAC .. [2] http://www.cs.columbia.edu/~belhumeur/courses/compPhoto/ransac.pdf .. [3] http://www.bmva.org/bmvc/2009/Papers/Paper355/Paper355.pdf """ def __init__(self, base_estimator=None, min_samples=None, residual_threshold=None, is_data_valid=None, is_model_valid=None, max_trials=100, stop_n_inliers=np.inf, stop_score=np.inf, stop_probability=0.99, residual_metric=None, 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.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 def fit(self, X, y): """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. 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 None: residual_metric = lambda dy: np.sum(np.abs(dy), axis=1) else: residual_metric = self.residual_metric 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 n_inliers_best = 0 score_best = np.inf inlier_mask_best = None X_inlier_best = None y_inlier_best = None # number of data samples n_samples = X.shape[0] sample_idxs = np.arange(n_samples) n_samples, _ = X.shape for self.n_trials_ in range(1, self.max_trials + 1): # 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)): continue # fit model for current random sample set base_estimator.fit(X_subset, y_subset) # 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)): continue # residuals of all data for current random sample model y_pred = base_estimator.predict(X) diff = y_pred - y if diff.ndim == 1: diff = diff.reshape(-1, 1) residuals_subset = residual_metric(diff) # 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: continue if n_inliers_subset == 0: raise ValueError("No inliers found, possible cause is " "setting residual_threshold ({0}) too low.".format( self.residual_threshold)) # 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 # break if sufficient number of inliers or score is reached if (n_inliers_best >= self.stop_n_inliers or score_best >= self.stop_score or self.n_trials_ >= _dynamic_max_trials(n_inliers_best, n_samples, min_samples, self.stop_probability)): break # if none of the iterations met the required criteria if inlier_mask_best is None: raise ValueError( "RANSAC could not find valid consensus set, because" " either the `residual_threshold` rejected all the samples or" " `is_data_valid` and `is_model_valid` returned False for all" " `max_trials` randomly ""chosen sub-samples. Consider " "relaxing the ""constraints.") # estimate final model using all inliers base_estimator.fit(X_inlier_best, y_inlier_best) self.estimator_ = base_estimator self.inlier_mask_ = inlier_mask_best return self 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) 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)